Deprecated: preg_match(): Passing null to parameter #2 ($subject) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/lbfactory/LBFactory.php on line 759

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 262

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::open($save_path, $session_name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 181

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 196

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::read($id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 210

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::write($id, $dataStr) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 238

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::destroy($id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 344

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php on line 365

Deprecated: strcasecmp(): Passing null to parameter #1 ($string1) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/CookieSessionProvider.php on line 101

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 262

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Return type of MediaWiki\Session\Session::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 593

Deprecated: Return type of MediaWiki\Session\Session::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 599

Deprecated: Return type of MediaWiki\Session\Session::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 611

Deprecated: Return type of MediaWiki\Session\Session::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 605

Deprecated: Return type of MediaWiki\Session\Session::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 623

Deprecated: Return type of MediaWiki\Session\Session::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 617

Deprecated: Return type of MediaWiki\Session\Session::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 633

Deprecated: Return type of & MediaWiki\Session\Session::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 646

Deprecated: Return type of MediaWiki\Session\Session::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 656

Deprecated: Return type of MediaWiki\Session\Session::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/Session.php on line 661

Deprecated: Message implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/language/Message.php on line 161

Deprecated: MapCacheLRU implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/MapCacheLRU.php on line 38

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/extensions/SimpleMathJax/SimpleMathJax.class.php on line 26

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/extensions/SimpleMathJax/SimpleMathJax.class.php on line 31

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/parser/Parser.php on line 4307

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/parser/Parser.php on line 4310

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/parser/Parser.php on line 4316

Deprecated: Using ${var} in strings is deprecated, use {$var} instead in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/parser/Parser.php on line 4318

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: RawMessage implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/RawMessage.php on line 35

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: Creation of dynamic property Parser::$scribunto_engine is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/extensions/Scribunto/includes/common/Hooks.php on line 81

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/changes/ChannelFeed.php on line 95

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/changes/ChannelFeed.php on line 100

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Warning: Cannot modify header information - headers already sent by (output started at /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/session/PHPSessionHandler.php:35) in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/WebResponse.php on line 74

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?action=history&feed=atom&title=Energia_numa_%C3%B3rbita 2026-07-25T22:59:16Z Histórico de edições para esta página nesta wiki MediaWiki 1.35.2
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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=559&oldid=prev 2015-10-28T11:52:04Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 11h52min de 28 de outubro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24" >Linha 24:</td> <td colspan="2" class="diff-lineno">Linha 24:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5 \times 10^3\,\)kg.  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5 \times 10^3\,\)kg.  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Determine as seguintes quantidades: energia potencial, velocidade orbital da nave, energia cinética, energia mecânica da nave e a relação entre a energia potencial e a energia cinética.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Determine as seguintes quantidades: energia potencial <ins class="diffchange diffchange-inline">(\(E_{Pg}\))</ins>, velocidade orbital da nave<ins class="diffchange diffchange-inline">(\(v_o\))</ins>, energia cinética <ins class="diffchange diffchange-inline">(\(E_c\))</ins>, energia mecânica da nave <ins class="diffchange diffchange-inline">(\(E_m\)) </ins>e a relação entre a energia potencial e a energia cinética.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:315px&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:315px&quot;&gt;</div></td></tr> </table>

Ist172693
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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=352&oldid=prev 2015-09-30T23:49:59Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 23h49min de 30 de setembro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l50" >Linha 50:</td> <td colspan="2" class="diff-lineno">Linha 50:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*\(\Delta E = \frac{1}{4} G \frac{Mm}{R} \simeq 7.11 \times 10^{10}\,\)J</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*\(\Delta E = \frac{1}{4} G \frac{Mm}{R} \simeq 7.11 \times 10^{10}\,\)J</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Ou seja, é necessário fornecer <del class="diffchange diffchange-inline">ao satélite </del>\(7.11 \times 10^{10}\,\)J para o levar para a órbita mais alta.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Ou seja, é necessário fornecer <ins class="diffchange diffchange-inline">à nave </ins>\(7.11 \times 10^{10}\,\)J para o levar para a órbita mais alta.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

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Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578
http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=351&oldid=prev 2015-09-30T23:49:23Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 23h49min de 30 de setembro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26" >Linha 26:</td> <td colspan="2" class="diff-lineno">Linha 26:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Determine as seguintes quantidades: energia potencial, velocidade orbital da nave, energia cinética, energia mecânica da nave e a relação entre a energia potencial e a energia cinética.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Determine as seguintes quantidades: energia potencial, velocidade orbital da nave, energia cinética, energia mecânica da nave e a relação entre a energia potencial e a energia cinética.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:<del class="diffchange diffchange-inline">210px</del>&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:<ins class="diffchange diffchange-inline">315px</ins>&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Respostas&#039;&#039;&#039;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Respostas&#039;&#039;&#039;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l44" >Linha 44:</td> <td colspan="2" class="diff-lineno">Linha 44:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Qual a energia que deve ser dissipada ou transferida para nave para que esta passe para uma órbita circular em torno da Terra de raio duas vezes superior ao raio de órbita inicial?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Qual a energia que deve ser dissipada ou transferida para nave para que esta passe para uma órbita circular em torno da Terra de raio duas vezes superior ao raio de órbita inicial?</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:<del class="diffchange diffchange-inline">210px</del>&quot;&gt;</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:<ins class="diffchange diffchange-inline">315px</ins>&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Respostas&#039;&#039;&#039;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&#039;&#039;&#039;Respostas&#039;&#039;&#039;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*\(<del class="diffchange diffchange-inline">v_A </del>= \<del class="diffchange diffchange-inline">sqrt</del>{<del class="diffchange diffchange-inline">121gR</del>} \simeq <del class="diffchange diffchange-inline">77 \,\)m</del>.<del class="diffchange diffchange-inline">s</del>\<del class="diffchange diffchange-inline">(</del>^{<del class="diffchange diffchange-inline">-1</del>}<del class="diffchange diffchange-inline">\)</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*\(<ins class="diffchange diffchange-inline">\Delta E </ins>= \<ins class="diffchange diffchange-inline">frac{1}{4} G \frac{Mm}</ins>{<ins class="diffchange diffchange-inline">R</ins>} \simeq <ins class="diffchange diffchange-inline">7</ins>.<ins class="diffchange diffchange-inline">11 </ins>\<ins class="diffchange diffchange-inline">times 10</ins>^{<ins class="diffchange diffchange-inline">10</ins>}\,\)<ins class="diffchange diffchange-inline">J</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*\(P = mg = 980</del>\, \)<del class="diffchange diffchange-inline">N</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*</del>\(<del class="diffchange diffchange-inline">N = 120mg = 117 600</del>\, \)<del class="diffchange diffchange-inline">N</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Ou seja, é necessário fornecer ao satélite </ins>\(<ins class="diffchange diffchange-inline">7.11 \times 10^{10}</ins>\,\)<ins class="diffchange diffchange-inline">J para o levar para a órbita mais alta.</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

Ist172693
Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /afs/ist.utl.pt/groups/mysolutions/web/wiki/includes/libs/rdbms/database/Database.php on line 578

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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=350&oldid=prev 2015-09-30T21:57:14Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 21h57min de 30 de setembro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >Linha 19:</td> <td colspan="2" class="diff-lineno">Linha 19:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Considere uma nave espacial em órbita circular em torno da Terra a uma  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Considere uma nave espacial em órbita circular em torno da Terra a uma  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>altitude de 600 km relativamente à superfície da  Terra.</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>altitude <ins class="diffchange diffchange-inline">h </ins>de 600 km relativamente à superfície da  Terra.</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Considere que a nave está unicamente sujeita à força</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Considere que a nave está unicamente sujeita à força</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gravítica terrestre. Raio da Terra: \(R_{\oplus}=6400\,\)km e  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>gravítica terrestre. Raio da Terra: \(R_{\oplus}=6400\,\)km e  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5 \times 10^3\,\)kg.  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5 \times 10^3\,\)kg.  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*<del class="diffchange diffchange-inline">Qual a energia mecânica da nave?</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*<ins class="diffchange diffchange-inline">Determine as seguintes quantidades</ins>: energia potencial, velocidade orbital da nave, energia cinética<ins class="diffchange diffchange-inline">, energia mecânica </ins>da nave e a relação entre a energia potencial e a energia <ins class="diffchange diffchange-inline">cinética</ins>.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Sugestão</del>: <del class="diffchange diffchange-inline"> indique as expressões para  a </del>energia potencial, <del class="diffchange diffchange-inline">a </del>velocidade orbital da nave, <del class="diffchange diffchange-inline">a </del>energia cinética da nave e a relação entre a energia potencial e a energia <del class="diffchange diffchange-inline">mecânica da nave</del>.</div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31" >Linha 31:</td> <td colspan="2" class="diff-lineno">Linha 30:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;mw-collapsible-content&quot;&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*\(<del class="diffchange diffchange-inline">v_A </del>= \sqrt{<del class="diffchange diffchange-inline">121gR</del>} \simeq <del class="diffchange diffchange-inline">77 </del>\,\)m.s\(^{-1}\)</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*\(<ins class="diffchange diffchange-inline">E_{Pg} = -G \frac{Mm}{R} \simeq -2.84 \times 10^{11}\,\)J</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*\(<del class="diffchange diffchange-inline">P </del>= <del class="diffchange diffchange-inline">mg </del>= <del class="diffchange diffchange-inline">980</del>\, \)<del class="diffchange diffchange-inline">N</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Com \(R = R_{\oplus} + h \)</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*\(<del class="diffchange diffchange-inline">N </del>= <del class="diffchange diffchange-inline">120mg = 117 600</del>\<del class="diffchange diffchange-inline">, </del>\)<del class="diffchange diffchange-inline">N</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*\(v_o </ins>= \sqrt{<ins class="diffchange diffchange-inline">\frac{GM}{R}</ins>} \simeq <ins class="diffchange diffchange-inline">7542</ins>\,\)m.s\(^{-1}\)</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*\(<ins class="diffchange diffchange-inline">E_m </ins>= <ins class="diffchange diffchange-inline">- E_c </ins>= <ins class="diffchange diffchange-inline">-\frac{1}{2} G \frac{Mm}{R} \simeq -1.42 \times 10^{11}</ins>\,\)<ins class="diffchange diffchange-inline">J</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*\(<ins class="diffchange diffchange-inline">E_c </ins>= <ins class="diffchange diffchange-inline">-</ins>\<ins class="diffchange diffchange-inline">frac{1}{2} E_{Pg}</ins>\)</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;/div&gt;</div></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=349&oldid=prev 2015-09-30T21:21:52Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 21h21min de 30 de setembro de 2015</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18" >Linha 18:</td> <td colspan="2" class="diff-lineno">Linha 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Considere uma nave espacial em <del class="diffchange diffchange-inline">\&#039;orbita </del>circular em torno da Terra a uma  </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Considere uma nave espacial em <ins class="diffchange diffchange-inline">órbita </ins>circular em torno da Terra a uma  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>altitude de 600 km relativamente à superfície da  Terra.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>altitude de 600 km relativamente à superfície da  Terra.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Considere que a nave <del class="diffchange diffchange-inline">est\&#039;a </del>unicamente sujeita <del class="diffchange diffchange-inline">\`a for\c{c}a</del></div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Considere que a nave <ins class="diffchange diffchange-inline">está </ins>unicamente sujeita <ins class="diffchange diffchange-inline">à força</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">grav\&#039;{\i}tica </del>terrestre. Raio da Terra: \(R_{\oplus}=6400\,\)km e  </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">gravítica </ins>terrestre. Raio da Terra: \(R_{\oplus}=6400\,\)km e  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5\times 10^3\,\)kg.  </div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>massa  da nave: \(m=5 \times 10^3\,\)kg.  </div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Qual a energia <del class="diffchange diffchange-inline">mec\^anica </del>da nave?</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Qual a energia <ins class="diffchange diffchange-inline">mecânica </ins>da nave?</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Sugestão:  indique as <del class="diffchange diffchange-inline">express\~oes </del>para  a energia potencial, a velocidade</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Sugestão:  indique as <ins class="diffchange diffchange-inline">expressões </ins>para  a energia potencial, a velocidade orbital da nave, a energia <ins class="diffchange diffchange-inline">cinética </ins>da nave e a <ins class="diffchange diffchange-inline">relação </ins>entre a energia potencial e a energia <ins class="diffchange diffchange-inline">mecânica </ins>da nave.</div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>orbital da nave, a energia <del class="diffchange diffchange-inline">cin\&#039;etica </del>da nave e a <del class="diffchange diffchange-inline">rela\c{c}\~ao </del>entre a energia  </div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>potencial e a energia <del class="diffchange diffchange-inline">mec\^anica </del>da nave.</div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">*Qual a energia que deve ser dissipada ou transferida \`a nave para que esta passe para uma \&#039;orbita circular em torno da Terra de raio duas vezes superior ao raio de \&#039;orbita inicial?</del></div></td><td colspan="2"> </td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&#039;&#039;&#039;Respostas&#039;&#039;&#039;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;div class=&quot;mw-collapsible-content&quot;&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*\(v_A = \sqrt{121gR} \simeq 77 \,\)m.s\(^{-1}\)</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*\(P = mg = 980\, \)N</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*\(N = 120mg = 117 600\, \)N</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;/div&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;/div&gt;</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*Qual a energia que deve ser dissipada ou transferida para nave para que esta passe para uma órbita circular em torno da Terra de raio duas vezes superior ao raio de órbita inicial?</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;</div></td></tr> </table>

Ist172693
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http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Energia_numa_%C3%B3rbita&diff=348&oldid=prev 2015-09-30T20:46:17Z

<p>Criou a página com &quot;&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt; &#039;&#039;&#039;Metadata&#039;&#039;&#039; &lt;div class=&quot;mw-collapsible-content&quot;&gt; *CONTEXTO : Primeiro ciclo universitário *AREA:...&quot;</p> <p><b>Página nova</b></p><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt;<br /> &#039;&#039;&#039;Metadata&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *CONTEXTO : Primeiro ciclo universitário<br /> *AREA: Física<br /> *DISCIPLINA: Mecânica e ondas<br /> *ANO: 1<br /> *LINGUA: pt<br /> *AUTOR: Ana Mourão<br /> *MATERIA PRINCIPAL: Trabalho e Energia Mecânica<br /> *DESCRICAO: Energia numa órbita<br /> *DIFICULDADE: **<br /> *TEMPO MEDIO DE RESOLUCAO: 600 [s]<br /> *TEMPO MAXIMO DE RESOLUCAO: 1200 [s]<br /> *PALAVRAS CHAVE: gravidade, forças, trabalho, energia, órbita<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> <br /> Considere uma nave espacial em \&#039;orbita circular em torno da Terra a uma <br /> altitude de 600 km relativamente à superfície da Terra.<br /> Considere que a nave est\&#039;a unicamente sujeita \`a for\c{c}a<br /> grav\&#039;{\i}tica terrestre. Raio da Terra: \(R_{\oplus}=6400\,\)km e <br /> massa da nave: \(m=5\times 10^3\,\)kg. <br /> <br /> *Qual a energia mec\^anica da nave?<br /> Sugestão: indique as express\~oes para a energia potencial, a velocidade<br /> orbital da nave, a energia cin\&#039;etica da nave e a rela\c{c}\~ao entre a energia <br /> potencial e a energia mec\^anica da nave.<br /> *Qual a energia que deve ser dissipada ou transferida \`a nave para que esta passe para uma \&#039;orbita circular em torno da Terra de raio duas vezes superior ao raio de \&#039;orbita inicial?<br /> <br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:210px&quot;&gt;<br /> &#039;&#039;&#039;Respostas&#039;&#039;&#039;<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> <br /> *\(v_A = \sqrt{121gR} \simeq 77 \,\)m.s\(^{-1}\)<br /> *\(P = mg = 980\, \)N<br /> *\(N = 120mg = 117 600\, \)N<br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;</div>

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