{"id":240,"date":"2023-06-23T12:42:01","date_gmt":"2023-06-23T12:42:01","guid":{"rendered":"https:\/\/physigeek.com\/pt\/potencial-gravitacional\/"},"modified":"2023-06-23T12:42:01","modified_gmt":"2023-06-23T12:42:01","slug":"potencial-gravitacional","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/potencial-gravitacional\/","title":{"rendered":"Potencial gravitacional"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 potencial gravitacional na f\u00edsica. Da mesma forma, voc\u00ea descobrir\u00e1 como \u00e9 calculado o potencial gravitacional, um exerc\u00edcio resolvido do potencial gravitacional e em que consiste uma superf\u00edcie equipotencial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-potencial-gravitatorio\"><\/span> O que \u00e9 potencial gravitacional?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Na f\u00edsica, o <strong>potencial gravitacional<\/strong> (ou <strong>potencial gravitacional<\/strong> ) \u00e9 uma quantidade usada para quantificar o campo gravitacional.<\/p>\n<p> Mais precisamente, o valor do potencial gravitacional num ponto indica o trabalho que uma for\u00e7a deve realizar para transportar um corpo a uma velocidade constante do infinito at\u00e9 aquele ponto do campo gravitacional.<\/p>\n<p> Tenha em mente que todos os corpos, independentemente da massa, geram um campo gravitacional. Portanto, todos os corpos tamb\u00e9m geram um potencial gravitacional. Por\u00e9m, apenas campos gravitacionais de massas suficientemente grandes, como os planetas, s\u00e3o levados em considera\u00e7\u00e3o, j\u00e1 que o restante \u00e9 praticamente zero. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-potencial-gravitatorio\"><\/span> F\u00f3rmula do potencial gravitacional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O potencial gravitacional criado por uma massa pontual em um ponto \u00e9 igual a menos a constante gravitacional universal vezes essa massa dividida pela dist\u00e2ncia entre a massa pontual e o ponto em que o potencial gravitacional \u00e9 calculado.<\/p>\n<p> Em outras palavras, a <strong>f\u00f3rmula do potencial gravitacional<\/strong> \u00e9 a seguinte:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-96c4ce259ef29fec7d7c42d7c67f57cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V=-\\cfrac{G\\cdot M}{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-54e215a7a583b4f357a5a627420bcf2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o potencial gravitacional, cujas unidades s\u00e3o J\/kg. <\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-1e40206e25474f738eeb7ca968031abf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"G\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a constante gravitacional universal, cujo valor \u00e9<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-9d75ef18969b22581b72ad88a7def60c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6,674\\cdot 10^{-11} \\ N\\cdot m^2\/kg^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"192\" style=\"vertical-align: -5px;\"><\/p>\n<p> . <\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-27d6692c77760dc1111628e74a6d272f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"M\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a massa do corpo que cria o campo gravitacional, expressa em quilogramas.<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a dist\u00e2ncia entre o corpo que cria o campo gravitacional e o ponto de interesse, expressa em metros.<\/span><\/li>\n<\/ul>\n<p> Al\u00e9m disso, o potencial gravitacional satisfaz o <strong>princ\u00edpio da superposi\u00e7\u00e3o<\/strong> , o que significa que se houver m\u00faltiplas massas criando o campo gravitacional, o potencial gravitacional num ponto \u00e9 a soma dos potenciais gravitacionais de todas as massas nesse ponto. <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5df3dc8c4cb5495099377cfe98118af4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle V_T=\\sum _{i=1}^n V_i=V_1+V_2+V_3+\\dots+ V_n\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"292\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-calculo-del-potencial-gravitatorio\"><\/span> Exemplo de c\u00e1lculo do potencial gravitacional<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o de potencial gravitacional e qual \u00e9 sua f\u00f3rmula, nesta se\u00e7\u00e3o voc\u00ea poder\u00e1 ver um exemplo resolvido de c\u00e1lculo desta grandeza f\u00edsica.<\/p>\n<ul>\n<li> Qual \u00e9 o potencial gravitacional gerado por um ponto de massa de 8,10 <sup>20<\/sup> kg em um ponto localizado a uma dist\u00e2ncia de 6,5,10 <sup>7<\/sup> m?<\/li>\n<\/ul>\n<p> Para determinar o potencial gravitacional, precisamos usar a f\u00f3rmula que vimos acima:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-96c4ce259ef29fec7d7c42d7c67f57cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V=-\\cfrac{G\\cdot M}{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Agora simplesmente substitu\u00edmos os dados na f\u00f3rmula e calculamos o potencial gravitacional:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7f0cf9c9a7f9cb1177d603420f0e147c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V=-\\cfrac{6,674\\cdot 10^{-11} \\cdot 8\\cdot 10^{20}}{6,5\\cdot 10^7}=-821,42 \\ J\/kg [\/ latex]\n\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;Superficie-equipotencial&quot;><\/span> surface \u00e9quipotentielle<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> Une <strong>surface \u00e9quipotentielle<\/strong> est constitu\u00e9e de tous les points de l&#8217;espace qui ont le m\u00eame potentiel gravitationnel. Dans l&#8217;image suivante, vous pouvez voir plusieurs surfaces \u00e9quipotentielles repr\u00e9sent\u00e9es. Chaque cercle correspond \u00e0 un potentiel gravitationnel diff\u00e9rent et constitue donc une surface \u00e9quipotentielle. <\/p>\n<figure class=&quot;wp-block-image aligncenter size-full is-resized&quot;><img decoding=&quot;async&quot; loading=&quot;lazy&quot; src=&quot;https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/potentiel-gravitationnel-de-surface-equipotentiel.png&quot; alt=&quot;surface \u00e9quipotentielle&quot; class=&quot;wp-image-3985&quot; width=&quot;290&quot; height=&quot;318&quot; srcset=&quot;https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/potentiel-gravitationnel-de-surface-equipotentiel-273x300.png 273w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/potentiel-gravitationnel-de-surface-equipotentiel.png 543w&quot; sizes=&quot;(max-width: 273px) 100vw, 273px&quot;><\/figure>\n<p> Notez que plus le point du champ gravitationnel est \u00e9loign\u00e9 du centre du corps qui cr\u00e9e le champ, plus le potentiel gravitationnel est grand. De plus, chaque point ne peut appartenir qu&#8217;\u00e0 une seule surface \u00e9quipotentielle, puisque le potentiel gravitationnel en un point a une seule valeur. <\/p>\n<h2 class=&quot;wp-block-heading&quot;><span class=&quot;ez-toc-section&quot; id=&quot;Potencial-gravitatorio-y-energia-potencial-gravitatoria&quot;><\/span> Potentiel gravitationnel et \u00e9nergie potentielle gravitationnelle<span class=&quot;ez-toc-section-end&quot;><\/span><\/h2>\n<p> <strong>L&#8217;\u00e9nergie potentielle gravitationnelle<\/strong> est l&#8217;\u00e9nergie potentielle qu&#8217;un corps acquiert lorsqu&#8217;il est plac\u00e9 en un point dans un champ gravitationnel. Ainsi, l&#8217;\u00e9nergie potentielle gravitationnelle peut \u00eatre calcul\u00e9e \u00e0 partir du potentiel gravitationnel, puisqu&#8217;ils sont li\u00e9s par la formule suivante : [latex]V=\\cfrac{E_p}{m}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;589&#8243; width=&#8221;2122&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-54e215a7a583b4f357a5a627420bcf2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o potencial gravitacional em um ponto, cujas unidades s\u00e3o J\/kg. <\/span><\/li>\n<li style=\"margin-bottom:8px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-09b2ab0fbfe1c76e7f3bf527fc17889c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E_p\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"20\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u00e9 a energia potencial gravitacional em um ponto, expressa em joules.<\/span><\/li>\n<li><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a massa do corpo colocado em um campo gravitacional e sobre o qual atua uma for\u00e7a gravitacional, expressa em quilogramas.<\/span><\/li>\n<\/ul>\n<p> Assim, o potencial gravitacional num ponto tamb\u00e9m pode ser definido como a energia potencial por unidade de mat\u00e9ria que um corpo adquire ao se colocar naquele ponto do campo gravitacional. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/physigeek.com\/pt\/energia-potencial-gravitacional\/\">f\u00f3rmula para energia potencial gravitacional<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 potencial gravitacional na f\u00edsica. Da mesma forma, voc\u00ea descobrir\u00e1 como \u00e9 calculado o potencial gravitacional, um exerc\u00edcio resolvido do potencial gravitacional e em que consiste uma superf\u00edcie equipotencial. O que \u00e9 potencial gravitacional? Na f\u00edsica, o potencial gravitacional (ou potencial gravitacional ) \u00e9 uma quantidade usada para quantificar o &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/potencial-gravitacional\/\"> <span class=\"screen-reader-text\">Potencial gravitacional<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[5],"tags":[],"class_list":["post-240","post","type-post","status-publish","format-standard","hentry","category-dinamico"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 O que \u00e9 potencial gravitacional? 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