{"id":240,"date":"2023-06-23T12:42:01","date_gmt":"2023-06-23T12:42:01","guid":{"rendered":"https:\/\/physigeek.com\/de\/gravitationspotential\/"},"modified":"2023-06-23T12:42:01","modified_gmt":"2023-06-23T12:42:01","slug":"gravitationspotential","status":"publish","type":"post","link":"https:\/\/physigeek.com\/de\/gravitationspotential\/","title":{"rendered":"Gravitationspotential"},"content":{"rendered":"<p>Dieser Artikel erkl\u00e4rt, was Gravitationspotential in der Physik ist. Ebenso erfahren Sie, wie das Gravitationspotential berechnet wird, eine gel\u00f6ste \u00dcbung zum Gravitationspotential und woraus eine \u00c4quipotentialfl\u00e4che besteht. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-potencial-gravitatorio\"><\/span> Was ist Gravitationspotential?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> In der Physik ist das <strong>Gravitationspotential<\/strong> (oder <strong>Gravitationspotential<\/strong> ) eine Gr\u00f6\u00dfe zur Quantifizierung des Gravitationsfeldes.<\/p>\n<p> Genauer gesagt gibt der Wert des Gravitationspotentials an einem Punkt die Arbeit an, die eine Kraft leisten muss, um einen K\u00f6rper mit konstanter Geschwindigkeit aus dem Unendlichen zu diesem Punkt im Gravitationsfeld zu transportieren.<\/p>\n<p> Bedenken Sie, dass alle K\u00f6rper, unabh\u00e4ngig von ihrer Masse, ein Gravitationsfeld erzeugen. Daher erzeugen alle K\u00f6rper auch ein Gravitationspotential. Ber\u00fccksichtigt werden jedoch nur Gravitationsfelder ausreichend gro\u00dfer Massen, etwa Planeten, da der Rest praktisch Null ist. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-potencial-gravitatorio\"><\/span> Gravitationspotentialformel<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Das von einer Punktmasse an einem Punkt erzeugte Gravitationspotential ist gleich minus der universellen Gravitationskonstante mal dieser Masse geteilt durch den Abstand zwischen der Punktmasse und dem Punkt, an dem das Gravitationspotential berechnet wird.<\/p>\n<p> Mit anderen Worten lautet die <strong>Formel f\u00fcr das Gravitationspotential<\/strong> wie folgt:<\/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\"> Gold: <\/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> ist das Gravitationspotential, dessen Einheit J\/kg ist. <\/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> ist die universelle Gravitationskonstante, deren Wert ist<\/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> ist die Masse des K\u00f6rpers, der das Gravitationsfeld erzeugt, ausgedr\u00fcckt in Kilogramm.<\/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> ist der Abstand zwischen dem K\u00f6rper, der das Gravitationsfeld erzeugt, und dem interessierenden Punkt, ausgedr\u00fcckt in Metern.<\/span><\/li>\n<\/ul>\n<p> Dar\u00fcber hinaus erf\u00fcllt das Gravitationspotential das <strong>Superpositionsprinzip<\/strong> , was bedeutet, dass, wenn mehrere Massen das Gravitationsfeld erzeugen, das Gravitationspotential an einem Punkt die Summe der Gravitationspotentiale aller Massen an diesem Punkt ist. <\/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> Beispiel f\u00fcr die Berechnung des Gravitationspotentials<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nachdem wir die Definition des Gravitationspotentials und seine Formel gesehen haben, k\u00f6nnen Sie in diesem Abschnitt ein gel\u00f6stes Beispiel f\u00fcr die Berechnung dieser physikalischen Gr\u00f6\u00dfe sehen.<\/p>\n<ul>\n<li> Welches Gravitationspotential erzeugt ein Punkt der Masse 8\u00b710 <sup>20<\/sup> kg an einem Punkt in 6,5\u00b710 <sup>7<\/sup> m Entfernung?<\/li>\n<\/ul>\n<p> Um das Gravitationspotential zu bestimmen, m\u00fcssen wir die Formel verwenden, die wir oben gesehen haben:<\/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> Jetzt setzen wir die Daten einfach in die Formel ein und berechnen das Gravitationspotential:<\/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}&#8220; title=&#8220;Rendered by QuickLaTeX.com&#8220; height=&#8220;589&#8243; width=&#8220;2122&#8243; style=&#8220;vertical-align: -12px;&#8220;><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Gold: <\/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> ist das Gravitationspotential an einem Punkt, dessen Einheit J\/kg ist. <\/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> ist die potenzielle Gravitationsenergie an einem Punkt, ausgedr\u00fcckt in Joule.<\/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> ist die Masse des K\u00f6rpers, der sich in einem Gravitationsfeld befindet und auf den eine Gravitationskraft einwirkt, ausgedr\u00fcckt in Kilogramm.<\/span><\/li>\n<\/ul>\n<p> Somit kann das Gravitationspotential an einem Punkt auch als die potentielle Energie pro Materieeinheit definiert werden, die ein K\u00f6rper erh\u00e4lt, wenn er sich an diesem Punkt im Gravitationsfeld befindet. <\/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>Siehe:<\/strong> <a href=\"https:\/\/physigeek.com\/de\/gravitationspotentialenergie\/\">Formel f\u00fcr die potentielle Gravitationsenergie<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dieser Artikel erkl\u00e4rt, was Gravitationspotential in der Physik ist. Ebenso erfahren Sie, wie das Gravitationspotential berechnet wird, eine gel\u00f6ste \u00dcbung zum Gravitationspotential und woraus eine \u00c4quipotentialfl\u00e4che besteht. Was ist Gravitationspotential? In der Physik ist das Gravitationspotential (oder Gravitationspotential ) eine Gr\u00f6\u00dfe zur Quantifizierung des Gravitationsfeldes. Genauer gesagt gibt der Wert des Gravitationspotentials an einem Punkt &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/de\/gravitationspotential\/\"> <span class=\"screen-reader-text\">Gravitationspotential<\/span> Mehr lesen &quot;<\/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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Was ist Gravitationspotential? 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