{"id":238,"date":"2023-06-23T13:31:07","date_gmt":"2023-06-23T13:31:07","guid":{"rendered":"https:\/\/physigeek.com\/de\/gravitationspotentialenergie\/"},"modified":"2023-06-23T13:31:07","modified_gmt":"2023-06-23T13:31:07","slug":"gravitationspotentialenergie","status":"publish","type":"post","link":"https:\/\/physigeek.com\/de\/gravitationspotentialenergie\/","title":{"rendered":"Gravitationspotentialenergie"},"content":{"rendered":"<p>In diesem Artikel erfahren Sie, was potenzielle Gravitationsenergie ist, wie Sie potenzielle Gravitationsenergie berechnen und au\u00dferdem eine gel\u00f6ste \u00dcbung zum besseren Verst\u00e4ndnis des Konzepts. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-energia-potencial-gravitatoria\"><\/span> Was ist die potentielle Gravitationsenergie?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Gravitationspotentialenergie<\/strong> , oder einfach <strong>Gravitationsenergie<\/strong> , ist die potentielle Energie, die mit dem Gravitationsfeld verbunden ist. Einfach ausgedr\u00fcckt ist die potentielle Gravitationsenergie die potentielle Energie, die ein K\u00f6rper erh\u00e4lt, wenn er an einem Punkt in einem Gravitationsfeld platziert wird.<\/p>\n<p> Je n\u00e4her sich der K\u00f6rper also an der Masse befindet, die das Gravitationsfeld erzeugt, desto geringer ist seine potenzielle Gravitationsenergie. Je weiter der K\u00f6rper vom Zentrum des Gravitationsfeldes entfernt ist, desto gr\u00f6\u00dfer ist seine potenzielle Gravitationsenergie. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-energia-potencial-gravitatoria\"><\/span> Formel f\u00fcr die potentielle Gravitationsenergie<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Die potenzielle Gravitationsenergie an einem Punkt ist gleich minus der universellen Gravitationskonstante mal der Masse, die das Gravitationsfeld erzeugt, mal der Masse, auf die die Gravitationskraft wirkt, dividiert durch den Abstand zwischen den beiden Massen.<\/p>\n<p> Mit anderen Worten, die <strong>Formel f\u00fcr die potentielle Gravitationsenergie<\/strong> lautet:<\/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-cedb92791ce76778cfdd2b67d5e51227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E_p=-G\\cdot \\cfrac{M\\cdot m}{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" 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-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 potentielle Gravitationsenergie, deren Einheit im Internationalen System das Joule 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 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-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, auf den das Gravitationsfeld einwirkt, 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 K\u00f6rper, der die Wirkung des Gravitationsfeldes empf\u00e4ngt, ausgedr\u00fcckt in Metern. <\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-calculo-de-la-energia-potencial-gravitatoria\"><\/span> Beispiel f\u00fcr die Berechnung der potentiellen Gravitationsenergie<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Nachdem wir die Bedeutung der potentiellen Gravitationsenergie verstanden haben, finden Sie unten ein konkretes Beispiel, damit Sie sehen k\u00f6nnen, wie diese physikalische Gr\u00f6\u00dfe berechnet wird.<\/p>\n<ul>\n<li> Wie gro\u00df ist die potenzielle Gravitationsenergie, die ein 60 kg schwerer K\u00f6rper in einem Abstand von 80 cm von einer Masse von 220 kg aufnimmt?<\/li>\n<\/ul>\n<p> Um die potentielle Gravitationsenergie 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-cedb92791ce76778cfdd2b67d5e51227_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle E_p=-G\\cdot \\cfrac{M\\cdot m}{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Um die Formel verwenden zu k\u00f6nnen, m\u00fcssen jedoch alle Werte in Einheiten des Internationalen Systems ausgedr\u00fcckt werden. Bevor Sie also die Berechnung durchf\u00fchren, m\u00fcssen Sie zun\u00e4chst die Entfernung in Meter umrechnen:<\/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-de6501492d43b4869d08fda828c0d6dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" 80 \\ cm \\div 100 =0,8 \\ m\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"165\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Nun wenden wir die Formel f\u00fcr die potentielle Gravitationsenergie an und berechnen ihren Wert:<\/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-d06d44b4063927438a8ab566279ae4d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\displaystyle E_p&amp;=-G\\cdot \\cfrac{M\\cdot m}{r}\\\\ &amp;=-6.674\\cdot 10^{-11}\\cdot \\cfrac{220\\cdot 60 }{0.8}\\\\ &amp;=-1.10 \\cdot 10^{-6} \\ J\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"227\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Wie Sie sehen k\u00f6nnen, ist der Wert der potentiellen Gravitationsenergie bei Massen in der Gr\u00f6\u00dfenordnung des Alltagslebens vernachl\u00e4ssigbar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-de-la-energia-potencial-gravitatoria\"><\/span> Eigenschaften der potentiellen Gravitationsenergie<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Die potentielle Gravitationsenergie hat die folgenden Eigenschaften:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Die potentielle Gravitationsenergie kann niemals positiv sein.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Und es kann nur Null bis Unendlich sein.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Die potentielle Gravitationsenergie ist daher immer negativ.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Dar\u00fcber hinaus nimmt die potentielle Gravitationsenergie ab, wenn die Massen einander n\u00e4her kommen.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Andererseits erh\u00f6ht sich die potentielle Energie, wenn sich die beiden Massen auseinander bewegen.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Energia-potencial-gravitatoria-y-potencial-gravitatorio\"><\/span> Gravitationspotentialenergie und Gravitationspotential<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Das <strong>Gravitationspotential<\/strong> an einem Punkt gibt 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> Somit h\u00e4ngen die potentielle Energie der Gravitation und das Gravitationspotential durch die folgende Formel zusammen:<\/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-a1eb7284ffd80fab3ea2a559f3ebdcd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E_p=V\\cdot m\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -6px;\"><\/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-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 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><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 die Gravitationskraft einwirkt, ausgedr\u00fcckt in Kilogramm.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In diesem Artikel erfahren Sie, was potenzielle Gravitationsenergie ist, wie Sie potenzielle Gravitationsenergie berechnen und au\u00dferdem eine gel\u00f6ste \u00dcbung zum besseren Verst\u00e4ndnis des Konzepts. Was ist die potentielle Gravitationsenergie? Gravitationspotentialenergie , oder einfach Gravitationsenergie , ist die potentielle Energie, die mit dem Gravitationsfeld verbunden ist. Einfach ausgedr\u00fcckt ist die potentielle Gravitationsenergie die potentielle Energie, die &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/de\/gravitationspotentialenergie\/\"> <span class=\"screen-reader-text\">Gravitationspotentialenergie<\/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 die potentielle Gravitationsenergie? 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