{"id":1619,"date":"2024-10-09T06:42:19","date_gmt":"2024-10-09T04:42:19","guid":{"rendered":"http:\/\/www.zsvltava.cz\/fyzika\/?p=1619"},"modified":"2025-04-10T07:31:25","modified_gmt":"2025-04-10T05:31:25","slug":"gravitacni-konstanty-planet","status":"publish","type":"post","link":"https:\/\/www.zsvltava.cz\/fyzika\/?p=1619","title":{"rendered":"Gravita\u010dn\u00ed s\u00edla"},"content":{"rendered":"<p><strong>Gravitace je ozna\u010den\u00ed p\u0159ita\u017eliv\u00e9ho p\u016fsoben\u00ed mezi t\u011blesy. Gravitac\u00ed na sebe p\u016fsob\u00ed ka\u017ed\u00e1 2 t\u011blesa. V b\u011b\u017en\u00fdch velikostech je v\u0161ak tato s\u00edla velmi mal\u00e1.<\/strong><\/p>\n<p>Krom\u011b toho, \u017ee je p\u0159ita\u017eliv\u00e1 <a href=\"\/fyzika\/?p=983\">s\u00edla<\/a> mezi b\u011b\u017en\u00fdmi t\u011blesy velmi mal\u00e1, tak se nav\u00edc <a href=\"\/fyzika\/?p=4113\">vz\u00e1jemn\u011b ru\u0161\u00ed<\/a> d\u00edky p\u016fsoben\u00ed z v\u00edce zdroj\u016f. V\u00fdznamn\u011b v\u0161ak poci\u0165ujeme s\u00edlu, kterou n\u00e1s p\u0159itahuje \u2013 dr\u017e\u00ed na\u0161e Zem\u011b. To proto, \u017ee je zde v\u00fdznamn\u00fd rozd\u00edl mezi na\u0161\u00ed hmotnost\u00ed a hmotnost\u00ed planety. M\u2295 = 5,972\u00d71024 kg. (\u010d\u00edslo kter\u00e9 m\u00e1 24 \u0159\u00e1d\u016f).<\/p>\n<p>Tuto s\u00edlu m\u016f\u017eeme vyj\u00e1d\u0159it jakou sou\u010din hmotnosti a <em>gravita\u010dn\u00ed konstanty<\/em>.<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 34px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-93a927e05038457822bfb1671b58dfb4_l3.png\" height=\"34\" width=\"141\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91; &#70;&#95;&#103;&#32;&#61;&#32;&#109;&#32;&#46;&#32;&#103; &#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<h2>T\u011b\u017ei\u0161t\u011b<\/h2>\n<p>M\u00edsto, kde p\u016fsob\u00ed gravita\u010dn\u00ed s\u00edla na t\u011bleso v\u00fdsledn\u011b naz\u00fdv\u00e1me t\u011b\u017ei\u0161t\u011b. Je to pomysln\u00fd st\u0159ed rovnov\u00e1hy t\u011blesa. I kdy\u017e je t\u011blo slo\u017eeno z mnoha \u010d\u00e1st\u00ed, ka\u017ed\u00e1 p\u0159isp\u00edv\u00e1 svou malou \u201ed\u00e1vkou\u201c hmotnosti a gravitace. V\u00fdsledkem je jeden bod, kter\u00fd celou tuhle s\u00edlu \u201eshrnuje\u201c. Pro pravideln\u00e1 t\u011blesa, jako je koule nebo krychle, je t\u011b\u017ei\u0161t\u011b uprost\u0159ed. U nepravideln\u00fdch t\u011bles je to slo\u017eit\u011bj\u0161\u00ed \u2013 t\u011b\u017ei\u0161t\u011b m\u016f\u017ee b\u00fdt i mimo samotn\u00e9 t\u011bleso<\/p>\n<h2>Gravita\u010dn\u00ed konstanta g<\/h2>\n<p>Ozna\u010dovan\u00e1 jako <em>g<\/em>, je \u010d\u00edslo, kter\u00e9 pom\u00e1h\u00e1 popsat, jak siln\u011b na sebe p\u016fsob\u00ed hmotn\u00e1 t\u011blesa.<\/strong> Jednotkou je N\/kg (s\u00edla p\u016fsob\u00edc\u00ed na 1 kg hmoty.) nebo se pou\u017e\u00edv\u00e1 jednotka zrychlen\u00ed  m\/s<sup>2<\/sup>. (Gravita\u010dn\u00ed konstanta m\u00e1 charakter zrychlen\u00ed &#8211; padaj\u00edc\u00ed t\u011bleso postupn\u011b zvy\u0161uje svou rychlost.)<\/p>\n<h3>Gravita\u010dn\u00ed konstanty<\/h3>\n<table>\n<thead>\n<tr>\n<th style=\"text-transform: none;\">planeta<\/th>\n<th style=\"text-transform: none;\">hmotnost <sup>*<\/sup><\/th>\n<th style=\"text-transform: none;\">g [m\/s<sup>2<\/sup>]<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<th>Merkur<\/th>\n<td>0,054<\/td>\n<td>3,61<\/td>\n<\/tr>\n<tr>\n<th>Venu\u0161e<\/th>\n<td>0,82<\/td>\n<td>8,82<\/td>\n<\/tr>\n<tr>\n<th>Zem\u011b<\/th>\n<td>1<\/td>\n<td>9,81<\/td>\n<\/tr>\n<tr>\n<th>Mars<\/th>\n<td>0,11<\/td>\n<td>3,75<\/td>\n<\/tr>\n<tr>\n<th>Jupiter<\/th>\n<td>318,43<\/td>\n<td>26,6<\/td>\n<\/tr>\n<tr>\n<th>Saturn<\/th>\n<td>95,14<\/td>\n<td>11,2<\/td>\n<\/tr>\n<tr>\n<th>Uran<\/th>\n<td>145,39<\/td>\n<td>10,5<\/td>\n<\/tr>\n<tr>\n<th>Neptun<\/th>\n<td>17,25<\/td>\n<td>13,3<\/td>\n<\/tr>\n<tr>\n<th>M\u011bs\u00edc<\/th>\n<td>0,12<\/td>\n<td>1,62<\/td>\n<\/tr>\n<tr>\n<th>Slunce<\/th>\n<td>333 000<\/td>\n<td>274<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li><sup>*<\/sup> Hmotnost je uvedena jako n\u00e1sobek hmotnosti na\u0161\u00ed planety.<\/li>\n<li><a href=\"http:\/\/solarsystem.nasa.gov\/planets\/index.cfm\">O planet\u00e1ch z NASA.GOV<\/a><\/li>\n<\/ul>\n<h2>Jak velk\u00e1 je gravita\u010dn\u00ed s\u00edla mezi 2 t\u011blesy?<\/h2>\n<p>S\u00edlu vz\u00e1jemn\u00e9ho p\u016fsoben\u00ed definuje Newton\u016fv gravita\u010dn\u00ed z\u00e1kon. Poch\u00e1z\u00ed z roku 1687, kdy jej Isaac Newton publikoval ve sv\u00e9m slavn\u00e9m d\u00edle Philosophi\u00e6 Naturalis Principia Mathematica (zkr\u00e1cen\u011b Principia). V tomto d\u00edle popsal nejen gravita\u010dn\u00ed z\u00e1kon, ale i <a href=\"\/fyzika\/?p=1089\">t\u0159i pohybov\u00e9 z\u00e1kony<\/a>, kter\u00e9 tvo\u0159\u00ed z\u00e1klad klasick\u00e9 mechaniky.<\/p>\n<p>Newton formuloval gravita\u010dn\u00ed z\u00e1kon na z\u00e1klad\u011b p\u0159edchoz\u00edch prac\u00ed, zejm\u00e9na pozorov\u00e1n\u00ed planet\u00e1rn\u00edch pohyb\u016f Johannesa Keplera a pr\u00e1ce Galilea Galileiho.<\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 63px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-2bf0d28d7a6e09ffb30c599f316d8bdc_l3.png\" height=\"63\" width=\"196\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91; &#70;&#32;&#61;&#32;&#71;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#109;&#95;&#49;&#32;&#109;&#95;&#50;&#125;&#123;&#114;&#94;&#50;&#125; &#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-f04dbe505acfab6c4685b5a6523d826a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"14\" style=\"vertical-align: 0px;\"\/> je gravita\u010dn\u00ed s\u00edla mezi t\u011blesy,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-531006075515a832ae3ece04e1700017_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#71;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"15\" style=\"vertical-align: 0px;\"\/> je gravita\u010dn\u00ed konstanta (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-7b7738fedc0fec95051a745d0e0df169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#54;&#55;&#52;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#49;&#48;&#94;&#123;&#45;&#49;&#49;&#125;&#32;&#92;&#44;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#125;&#94;&#51;&#32;&#92;&#44;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#107;&#103;&#125;&#94;&#123;&#45;&#49;&#125;&#32;&#92;&#44;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#94;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"209\" style=\"vertical-align: -4px;\"\/>),<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-b7c82e1506cfcc4fbd26da482c555b33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"\/> a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-10e48dd77188405a44fa2374b2cef88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"23\" style=\"vertical-align: -3px;\"\/> jsou hmotnosti t\u011bles,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/ql-cache\/quicklatex.com-a05d21231b95a3cca8e9f374ca9465cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> je vzd\u00e1lenost mezi t\u011blesy.<\/p>\n<h2>Kde se vzala gravita\u010dn\u00ed konstanta?<\/h2>\n<p>Ve sv\u00e9 dob\u011b Newton neznal p\u0159esnou hodnotu gravita\u010dn\u00ed konstanty G, proto\u017ee se tato konstanta z Newtonova z\u00e1kona nedala p\u0159\u00edmo vypo\u010d\u00edtat.<\/p>\n<p>Prvn\u00ed experiment\u00e1ln\u00ed ur\u010den\u00ed hodnoty gravita\u010dn\u00ed konstanty provedl a\u017e britsk\u00fd v\u011bdec Henry Cavendish v roce 1798 pomoc\u00ed citliv\u00e9 torzn\u00ed v\u00e1hy, tedy v\u00edce ne\u017e 100 let po Newtonov\u011b smrti. <\/p>\n<p>Nejnov\u011bj\u0161\u00edch m\u011b\u0159en\u00ed bylo publikov\u00e1no v roce 2018 Mezin\u00e1rodn\u00ed uni\u00ed \u010dist\u00e9 a aplikovan\u00e9 fyziky (IUPAP). Hodnota gravita\u010dn\u00ed konstanty je zn\u00e1ma s p\u0159esnost\u00ed \u00b1 0.00015.<\/p>\n<h2>V\u0161echno je tak trochu jinak<\/h2>\n<p>Podle Einsteinovy obecn\u00e9 teorie relativity, kter\u00e1 byla publikov\u00e1na v roce 1915, gravitace nen\u00ed skute\u010dnou silou, kter\u00e1 by p\u0159\u00edmo p\u016fsobila mezi dv\u011bma t\u011blesy, jak to popisuje Newton\u016fv gravita\u010dn\u00ed z\u00e1kon. <strong>M\u00edsto toho je gravitace v\u00fdsledkem zak\u0159iven\u00ed prostoro\u010dasu v p\u0159\u00edtomnosti hmoty a energie. Gravitace je tedy geometrick\u00fd efekt, kter\u00fd zp\u016fsobuje, \u017ee t\u011blesa n\u00e1sleduj\u00ed zak\u0159iven\u00e9 trajektorie.<\/strong><\/p>\n<p>V klasick\u00e9 fyzice, podle Newtonova pojet\u00ed, byla gravitace p\u0159\u00edmou silou p\u016fsob\u00edc\u00ed mezi dv\u011bma hmotn\u00fdmi t\u011blesy na d\u00e1lku. Tato s\u00edla byla pova\u017eov\u00e1na za okam\u017eitou, co\u017e vedlo k ur\u010dit\u00e9mu probl\u00e9mu, jak m\u016f\u017ee t\u011bleso &#8222;v\u011bd\u011bt&#8220;, kde se nach\u00e1z\u00ed jin\u00e9 t\u011bleso ve vesm\u00edru a jak s n\u00edm interagovat bezprost\u0159edn\u011b. Einsteinovo pojet\u00ed tuto &#8222;akci na d\u00e1lku&#8220; vy\u0159e\u0161ilo t\u00edm, \u017ee nahradilo s\u00edlu zak\u0159iven\u00edm prostoro\u010dasu, \u010d\u00edm\u017e poskytlo hlub\u0161\u00ed vysv\u011btlen\u00ed gravita\u010dn\u00edch jev\u016f. V t\u00e9to nov\u00e9 interpretaci se hmotn\u00e1 t\u011blesa nepohybuj\u00ed d\u00edky &#8222;s\u00edle&#8220;, ale proto\u017ee n\u00e1sleduj\u00ed nejp\u0159\u00edm\u011bj\u0161\u00ed mo\u017en\u00e9 trajektorie v zak\u0159iven\u00e9m prostoru, co\u017e se naz\u00fdv\u00e1 geodetiky. Ani zde to nen\u00ed zcela bez probl\u00e9m\u016f. P\u0159in\u00e1\u0161\u00ed toti\u017e pot\u0159ebu vy\u0159e\u0161it koncept prostoru.<\/p>\n<p>Pro b\u011b\u017en\u00e9 pot\u0159eby konstrukc\u00ed a v\u00fdpo\u010dt\u016f n\u00e1m dob\u0159e slou\u017e\u00ed zjednodu\u0161en\u00fd Newton\u016fv model. Pokud v\u00e1m spadne cihla na nohu, lze dob\u0159e vyj\u00e1d\u0159it jakou silou a jak\u00fdm zrychlen\u00edm se pohybovala. Ani\u017e bychom museli studovat zak\u0159iven\u00ed prostoro\u010dasu.<\/p>\n<h3>Model zak\u0159iven\u00ed prostoro\u010dasu<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis.webp\" alt=\"\" width=\"1024\" height=\"1024\" class=\"aligncenter size-full wp-image-4829\" srcset=\"https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis.webp 1024w, https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis-300x300.webp 300w, https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis-150x150.webp 150w, https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis-768x768.webp 768w, https:\/\/www.zsvltava.cz\/fyzika\/wp-content\/uploads\/2024\/10\/3d-space-vis-400x400.webp 400w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<h3>Co je prostoro\u010das?<\/h3>\n<p>Prostoro\u010das si m\u016f\u017ee\u0161 p\u0159edstavit jako \u010dty\u0159rozm\u011brnou s\u00ed\u0165, kter\u00e1 kombinuje t\u0159i rozm\u011bry prostoru (d\u00e9lku, \u0161\u00ed\u0159ku, v\u00fd\u0161ku) s jedn\u00edm rozm\u011brem \u010dasu. Funguje jako &#8222;sc\u00e9na,&#8220; kde se odehr\u00e1vaj\u00ed v\u0161echny ud\u00e1losti ve vesm\u00edru.<\/p>\n<ul>\n<li><strong>Prostor:<\/strong> V b\u011b\u017en\u00e9m \u017eivot\u011b zn\u00e1me t\u0159i rozm\u011bry \u2013 nap\u0159\u00edklad ve sv\u00e9m pokoji m\u00e1\u0161 d\u00e9lku (nap\u0159. st\u011bna), \u0161\u00ed\u0159ku (nap\u0159. podlaha) a v\u00fd\u0161ku (nap\u0159. strop).<\/li>\n<li><strong>\u010cas:<\/strong> Vn\u00edm\u00e1\u0161, \u017ee v\u011bci se m\u011bn\u00ed nebo pohybuj\u00ed v \u010dase. Nap\u0159\u00edklad te\u010f \u010dte\u0161 tuto zpr\u00e1vu, ale p\u0159ed chv\u00edl\u00ed jsi ji je\u0161t\u011b nevid\u011bl.<\/li>\n<li><strong>Prostoro\u010das:<\/strong> Einstein uk\u00e1zal, \u017ee prostor a \u010das nejsou odd\u011blen\u00e9, ale tvo\u0159\u00ed jednotn\u00fd celek. Ka\u017ed\u00fd bod v prostoro\u010dase je specifikov\u00e1n svou polohou (kde je) a \u010dasem (kdy se tam n\u011bco stane).<\/li>\n<\/ul>\n<h3>Ohnut\u00ed prostoro\u010dasu<\/h3>\n<p>Gravitace podle teorie relativity nen\u00ed &#8222;s\u00edla&#8220; v klasick\u00e9m smyslu, ale zak\u0159iven\u00ed prostoro\u010dasu, zp\u016fsoben\u00e9 hmotou nebo energi\u00ed. T\u011b\u017ek\u00e9 objekty, jako hv\u011bzdy nebo planety, si m\u016f\u017ee\u0161 p\u0159edstavit jako koule polo\u017een\u00e9 na nata\u017een\u00e9 gumov\u00e9 placht\u011b \u2013 ta plachta se prohne, a t\u00edm ovlivn\u00ed pohyb jin\u00fdch objekt\u016f.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Gravitace je ozna\u010den\u00ed p\u0159ita\u017eliv\u00e9ho p\u016fsoben\u00ed mezi t\u011blesy. Gravitac\u00ed na sebe p\u016fsob\u00ed ka\u017ed\u00e1 2 t\u011blesa. V b\u011b\u017en\u00fdch velikostech je v\u0161ak tato s\u00edla velmi mal\u00e1. Krom\u011b toho, &#8230;. <\/p>\n","protected":false},"author":1,"featured_media":1624,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[35,10],"tags":[53],"class_list":["post-1619","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-sila","category-vesmir","tag-gravitace"],"_links":{"self":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/1619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1619"}],"version-history":[{"count":0,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/posts\/1619\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=\/wp\/v2\/media\/1624"}],"wp:attachment":[{"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zsvltava.cz\/fyzika\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}