{"id":3784,"date":"2021-12-21T20:01:39","date_gmt":"2021-12-21T20:01:39","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3784"},"modified":"2022-03-24T15:10:24","modified_gmt":"2022-03-24T15:10:24","slug":"newtons-law-of-gravitation","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/newtons-law-of-gravitation\/","title":{"rendered":"\u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0 (Newton’s Law of Gravitation)"},"content":{"rendered":"

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 <\/b>(Gravitation)<\/b><\/h2>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7:<\/span> \u09a8\u09ad\u09cb\u09ae\u09a3\u09cd\u09a1\u09b2\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ac\u09be \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0995\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u0964\u00a0<\/span><\/p>\n

\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7:<\/span> \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u098f\u09ac\u0982 \u0985\u09a8\u09cd\u09af \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ac\u09be \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09be \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\u0989\u09a6\u09be\u09b9\u09b0\u09a3:<\/span> \u09b8\u09c2\u09b0\u09cd\u09af \u0993 \u099a\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u0985\u09a8\u09cd\u09af\u09a6\u09bf\u0995\u09c7 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u098f\u09ac\u0982 \u0986\u09ae\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0964<\/span><\/p>\n

\u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Newton’s Law of Gravitation)<\/b><\/h2>\n

1687<\/span> \u0996\u09cd\u09b0\u09bf\u09b8\u09cd\u099f\u09be\u09ac\u09cd\u09a6\u09c7 \u09ac\u09bf\u0996\u09cd\u09af\u09be\u09a4 \u09ac\u09bf\u099c\u09cd\u099e\u09be\u09a8\u09c0 \u09b8\u09cd\u09af\u09be\u09b0 \u0986\u0987\u099c\u09cd\u09af\u09be\u0995 \u09a8\u09bf\u0989\u099f\u09a8 \u0986\u09aa\u09c7\u09b2 \u09aa\u09a4\u09a8 \u098f\u09ac\u0982 \u0997\u09cd\u09b0\u09b9 \u0989\u09aa\u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u0997\u09a4\u09bf \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7 \u09ae\u09b9\u0995\u09b0\u09cd\u09b7\u09c7\u09b0 \u09af\u09c7 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0986\u09ac\u09bf\u09b7\u09cd\u0995\u09be\u09b0 \u0995\u09b0\u09c7\u09a8 \u09a4\u09be\u0995\u09c7 \u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0 (Newton’s Law of Gravitation)\u09ac\u09b2\u09c7\u0964\u00a0<\/span><\/p>\n

\u09b8\u09c2\u09a4\u09cd\u09b0: <\/span>\u09ae\u09b9\u09be\u09ac\u09bf\u09b6\u09cd\u09ac\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0\u0995\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u098f\u0987 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a6\u09c1\u099f\u09bf\u09b0 \u09ad\u09b0\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u098f\u09ac\u0982 \u098f\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/span><\/p>\n

\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be:<\/span>\u00a0 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ad\u09b0 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 <\/span>\\mathbf{m}_1 <\/span><\/span> \u0993 \\mathbf{m}_2 <\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 F \u09b9\u09af\u09bc, \u09a4\u09be\u09b9\u09b2\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n

(i) <\/span> F<\/span>\u221d\\mathbf{m}_1 <\/span>\\mathbf{m}_2 <\/span><\/span><\/p>\n

(ii) <\/span>F <\/span>\u221d\\frac{1}{\\mathrm{~d}^{2}}\u00a0<\/span><\/span><\/p>\n

(i) \u0993 (ii)-\u0995\u09c7 \u09af\u09c1\u0995\u09cd\u09a4 \u0995\u09b0\u09b2\u09c7,\u00a0<\/span><\/p>\n

F <\/span>\u221d \\frac{\\mathrm{m}_{\\mathbf{1}} \\mathrm{m}_{\\mathbf{2}}}{\\mathrm{d}^{2}}<\/span><\/span><\/p>\n

F <\/span>=<\/span>\u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \\frac{\\mathrm{m}_{\\mathbf{1}} \\mathrm{m}_{\\mathbf{2}}}{\\mathrm{d}^{2}}<\/span><\/span><\/p>\n

F <\/span>= G<\/span> \\frac{\\mathrm{m}_{\\mathbf{1}} \\mathrm{m}_{\\mathbf{2}}}{\\mathrm{d}^{2}}<\/span><\/span>\u2026\u2026\u2026\u00a0\u00a0\u00a0(6.1)<\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 G <\/span><\/span>\u00a0=<\/span> \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09ac\u09be \u09b8\u09be\u09b0\u09cd\u09ac\u099c\u09a8\u09c0\u09a8 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u0987\u09b9\u09be \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf, \u09af\u09c7\u09ae\u09a8- \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6\u09cd\u09af\u09a4\u09be, \u09aa\u09cd\u09b0\u09ac\u09a3\u09a4\u09be, \u09a6\u09bf\u0995\u09a6\u09b0\u09cd\u09b6\u09bf\u09a4\u09be \u098f\u09ac\u0982 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u09a6\u09c1\u099f\u09bf\u09b0 \u09ad\u09cc\u09a4 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964\u00a0<\/span><\/p>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09c2\u09aa:<\/span><\/p>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0\u0995\u09c7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf\u09b0 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09a8\u09bf\u09ae\u09cd\u09a8\u09b2\u09bf\u0996\u09bf\u09a4\u09ad\u09be\u09ac\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc:<\/span><\/p>\n

\\overrightarrow{\\mathrm{F}_{21}} <\/span>= -\\mathrm{G} \\frac{\\mathrm{m}_{1} \\mathrm{~m}_{2}}{\\mathrm{r}_{12}^{3}} <\/span>\\overrightarrow{\\mathrm{r}_{12}} <\/span><\/span><\/p>\n

\u098f\u0996\u09be\u09a8\u09c7 \\overrightarrow{\\mathrm{F}_{21}}<\/span><\/span> \u09b9\u099a\u09cd\u099b\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09a6\u09bf\u0995 \u09ac\u09b2 (\u0986\u0995\u09b0\u09cd\u09b7\u09a3), \\overrightarrow{\\mathrm{r}_{12}} <\/span><\/span>\u00a0\u09b9\u099a\u09cd\u099b\u09c7 \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09b8\u09cd\u09a4\u09c1 \u09b9\u09a4\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09a6\u09bf\u0995 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0964\u00a0<\/span><\/p>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \u09aa\u09cd\u09b0\u09a5\u09ae \u09ac\u09b8\u09cd\u09a4\u09c1 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7 \u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u09a8\u09bf\u099c\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099f\u09be\u09a8\u099b\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \\overrightarrow{\\mathrm{F}_{21}} <\/span><\/span> \u098f\u09ac\u0982 \u09a6\u09bf\u0995 \\overrightarrow{\\mathrm{r}_{12}}<\/span><\/span>\u00a0\u098f\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4, \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u0989\u09aa\u09b0\u09bf\u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09bf\u09b9\u09cd\u09a8 \u09ac\u09cd\u09af\u09ac\u09b9\u09c3\u09a4 \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09c2\u099a\u0995\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09bf\u09b9\u09cd\u09a8 \u09ac\u09cd\u09af\u09ac\u09b9\u09c3\u09a4 \u09b9\u09af\u09bc\u09a8\u09bf\u0964<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 <\/span>(6.16)<\/span> \u09a5\u09c7\u0995\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf \u09b8\u09ae\u09cd\u09ac\u09a8\u09cd\u09a7\u09c7\u0993 \u099c\u09be\u09a8\u09be \u09af\u09be\u09af\u09bc\u0964\u00a0\u00a0<\/span><\/p>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf (Nature of Gravitational Force):\u00a0<\/strong><\/h3>\n
    \n
  1. \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0964\u00a0<\/span><\/li>\n
  2. \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a6\u09c1\u099f\u09bf\u09b0 \u09b8\u0982\u09af\u09cb\u0997 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964\u00a0<\/span><\/li>\n
  3. \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b9\u09c1\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ae\u09be\u09a7\u09cd\u09af\u09ae\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09bf\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/li>\n
  4. \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ad\u09b0\u09c7\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995 \u09b9\u09af\u09bc\u0964<\/span><\/li>\n<\/ol>\n

    \u0989\u09aa\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u0985\u09ac\u09be\u09a7\u09c7 \u09a8\u09bf\u099a\u09c7 \u09aa\u09a1\u09bc\u09a4\u09c7 \u09a6\u09bf\u09b2\u09c7 \u09a4\u09be \u09a8\u09bf\u099a\u09c7 \u09aa\u09a1\u09bc\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u09aa\u09c3\u09b7\u09cd\u09a0\u09c7 \u09aa\u09a1\u09bc\u09c7\u0964 \u0986\u09ae \u0997\u09be\u099b\u09c7\u09b0 \u0986\u09ae \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u09ae\u09be\u099f\u09bf\u09a4\u09c7 \u09aa\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0995\u0996\u09a8\u0993 \u0995\u09bf \u09ad\u09c7\u09ac\u09c7 \u09a6\u09c7\u0996\u09c7\u099b, \u0986\u09ae \u0995\u09c7\u09a8 \u0997\u09be\u099b \u09a5\u09c7\u0995\u09c7 \u09aa\u09a1\u09bc\u09c7 \u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09af\u09be\u09df \u09a8\u09be? \u0986\u09b8\u09b2\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u09a4\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099f\u09be\u09a8\u09c7\u0964 \u0986\u09ac\u09be\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0993 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u0995\u09c7 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09aa\u09be\u09b0\u09cd\u09a5\u09bf\u09ac \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u09ad\u09b0 \u09ac\u09b9\u09c1\u0997\u09c1\u09a3\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b9\u09af\u09bc\u0964 \u09a4\u09be\u0987 \u098f\u0987 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09af\u09bc \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u0997\u09a4\u09bf \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09a3\u09c0\u09af\u09bc \u09b9\u09af\u09bc, \u09a4\u09be\u0987 \u09b8\u09ac \u09b8\u09ae\u09af\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u09a6\u09bf\u0995\u09c7 \u09aa\u09a1\u09bc\u09c7, \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09bf\u0995\u09c7 \u098f\u0997\u09bf\u09af\u09bc\u09c7 \u09af\u09be\u09af\u09bc \u09a8\u09be\u0964 \u09b8\u09c7\u099c\u09a8\u09cd\u09af \u0986\u09ae \u0997\u09be\u099b \u09a5\u09c7\u0995\u09c7 \u09aa\u09a1\u09bc\u09c7 \u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09af\u09be\u09af\u09bc \u09a8\u09be\u0964<\/span><\/p>\n

    \u0989\u09aa\u09b0\u09c7\u09b0 \u0986\u09b2\u09cb\u099a\u09a8\u09be\u09af\u09bc \u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u09af\u09c7, \u09aa\u09cd\u09b0\u09a4\u09cd\u09af\u09c7\u0995 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u09a4\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099f\u09be\u09a8\u09c7 \u09ac\u09be \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u098f\u0987 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0987 \u09b9\u09b2\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0993\u099c\u09a8 \u09b9\u09b2\u09cb \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u0964 \u098f\u0987 \u0993\u099c\u09a8 \u09b8\u09b0\u09cd\u09ac\u09a6\u09be \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09be\u09b0\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09a8\u09bf\u09af\u09bc\u09c7 \u0996\u09be\u09a1\u09bc\u09be \u09a8\u09bf\u099a\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u0995\u09b0\u09c7\u0964\u00a0<\/span><\/p>\n

    m <\/span><\/span> \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8 <\/span> W<\/span><\/span> \u09b9\u09b2\u09c7 \u0986\u09ae\u09b0\u09be \u09b2\u09c7\u0996\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf,<\/span><\/p>\n

    W <\/span>=mg <\/span>\u00a0<\/span><\/p>\n

    \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0993\u099c\u09a8 = \u09ad\u09b0 \u00d7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u099c \u09a4\u09cd\u09ac\u09b0\u09a3<\/span><\/p>\n

    \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u099c \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a8 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8\u0993 \u09b8\u09ae\u09b9\u09be\u09b0\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2, \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8 \u09b8\u09cd\u09a5\u09be\u09a8 \u09a8\u09bf\u09b0\u09aa\u09c7\u0995\u09cd\u09b7 \u09a8\u09af\u09bc\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8 \u09a4\u09be\u09b0 \u098f\u0995\u099f\u09bf \u09ae\u09cc\u09b2\u09bf\u0995 \u09ac\u09c8\u09b6\u09bf\u09b7\u09cd\u099f\u09cd\u09af \u09a8\u09af\u09bc\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993\u099c\u09a8 \u09a5\u09be\u0995\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7, \u09a8\u09be\u0993 \u09a5\u09be\u0995\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/span><\/p>\n

    \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09af\u09c7 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0986\u0995\u09c3\u09b7\u09cd\u099f \u09b9\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09a4\u09be\u09b0 \u0993\u099c\u09a8 \u09b2\u09cb\u09ad \u09ac\u09b2\u09c7\u0964\u00a0<\/span><\/p>\n

    \u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 \u09a5\u09c7\u0995\u09c7 \u0995\u09c7\u09aa\u09b2\u09be\u09b0\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0 <\/b>(Kepler’s Law from Newton’s Law)<\/b><\/h3>\n

    \"Gravitation\"<\/p>\n

    \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u09b8\u09c2\u09b0\u09cd\u09af\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 <\/span>r <\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u098f\u0995\u099f\u09bf \u0997\u09cd\u09b0\u09b9 <\/span>v <\/span><\/span> \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09a4\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u099b\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0 \u09ec.\u09ea] \u09b8\u09c2\u09b0\u09cd\u09af\u09c7\u09b0 \u09ad\u09b0 <\/span>M <\/span><\/span>, \u0997\u09cd\u09b0\u09b9\u09c7\u09b0 (\u09aa\u09c3\u09a5\u09bf\u09ac\u09c0) \u09ad\u09b0 <\/span> m<\/span><\/span> \u098f\u09ac\u0982 \u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2 <\/span>T <\/span><\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\n

    \u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0 \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2,<\/a>\u00a0<\/span><\/p>\n

    \\mathbf{F}_{\\mathbf{g}} <\/span>= \\frac{\\mathbf{G M m}}{r^{2}}<\/span><\/span><\/p>\n

    \u098f\u0996\u09be\u09a8\u09c7 <\/span>G <\/span>=\u00a0<\/span>\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u00a0<\/span><\/p>\n

    \u0986\u09ac\u09be\u09b0 \u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u0997\u09a4\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8\u09c0\u09af\u09bc \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2,\u00a0\u00a0<\/span><\/p>\n

    \\mathbf{F}_{\\mathbf{c}} <\/span>=\\frac{\\mathbf{m v}^{2}}{\\mathbf{r}} <\/span><\/span><\/p>\n

    \u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u0989\u09aa\u09b0 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0987 \u098f\u0987 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ae\u09c1\u0996\u09c0 \u09ac\u09b2 \u09af\u09cb\u0997\u09be\u09a8 \u09a6\u09c7\u09af\u09bc\u0964<\/span><\/p>\n

    \u2234 \\mathbf{F}_{\\mathbf{g}}<\/span><\/span>=\\mathbf{F}_{\\mathbf{c}} <\/span><\/span><\/p>\n

    \u09ac\u09be,\u00a0 \\frac{\\mathrm{GMm}}{\\mathrm{r}^{2}} <\/span><\/span>=\\frac{\\mathrm{mv}^{2}}{\\mathrm{r}} <\/span><\/span><\/p>\n

    \u09ac\u09be, \\frac{\\mathrm{GM}}{\\mathrm{r}} <\/span><\/span>=\\mathrm{v}^{2} <\/span><\/span>\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(6.5)<\/span><\/p>\n

    \u0989\u09aa\u0997\u09cd\u09b0\u09b9\u099f\u09bf\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2 <\/span>T <\/span>\u00a0<\/span>\u09b9\u09b2\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce<\/span> r <\/span><\/span> \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7 \u09b8\u09c2\u09b0\u09cd\u09af\u0995\u09c7 \u098f\u0995\u09ac\u09be\u09b0 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09a4\u09c7 T <\/span><\/span> \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u099c\u09a8 \u09b9\u09b2\u09c7 \u098f\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997 \u09b9\u09ac\u09c7 <\/span>v <\/span>=<\/span>\\frac{2 \\pi r}{T} <\/span><\/span><\/p>\n

    \u2234 (6.3)<\/span> \u09a8\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09af\u09bc\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n

    \\frac{\\mathrm{GM}}{\\mathrm{r}} <\/span>=<\/span>\\left(\\frac{2 \\mathrm{mr}}{\\mathrm{T}}\\right)^{2} <\/span><\/span><\/p>\n

    \u09ac\u09be, \\frac{\\mathrm{GM}}{\\mathrm{r}} <\/span><\/span>=<\/span>\\frac{4 \\pi^{2} r^{3}}{T^{2}} <\/span><\/span><\/p>\n

    \u2234\\mathrm{T}^{2} <\/span><\/span>=\\left(\\frac{4 \\pi^{2}}{\\mathrm{GM}}\\right) <\/span>x \\mathrm{r}^{3}<\/span><\/span>\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(6.6)<\/span><\/p>\n

    \u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 \\left(\\frac{4 \\pi^{2}}{\\mathrm{GM}}\\right) <\/span><\/span>\u00a0\u09a7\u09cd\u09b0\u09c1\u09ac\u09b0\u09be\u09b6\u09bf\u0964<\/span><\/p>\n

    \u2234<\/span> \\mathrm{T}^{2} <\/span><\/span>=<\/span>\u00a0 \u09a7\u09c1\u09ac\u0995 \u00d7 \\mathrm{r}^{3} <\/span><\/span><\/p>\n

    \\mathrm{T}^{2} \\propto \\mathrm{r}^{3} <\/span> \u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0\u2026\u00a0\u00a0\u00a0(6.7)<\/span><\/p>\n

    \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09cd\u09b0\u09b9\u09c7\u09b0 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997 \u0995\u0995\u09cd\u09b7\u09aa\u09a5\u09c7\u09b0 \u0997\u09cd\u09b0\u09b9 \u09b9\u09a4\u09c7 \u09b8\u09c2\u09b0\u09cd\u09af\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u0998\u09a8-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0987\u09b9\u09be\u0987 \u0995\u09c7\u09aa\u09b2\u09be\u09b0\u09c7\u09b0 \u09b8\u09c2\u09a4\u09cd\u09b0<\/a> (\u09a4\u09c3\u09a4\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0)\u0964\u00a0<\/span><\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 (Gravitation) \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7: \u09a8\u09ad\u09cb\u09ae\u09a3\u09cd\u09a1\u09b2\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ac\u09be \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u09aa\u09be\u09b0\u09b8\u09cd\u09aa\u09b0\u09bf\u0995 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0995\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u0964\u00a0 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7: \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u098f\u09ac\u0982 \u0985\u09a8\u09cd\u09af \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ac\u09be \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09be \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2\u09c7\u0964 \u0989\u09a6\u09be\u09b9\u09b0\u09a3: \u09b8\u09c2\u09b0\u09cd\u09af \u0993 \u099a\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u0985\u09a8\u09cd\u09af\u09a6\u09bf\u0995\u09c7 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0<\/p>\n

    Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4240,3028,50,51],"tags":[2620,2624,2622,2623,2621],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3784"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3784"}],"version-history":[{"count":8,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3784\/revisions"}],"predecessor-version":[{"id":7760,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3784\/revisions\/7760"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}