Question

The Earth and Jupiter are two planets of the sun. The orbital radius of the earth is `10^(7)m` and that of Jupiter is `4 xx 10^(7)m` If the time period of revolution of earth is `T = 365` days find time period of revolution of the Jupiter
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Answer 1

For both the planets
`T^(2) prop r^(3)`
`((T_("Jupiter"))/(T_(earth)))^(2)=((T_("jupiter"))/(r_(earth)))rArr((T_("jupiter"))/(365days))^(2)=((4xx10^(7))/(10^(7)))^(3)`
`T_("jupiter") = 8 xx 365` days
Graph of `T` vs r ?
Graph o log T v/s log `R`
`T^(2)=((4pi^(2))/(GM)_(s))R^(3)`
`rArr2logT = log ((4pi^(2))/(GM_(s)))+3 logR`
`log T = (1)/(2) log ((4pi^(2))/(GM_(s)) + (3)/(2))log R`
`C =(1)/(2) ((4pi^(2))/(GM_(s)))`


If planets are moving in elliptical orbit, then `T^2 prop a^3` where a=semi major axis of the elliptical path.