Kepler's third law states that square of | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Gravitational force of attraction between sun and planet provides centripetal force for the or

Vedclass · Accepted Answer

$GMK=4$${\pi ^2}$

Vedclass · Answer

Gravitational force of attraction between sun and planet provides centripetal force for the orbit of planet.

$	herefore \frac{{GMm}}{{{r^2}}} = \frac{{m{v^2}}}{r}\,;\,{v^2} = \frac{{GM}}{r}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)$

Time period of the planet is given by

$T = \frac{{2\pi r}}{v},{T^2} = \frac{{4{\pi ^2}{r^2}}}{{{v^2}}} = \frac{{4{\pi ^2}{r^2}}}{{\left( {\frac{{GM}}{r}} ight)}}$                    $(Using\,\,(i))$

${T^2} = \frac{{4{\pi ^2}{r^3}}}{{GM}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)$

According to question,

${T^2} = K{r^3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {iii} ight)$

Comparing equation $(ii)$ and $(iii)$, we get 

$K = \frac{{4{\pi ^2}}}{{GM}}\,\,\,	herefore GMK = 4{\pi ^2}$

Similar Questions

A planet is moving in an elliptical orbit around the sun. If $T, V, E$ and $L$ stand respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct ?

A satellite is in a circular equatorial orbit of radius $7000\,km$ around the Earth. If it is transferred to a circular orbit of double the radius then its angular momentum will be

The time period of a satellite of earth is $5$ hours. If the separation between the earth and the satellite is increased to four times the previous value, the new time period will become ......... $hours$

The time period of a satellite of earth is $24$ hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become $.......\,hours$