BITSAT2016PhysicsGravitationActual
Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T ²= Kr ³ here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = GMm r ² , here G is gravitational constant. The relation between G and K is de
Options
- AGMK =4 ²
- BK = G
- CK = 1 G
- DGK =4 ²
Correct answer
A. GMK =4 ²
Step-by-step solution
As we know, orbital speed, V_ orb = GM r Time period T = 2 r v _ orb = 2 r GM r Squarring both sides, T ²= ( 2 r r GM )²= 4 ² GM r ³ T ² r ³ = 4 ² GM = K GMK =4 ²