derivation of T² = 8H/g please
Answers
Explanation:
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 than as per Newton's law of gravitation force of attraction between them is
F=
r
2
GMm
, here G is gravitational constant The relation between G and K is described as
HARD
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ANSWER
The gravitational force is providing centripetal force to the planets oribital circular motion
r
2
GMm
=
r
mv
2
⇒v=
r
GM
The time period for planet in one revolution will be T=
v
2πr
=
r
GM
2πr
squaring each side
T
2
=
GM
4π
2
r
3
comparing with given equation T
2
=Kr
3
K=
GM
4π
2