Question

(1)Derive expression for inverse square law using keplers third law.​

Answer 1

Centripetal force on planet is calculated as :

F =

r

mv

2

=

r

m

(

T

2πR

)

2

=

rT

2

4π

2

mr

2

F =

r

2

4π

2

m

T

2

r

3

But from Kepler's law,

T

2

r

3

is constant for planets

Therefore F =

r

2

4π

2

m

i.e K =

r

2

G

From this the square inverse nature of gravitational force was derived by Newton.

Answer 2

Answer

A-r, B-s, C-p, D-a

SOLUTION

According to Kepler's first law, all planets move in elliptical orbits with the sun situated at one of the foci.( A-r )

Kepler's second law is a consequence of law of conservation of angular momentum. (B-s)

According to the Kepler's third law, the square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.

(T^2 twise a^2 •°• C-p)

According to Newton's law of gravitation. everybody in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. (D-q)

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