Question

According to one of the Kepler's laws of planetary motion (a) r2 ∝ T3
(b) r ∝ T2
(c) r3 ∝ T2
(d) r3 ∝1T2

Answer 1

$\huge{\star}{\underline{\boxed{\red{\mathfrak{Answer :}}}}}{\star}$

(a) is correct answer

=============================

$\huge{\star}{\underline{\boxed{\red{\mathfrak{Explanation :}}}}}{\star}$

Considerd a planet of mass m is orbiting around the sun of mass M in circular orbit of radius r , with constant angular velocity ω .

_______

Then,

$\Large \implies {\sf{\frac{GMm}{r^2} \: = \: mr {\omega}^2 \: = \: mr( \frac{4 {\pi}^2}{GM})r^3}}$

$\Large \implies {\sf{T^2 \: = \: ( \frac{4 {\pi}^2}{GM})r^3}}$

Now,

$\huge{\boxed{\boxed{\sf{T^2 \: \propto \: r^3}}}}$

Where,

∴ [4π²/GM = constant]

=============

So, The Answer is a

__________________________

Mark as Brainliest

✌ ✌ ✌ ✌

Answer 2

$\huge{\boxed{\boxed{\mathfrak{\pink{Answer}}}}}$

(a) r2 ∝ T3