Question

The mass of planet Jupiter is 1.9 × 10^27 kg and that of the sun is 1.99 × 10^30 kg. The mean distance of the Jupiter from the sun is 7.8 × 10^11 m. Calculate the gravitational force which the sun exerts on Jupiter. ​

Answer 1

Given :-

The mass of planet Jupiter is 1.9 × 10²⁷ kg and that of the sun is 1.99 × 10³⁰ kg. The mean distance of the Jupiter from the sun is 7.8 × 10¹¹ m. Calculate the gravitational force which the sun exerts on Jupiter.

Solution :-

We know that,

$\sf{F = \dfrac{GMm}{r^{2}}}$

$\sf{F = \dfrac{6.67 \times {10}^{ - 11} \times 1.99 \times {10}^{30} \times 1.9 \times {10}^{27} }{{(7.8 \times {10}^{11} )}^{2} } }$

$\to\sf{F = 4.1 × 10^{23}N}$

Nextly,

v = $\sf\sqrt{\dfrac{Gm}{r}}$ = $\sf\sqrt{\dfrac{Gm}{r}}$

$\to\sf\sqrt{\dfrac{6.67 × 10^{-11}×1.9×10^{30}}{7.8×10^{11}}}$

v = $\sf{1.3 × 10^{4}ms^{-1}}$

• Hence, the gravitational force which the sun exerts on Jupiter is $\bf{1.3 × 10^{4}ms^{-1}}$.