Question

The gravitational force between the Sun (mass = 1.99 × 1030 kg) and Mercury (mass = 3.30 × 1023 kg) is 8.99 × 1021 N. How far is Mercury from the Sun?

Answer 1

The answer is B - 6.98 x 10^7 km

Answer 2

Answer : Distance, d=6.98 × 10⁷ Km

Explanation :

Given that,

Mass of the sun, m₁ = 1.99 × 10³⁰ kg

Mass of Mercury, m₂ = 3.30 × 10²³ kg

Gravitational force between the sun and mercury, F = 8.99 × 10²¹ N

According to Universal law of gravitation,

$F=G\dfrac{m_1m_2}{d^2}$

d is the distance of mercury from the sun

$d=\sqrt{\dfrac{Gm_1m_2}{F}}$

$d=\sqrt{\dfrac{6.67\times 10^{-11}\times 1.99\times {30}\times 3.30\times 10^{23}}{8.99\times 10^{21}}}$

$d=\sqrt{4.87\times 10^{21}} m$

$d=6.98\times 10^{10}\ m$

or

$d=6.98\times 10^{7}\ Km$

So, mercury is $6.98\times 10^{7}\ Km$ far from the sun.