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(m_1m_2)/(d^2)`

d is the distance of mercury from the sun

`d=\sqrt{(Gm_1m_2)/(F)}`

`d=\sqrt{\frac{6.67* 10^(-11)* 1.99* {30}* 3.30* 10^(23)}{8.99* 10^(21)}}`

`d=\sqrt{4.87* 10^(21)} m`

`d=6.98* 10^(10)\ m`

or

`d=6.98* 10^(7)\ Km`

So, mercury is
`6.98* 10^(7)\ Km` far from the sun.