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,
[tex]F=G\dfrac{m_1m_2}{d^2}[/tex]
d is the distance of mercury from the sun
[tex]d=\sqrt{\dfrac{Gm_1m_2}{F}}[/tex]
[tex]d=\sqrt{\dfrac{6.67\times 10^{-11}\times 1.99\times {30}\times 3.30\times 10^{23}}{8.99\times 10^{21}}}[/tex]
[tex]d=\sqrt{4.87\times 10^{21}} m[/tex]
[tex]d=6.98\times 10^{10}\ m[/tex]
or
[tex]d=6.98\times 10^{7}\ Km[/tex]
So, mercury is [tex]6.98\times 10^{7}\ Km[/tex] far from the sun.
