Question

Let planet A have a mass of 5.44 x 10⁴⁵ kg and planet B have a mass of 2.77 x 10³³ kg. If they are attracted by a gravitational force of 6.59 x 10³ N, how far apart are their centers of mass?

Answer 1

Let ,

mass of planet A =m₁ = 5.44 × 10⁴⁵ kg

and Mass of planet B =m₂ = 2.77× 10³³ kg

Force of atraction = F = 6.59× 10³³  N

the distance between their centre of mass will be R.

To find R we use Newton's Law of gravitational attraction,

F= Gm₁m₂ / R²

^{where G = Gravitational constant =}6.67 × 10^-11 m³ kg^-1 s^-2

^{there fore ,}

R²  = Gm₁m₂ / F

=  6.67 × 10^-11× 5.44 × 10⁴⁵ × 2.77× 10³³ / 6.59× 10³³

=100.50× 10⁶⁷ / 6.59× 10³³

R² =15.25 × 10³⁴

R = 15.25 × 10³⁴

R = 3.91 × 10¹⁷ m