Question

The mass of sun is 2 ✕ 10³⁰ kg and the mass of earth is 6 ✕ 10²⁴ kg. If the average distance between the sun and the earth be 1.5 ✕ 10⁸ km, calculate the force of gravitation between them.

Answer 1

F (gravitational force) = ?
G (gravitational constant) = 6.673 × 10⁻¹¹ Nm² kg⁻²
M (mass of sun) = 2×10³⁰ kg
m (mass of earth)= 6×10²⁴  kg
d (average distance between sun and earth) = 1.5×10⁸ km = 1.5 ×10⁸ ×1000 = 1.5×10¹¹m
`F = (GMm)/d^2`
= `(6.673 xx 10^-11 xx 2 xx 10^30 xx 6 xx 10^24)/(1.5 xx 10^11)^2`
= `(6.673 xx 10^-11 xx 2 xx 10^30 xx 6 xx 10^24)/(1.5 xx 1.5 xx 10^22)`  `(10^(24+30-11)=10^43)`
= `(6.673 xx 2 xx 6 xx 10^43)/(1.5 xx 1.5 xx 10^22)`   (`10^(43-22)=10^21`)
= `(6.673 xx 2 xx 6 xx 10^21)/(1.5 xx 1.5)  (10^(43-22)=10^21)`
= `(80.076 xx 10^21)/(1.5 xx 1.5)`
= `35.59 xx 10^21 N = 3.57 xx 10^22 N`
 Answer : Force of gravity = `3.57 xx 10^22` N