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
$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{d}}^2}$
$$\begin{gathered} =\frac{6.673\times {10}^{-11}\times 2\times {10}^{30}\times 6\times {10}^{24}}{{\left(1.5\times {10}^{11}\right)}^2} \\ =\frac{6.673\times {10}^{-11}\times 2\times {10}^{30}\times 6\times {10}^{24}}{1.5\times 1.5\times {10}^{22}}\left({10}^{24+30-11}={10}^{43}\right) \\ =\frac{6.673\times 2\times 6\times {10}^{43}}{1.5\times 1.5\times {10}^{22}}\left({10}^{43-22}={10}^{21}\right) \\ =\frac{6.673\times 2\times 6\times {10}^{21}}{1.5\times 1.5}\left({10}^{43-22}={10}^{21}\right) \\ =\frac{80.076\times {10}^{21}}{1.5\times 1.5} \\ =35.59\times 10 \end{gathered}$$²¹ N =3.57×10²² N
Answer: Force of gravity = 3.57×10²² N