Answer to Question #168826 in Astronomy | Astrophysics for Joseph Masker

Question

A 1 kilogram object is located at a distance of 6.4x10 to the 6th m from the center of a larger object whose mass is 6 by 10 to the 24th kg. Find the gravitational attraction between them.

Answer 1

According to the Newton's law of gravitation, $F = \dfrac{Gm_1m_2}{r_{12}^2}$ .

If the large object is spherically symmetric, we may replace it with a point with the same mass located at the center of the sphere. Therefore, the force will be

$F= \dfrac{6.67\cdot10^{-11}\,\mathrm{N m^2/kg^2}\cdot1\,\mathrm{kg}\cdot6\cdot10^{24}\,\mathrm{kg}}{(6.4\cdot10^6\,\mathrm{m})^2} = 9.77\,\mathrm{N}$