F GM M =− has one inherent assumption that both M and M are treated as point masses. When it is said that Earth orbits around the Sun due to Sun’s gravitational force, we assumed Earth and Sun to be point masses. This assumption is a good approximation because the distance between the two bodies is very much larger than their diameters. For some irregular and extended objects separated by a small distance, we cannot directly use the equation ( .
). Instead, we have to invoke separate mathematical treatment which will be brought forth in higher classes. However, this assumption about point masses holds even for small distance for one special case. To calculate force of attraction between a hollow sphere of mass M with uniform density and point mass m kept outside the hollow sphere, we can replace the hollow sphere of mass M as equivalent to a point mass M located at the center of the hollow sphere.
The force of attraction between the hollow sphere of mass M and point mass m can be calculated by treating the (a) (b) - - - - Unit Gravitation k ( . ) By substituting equation . in the force expression, we can arrive at the law of gravitation. F mk ( .
) Here negative sign implies that the force is attractive and it acts towards the center. In equation ( . ), mass of the planet ‘m’ comes explicitly. But Newton strongly felt that according to his third law, if Earth is attracted by the Sun, then the Sun must also be attracted by the Earth with the same magnitude of force.
So he felt that the Sun’s mass (M) should also occur explicitly in the expression for force ( . ). From this insight, he equated the constant π k to GM which turned out to be the law of gravitation. F GMm Again the negative sign in the above equation implies that the gravitational force is attractive.
In the above discussion we assumed that the orbit of the planet to be circular which is not true