Two point masses 5M and M are separated by a fixed distance L. For the unaltered system the position of zero net gravitational field lies at a distance x0 from the mass M.
Suppose the larger mass is reduced to (1−0.020)(5M) (i.e. a 2% decrease) while M and L remain unchanged.
(i) Derive an expression for the new distance x of the null point from the mass M in terms of x0 and the fractional change in the larger mass. Retain terms up to first order in the small fractional change and neglect higher powers.
(ii) Hence find the fractional shift x0x−x0 in the position of the null point and state whether the point shifts towards or away from the larger mass.
(iii) If L=1.00m and x0=0.25m, compute the numerical value of the shift in centimetres.