While investigating the planet Norc in another solar system, we find that the radius of Norc is `9.54 xx 10^(6) m` and that the period of a satellite put in circular orbit of radius `1.476 xx 10^(7) m` is `8.09 xx 10^(3) s`. Determine (a) the mass of Norc, (b) The average, mass density of Norc, (c) the value of the gravitational field on the surface of Norc. (d) If the period of Norc's rotation about its axis is `1.04 xx 10^(4) s`, what will be the reading on a spring scale (calibrated on earth) supporting a `1.0 kg` object at Norc's equator ?

Answer

(a) `2.908 xx 10^(25) kg;` (b) `8.00 xx 10^(3) g//m^(3-);` (c) `21.3 N//kg;` (d) `17.8 N`