The asteroid Ceres has a diameter of 785 km and a mass of 1.0 × 10²⁰ kg.  Calculate:

(a)    the strength of the gravitational field;

(b)   the gravitational potential at the surface.                                                                    

(a) Radius = 785 × 10³ ÷ 2 = 392.5 × 10³ m (P)

g = - 6.67 ´ 10 ^–11 Nm² kg^-2 × 1.0 × 10²⁰ kg (P)

                          (392.5 × 10³ m)²        

g = - 0.043 m/s² (P)

(b) V = -GM = - 6.67 ´ 10 ^–11 Nm² kg^-2 × 1.0 × 10²⁰ kg (P)

             r                       392.5 × 10³ m 

V = (-) 17 000 J/kg (P)