(a) (i) State Newton’s Law of Universal Gravitation.

(ii) Define gravitational field.                                                     

(b) (i) Derive the equation relating the universal gravitational constant, G, and the acceleration of free fall, g, at the surface of the earth from Newton’s law of universal gravitation.

(ii) State two assumptions for which the relationship in 8(b)(i) holds.   

 

(c) Calculate the force of attraction between a star of mass 2.00 x 1030 kg and the earth assuming the star is located 1.50 x 108 km from the earth.  [Mass of the earth = 5.98 x 1024kg; G = 6.67 x 10-11N m\(^{2}\) kg-2; g = 10 m s\(^{-2}\)

 

(d) (i) Define escape velocity.

(ii) State two differences between the acceleration of free fall (g) and the universal gravitational constant (G).