Question

(1) At t= 472 s after midnight, a spacecraft of mass 1000 kg is located at position <4 × 10⁵, 2 × 10⁵, -9 × 10⁵> m, and at that time an asteroid whose mass is 5 × 10¹⁵ kg is located at position <4 × 10⁵, -5 × 10⁵, -16 × 10⁵ > m. There are no other objects nearby.
(a) Calculate the (vector) force acting on the spacecraft.

(b) At t= 472 s the spacecraft's momentum was p→i, and at the later time t= 481 s its momentum was p→f. Calculate the (vector) change of momentum p→f-p→i.

(2) A planet of mass 4 × 10²⁴ kg is at location <-9 × 10¹¹, 5 × 10¹¹, 0> m. A star of mass 6 × 10³⁰ kg is at location <9 ×10¹¹, -6 × 10¹¹, 0> m. What is the force exerted on the planet by the star? (It will probably be helpful to draw a diagram, including the relevant vectors.)

Answer 1