Question

Consider a star 1 of mass m1 = 2 * 10^30kg located at r1= <-2*10^11,-1*10^11,0>m and another star 2 of mass m2 = 3 *10^30kg located at r2 =<2*10^11,3*10^11,0>m that are isolated from all the other objects in the universe.

a) What is the vector that points from star 1 to star 2?

b) What is the unit vector that points from star 1 to star 2?

c) What is the gravitational Fg on 1 by 2? (Draw picture)

d)Suppose Fg on 1 by 2 act for \bigtriangleup t=20s. What is the change in momentum of the first star?

e) Define the system as both stars and the surrounding as empty space. Using momentum conservation and reciprocity of the gravitational force, what is the momentum change of the second star.

Answer 1

a)

r₁₂ = r₂ - r₁ = ((2 x 10¹¹) i + (3 x 10¹¹) j + 0 k) - (- 2 x 10¹¹) i + (- 1 x 10¹¹) j + 0 k

r₁₂ = (4 x 10¹¹) i + (4 x 10¹¹) j + 0 k

b)

magnitude of r₁₂ = sqrt((4 x 10¹¹)² + (4 x 10¹¹)² + 0²) = sqrt(2) (4 x 10¹¹)

r₁₂^ = r₁₂ /magnitude of r₁₂ = ((4 x 10¹¹) i + (4 x 10¹¹) j + 0 k )/(sqrt(2) (4 x 10¹¹)) = 0.71 i + 0.71 j + 0 k

c)

F_g = G m₁ m₂ /r₁₂² = (6.67 x 10^-11) (2 x 10³⁰) (3 x 10³⁰) /(sqrt(2) (4 x 10¹¹))² = 1.25 x 10²⁷ N

d)

Change in momentum = Ft = (1.25 x 10²⁷ ) (20) = 2.5 x 10²⁸ kgm/s