Question

2. (10 points) The Hohmann transfer orbit, proposed by Walter Hohmann in 1925, is the most energy- efficient means of traveling from a circular orbit of radius r, to another circular orbit of radius r. The maneuver consists of two engine burns. The first burm places the spacecraft into an elliptical orbit with ri and r2 as the distances of closest and farthest approach (not necessarily respectively). Once the distance rz is reached, a second burn takes the spacecraft into a circular orbit. Find the amount of energy required to execute a Hohmann transfer from the radius of the Earth's orbit around the sun (~1.5 x 10 m) to the radius of Mars's orbit (~2.25 x 10 m). Assume that the mass of the spacecraft is 1000 kg and that the mass of the sun is 2 x 100 kg. Ignore the gravitational effects of Earth and Mars.

Answer 1

Hoffman Transfer Transfer a space craft brom a circular orbit of reading ey to a circular orlit ob radius 72 around some celestial body. we know that the potential Energy of a circular oberbit M = mass of is - Gm η = sun η ο ο - spacecraft so Energy reamired for Hoffman Transfer - Change in Energy between Two circular orbits Energy - M - Gm 1 = 6.674810" x 2x10 30 x 1000 x (s . 225*10") = 6.674 X2X1050 2,000 ( 225) 1 = 2.9662 x 10 33 Joules