A 2500-kg rocket blasts off from Planet A headed directly towards Planet B. The masses of Planet A and B are 6x10^24 kg and 3x10^25 kg respectively and the distance between the planets is 4x10^8 m. How far from Planet A will the rocket have traveled when the net gravitational force on the rocket from the two planets is zero?

Question

anonymous · Answer

We'll use Newton's law of universal gravitation, which is given as$$F = G {m_1 m_2 \over r^2}$$

We want the force from each plant to cancel out. Realize conceptually that gravity from planet A will act opposite to gravity from Planet B as long as the rocket is traveling along a straing line between them. 

Therefore, when the magnitude of the gravitational pulls from each planet equal each other in magnitude, the net gravity will be zero. 

This is expressed as$$F_A = F_B$$$${m_r m_A \over r_A^2} = {m_r m_B \over r_B^2}$$

If we express the radius from a common point, let's say, the center of mass of Planet A, we get $$F_A = F_B$$$${m_r m_A \over r^2} = {m_r m_B \over r_{AB} - r}$$ where $r_{AB}$ is the distance between the two planets.

anonymous · Answer

Yes, but need r.h.s. denominator to be (r sub AB - r)^2. Squared missing.