# Homework Help: Escape velocity

1. Dec 14, 2008

### hodgepodge

1. The problem statement, all variables and given/known data
when a spacecraft escapes from the earth, it still has to escape from the sun, in order to leave the solar system. at what velocity should a spacecraft be launched if it is 6.4x10^6 meters from earth's centre and 1.5x10^11 meteres from the sun (M=2x10^30 kg) if it is to escape the solar system.

G=6.672x10^-11

2. Relevant equations
i think Vesc.=(2GM)/r

3. The attempt at a solution
i was thinking to plug in the sun's mass for M, but for r, i was thinking to put in 6.4x10^6 + 1.5x10^11 for r, am i even using the right formula? i'm pretty sure that i am, i just am confused over the use of 2 distances

2. Dec 14, 2008

### LowlyPion

But you can add the potential energies together such that the potential energy that you need to overcome with respect to Earth and the potential energy you need to overcome with respect to the Sun both can be figured and added which becomes the root sum of the squares of the individual escape velocities.

PE = GMe/Re + GMs/Rs = 1/2v2 - which is the KE needed.

(The m's of the space shot cancel out.)

In case you don't recognize that what you have is:

V2 = Ve2 +Vs2

3. Dec 16, 2008

### hodgepodge

thank you so much