Calculate Escape Velocity to Leave Solar System

[hodgepodge]

Homework Statement

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

Homework Equations

i think Vesc.=(2GM)/r

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

 

[LowlyPion]

You certainly wouldn't add the radii together.

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

 

[hodgepodge]

thank you so much