# Pioneer 10 Spacecraft travelling in space

## Homework Statement

To escape from the solar system, how fast did the Pioneer 10 have to be travelling as it passed the orbit of Jupiter? Assume the mass of the solar system is essentially concentration in the Sun. The mass of the Sun is 1.99 x 10^30 kg and the radius of Jupiter's orbit is 7.78 x 10^11 m.

## Homework Equations

Gravitational Potential Energy
Total Orbital Energy
Kinetic Energy
Escape Velocity
Escape Energy

## The Attempt at a Solution

I am confused as to what quantities are relevant in this situation. I know that Jupiter must be used to carry out with escape velocity, but I don't have the mass of it.

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Well, I haven't gotten to this part yet, we just started the chapter concerning this type of problem.
However, looking in the book I found that the escape speed (v) = √(2GM/R)
I don't think you need the mass of Jupiter since you aren't launching from its surface, you're just flying past it's orbit. The key here is that you're finding the escape velocity of the solar system. Also, the problem states that you can assume the solar system's mass is concentrated in the sun, so you can use the M = mass of the sun, and R can be the radius of Jupiter's orbit, (since thats the distance Pioneer 10 is from the sun at this point)

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You have the data to substitute and solve in the escape velocity formula (at least for one of the two forms of that equations I know).

If that is not clear to you, I suspect you have the other form or are misinterpreting the variables. Can you post the equation and what the variables mean?