Gravitation

[yxgao]

When it is about the same distance from Jupiter, spacecraft on a mission to the outer planets has a speed that is 1.5 times the speed of Jupiter in its orbit. Why does the orbit of the spacecraft about the sun follow a hyperbolic orbit?

Can you assume that Jupiter has a circular orbit? So far I've tried caltulating the total energies of the spacecraft and of Jupiter but I don't think that's correct.

[enigma]

Use the Vis-Viva equation



V=\sqrt{\frac{2}{r}-\frac{1}{a}}



It's a safe assumption (unless they give it to you explicitly) that the eccentricity of planetary orbits are very small. That means that r~=a.

What is the semimajor axis of a parabolic (or hyperbolic) orbit? You can solve for escape velocity with that.

[enigma]

I made a mistake.

Vis Viva is:



V=\sqrt{\mu*(\frac{2}{r}-\frac{1}{a})}



Where mu is the gravitational parameter, G*M or 398600.4 km^3/sec^2