# Can you assume that Jupiter has a circular orbit?

1. Dec 30, 2003

### 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.

2. Dec 30, 2003

### enigma

Staff Emeritus
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.

3. Dec 30, 2003

### enigma

Staff Emeritus
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