# Homework Help: Satellites in Orbite

1. Dec 29, 2009

### tigerwoods99

1. The problem statement, all variables and given/known data
you are in charge of placing a satellite of mass 5130kg into an orbit around the planet Jupiter. The orbit has an altitude of 3.59E+5m.

What is the orbital velocity of the satellite?

2. Relevant equations

Velocity = square root (G * m/r)

3. The attempt at a solution

Velocity = square root (6.67e-11 * 5130/3.59e+5)
V = 9.76e-7 which is Incorrect.

Any Help would be much appreciated!!!!!

2. Dec 29, 2009

### rock.freak667

3. Dec 29, 2009

### tigerwoods99

I have tried that:
V = square root( 6.67e-11 * 5130/7.218e7)
v=6.884e-8 m/s which is also Incorrect.

4. Dec 29, 2009

### rock.freak667

your formula is missing a '2' in it. If I recall correctly it should be

$$v=\sqrt{2 \frac{GM}{r}}=\sqrt{2gr}$$

5. Dec 29, 2009

### tigerwoods99

I can't get that to work either!!

6. Dec 29, 2009

### rock.freak667

Sorry sorry, I remember it now.

$$\frac{mv^2}{r}=\frac{GMm}{r^2} \Rightarrow v = \sqrt{\frac{GM}{r}}$$

But I don't think M= mass of the satellite, m should be that mass of the planet.

(please excuse me, it's been 3 years since I've done these problems)

7. Dec 29, 2009

### pgardn

The centripetal force required to keep the satellite in orbit around jupiter is mv^2/r.
The attraction between the satellite and jupiter is GMm/r^2.

If you set these two statements equal to each other, and little m is the mass of the satellite, does m not cancel? What do you get for v when you set these two equations equal to each other just using the symbols?

and the poster above has just shown this. You should be using the mass of Jupiter... that may be the problem.

8. Dec 29, 2009

### tigerwoods99

Thanks for the explanation!

9. Dec 29, 2009

### tigerwoods99

thanks!!

10. Dec 29, 2009

### pgardn

No problem.

The beauty is that it takes Newton's law of gravitation and says hey this is what is supplying the centripetal force to keep the satellite and orbit. You can do all sorts of interesting stuff with this equality.