Calculate Orbital Velocity for 5130kg Satellite at Jupiter Orbit

[tigerwoods99]

Homework Statement

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?

Homework Equations

Velocity = square root (G * m/r)

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!

 

[rock.freak667]

I think you'd need to add the radius of Jupiter to the 'r' in your equation.

 

[tigerwoods99]

I think you'd need to add the radius of Jupiter to the 'r' in your equation.

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

 

[rock.freak667]

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

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

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

 

[tigerwoods99]

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

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

I can't get that to work either!

 

[rock.freak667]

I can't get that to work either!

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)

 

[pgardn]

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

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.

 

[tigerwoods99]

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.

Thanks for the explanation!

 

[tigerwoods99]

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)

thanks!

 

[pgardn]

Thanks for the explanation!

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.