Calculate Orbital Velocity for 5130kg Satellite at Jupiter Orbit

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In summary, the centripetal force required to keep the satellite in orbit around Jupiter is mv^2/r. 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?
  • #1
tigerwoods99
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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!
 
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  • #2
I think you'd need to add the radius of Jupiter to the 'r' in your equation.
 
  • #3
rock.freak667 said:
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.
 
  • #4
tigerwoods99 said:
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

[tex]v=\sqrt{2 \frac{GM}{r}}=\sqrt{2gr}[/tex]
 
  • #5
rock.freak667 said:
your formula is missing a '2' in it. If I recall correctly it should be

[tex]v=\sqrt{2 \frac{GM}{r}}=\sqrt{2gr}[/tex]

I can't get that to work either!
 
  • #6
tigerwoods99 said:
I can't get that to work either!

Sorry sorry, I remember it now.

[tex]\frac{mv^2}{r}=\frac{GMm}{r^2} \Rightarrow v = \sqrt{\frac{GM}{r}}[/tex]


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
tigerwoods99 said:
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.
 
  • #8
pgardn said:
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!
 
  • #9
rock.freak667 said:
sorry sorry, i remember it now.

[tex]\frac{mv^2}{r}=\frac{gmm}{r^2} \rightarrow v = \sqrt{\frac{gm}{r}}[/tex]


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!
 
  • #10
tigerwoods99 said:
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.
 

1. How do you calculate orbital velocity for a satellite at Jupiter orbit?

To calculate the orbital velocity for a satellite at Jupiter orbit, you will need to use the following equation:
V = √(GM/r)
Where V is the orbital velocity, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2), M is the mass of Jupiter (1.898 × 10^27 kg), and r is the distance between the satellite and the center of Jupiter. This equation is known as the orbital velocity formula and is used to calculate the speed at which an object must orbit around a larger body, such as a planet.

2. What is the mass of a satellite at Jupiter orbit for calculating orbital velocity?

The mass of the satellite at Jupiter orbit is an important factor in calculating its orbital velocity. For the given question, the mass of the satellite is 5130kg. This value is necessary to plug into the orbital velocity formula alongside the mass of Jupiter and the distance between the satellite and the planet's center.

3. What is the distance between a satellite and the center of Jupiter for calculating orbital velocity?

The distance between a satellite and the center of Jupiter is a crucial factor in determining its orbital velocity. For this specific scenario, the distance between the satellite and Jupiter's center is not provided. Therefore, the distance value must be obtained or determined through other means, such as using the satellite's orbital period and the law of gravitation.

4. How does the mass of a planet affect the orbital velocity of a satellite?

The mass of a planet has a direct impact on the orbital velocity of a satellite. As stated in the orbital velocity formula, the mass of the planet is one of the factors used to calculate the orbital speed. The greater the mass of the planet, the stronger its gravitational pull, and the faster the satellite must orbit to maintain its position.

5. Can the orbital velocity of a satellite at Jupiter orbit be greater than the speed of light?

No, the orbital velocity of a satellite at Jupiter orbit cannot exceed the speed of light. According to the laws of physics, the speed of light, which is approximately 299,792,458 meters per second, is the ultimate speed limit in the universe. Therefore, no object, including a satellite, can travel faster than the speed of light.

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