Why is the velocity of a satellite in a circular orbit twice the orbital radius?

In summary, the conversation discusses the velocity of a satellite in a circular orbit around Earth at a distance of one Earth radius above the surface. The formula used is v = (GMearth/r)^.5, but there is confusion about doubling the radius and the use of the correct numbers. The final calculated velocity is approximately 5000m/s.
  • #1
Maiia
79
0

Homework Statement


A satellite is in a circular orbit about the Earth at a distance of one Earth radius above the surface. What is the velocity of the satellite?

The Attempt at a Solution


I assumed the orbital radius was twice the radius of the Earth so
GMearth/r= velocity
but that leaves me with a very small velocity...
 
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  • #2
Can you show your answer and your work? If you do have a mistake, I can't find it without seeing both.
 
  • #3
well since I assumed orbital radius was 2Eradius, then
(GMearth/r)^.5= v
I plugged in (6.67*10^-11(5.98*10^24)/6.37*10^6)6.5= 7913.048m/s
 
  • #4
Maiia said:
well since I assumed orbital radius was 2Eradius, then
(GMearth/r)^.5= v
I plugged in (6.67*10^-11(5.98*10^24)/6.37*10^6)6.5= 7913.048m/s

Why are you multiplying by 6.5? Also, you never doubled the radius when you plugged in the numbers. According the the formula you give, which is correct, the velocity should be:

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

Plugging in the numbers you give, I get an answer around 5000m/s.
 
  • #5
why do you double the radius?
 
  • #6
Maiia said:
why do you double the radius?

You said it yourself before. The orbital radius is twice the radius of Earth. In your formula, you used the radius of Earth, not double the radius of Earth.
 

Related to Why is the velocity of a satellite in a circular orbit twice the orbital radius?

1. What is the velocity of a satellite in orbit?

The velocity of a satellite in orbit depends on its altitude and the mass of the object it is orbiting. Generally, the closer a satellite is to the Earth, the faster it will travel. Satellites in low Earth orbit have an average velocity of about 17,500 miles per hour (28,000 kilometers per hour).

2. How is the velocity of a satellite calculated?

The velocity of a satellite can be calculated using the formula v = √(GM/r), where v is the velocity, G is the gravitational constant, M is the mass of the object being orbited, and r is the distance between the satellite and the object. This formula is known as Kepler's third law of planetary motion.

3. Can the velocity of a satellite change?

Yes, the velocity of a satellite can change due to factors such as atmospheric drag, gravitational pull from other objects, or propulsion from onboard engines. In order to maintain a stable orbit, the velocity of a satellite must be constantly adjusted.

4. What happens to the velocity of a satellite as it gets closer to Earth?

As a satellite gets closer to the Earth, its velocity will increase due to the stronger gravitational pull. This is because the object being orbited has a greater influence on the satellite's motion at closer distances.

5. How does the velocity of a satellite affect its orbit?

The velocity of a satellite is directly related to its orbit. A higher velocity will result in a larger orbit, while a lower velocity will result in a smaller orbit. This is why satellites in low Earth orbit have a higher velocity than those in geostationary orbit.

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