What is the Orbital Speed of a Satellite in a Circular Orbit?

In summary, the conversation involves two questions relating to satellites and their orbits. The first question asks for the orbital speed of a satellite with a given radius around an unknown planet. The second question involves finding the period of the moon's orbit around the Earth using Kepler's 3rd law.
  • #1
Whotto
16
0

Homework Statement



#1
A satellite is in a circular orbit around an unknown planet/ The satellite has a speed of 1.70 x 104 m/s, and the radius of the orbit is 5.25 x 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60 x 10^6 m. What is the orbital speed of the second satellite.

#2
The moon orbits the Earth at a distance of 3.85 x 108 m. Assume that this distance is between the centers of the Earth and the moon and that the mass of the Earth is 5.98 x 1024 kg. Find the period for the moon's motion around the Earth. Express the answer in days and compare it to the length of a month.

Homework Equations



I have no clue. Maybe this?

v = sqrt(GM/r)

F = G (m1m2/r2)

a = v2 / r

a = 4pi2r / T2

The Attempt at a Solution



# 1: Well, I know there is something that the two satellites could be compared to, but I can't figure what. I tried a futile stab at the question by using v12 / r = v22 / r but that didn't give me the right answer.

The answer at the back of the book is 1.3 x 104 m/s.

# 2: I don't even know how to get started on this question...I know I have radius and mass of the Earth, and I need to find the period.

Any help towards these questions would be greatly appreciated!
 
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  • #2
[tex]v = \frac{2{\pi}r}{T}[/tex]

Should help you in the second part if you equate it to another equation with known variables.
 
  • #3
Start with Kepler's 3rd law.
 
  • #4
Thanks! I got #2 with the formula T = ( 2 pi r3/2 ) / sqrt(GMe).


But I still don't get #1. Can I get some more pointers?
 

1. What is a satellite in a circular orbit?

A satellite in a circular orbit is an object that is revolving around a larger body, such as a planet, in a circular path. In this type of orbit, the satellite maintains a constant distance from the body it is orbiting.

2. How do satellites stay in circular orbits?

Satellites stay in circular orbits due to the balance between the gravitational pull of the larger body they are orbiting and their own forward motion. This balance is maintained by the speed and altitude of the satellite.

3. What are the advantages of circular orbits for satellites?

Circular orbits are advantageous for satellites because they are stable and require less fuel for maintenance. They also provide constant coverage of a specific area on the surface of the larger body.

4. How do scientists calculate the speed and altitude of satellites in circular orbits?

Scientists use a formula called the vis-viva equation to calculate the speed and altitude of satellites in circular orbits. This equation takes into account the mass of the larger body, the gravitational constant, and the distance between the satellite and the larger body.

5. Can satellites in circular orbits change their altitude?

Yes, satellites in circular orbits can change their altitude by using their onboard thrusters to apply a force in the direction of the desired change. This can be done to adjust the satellite's orbit or to deorbit the satellite when it reaches the end of its lifespan.

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