Angular Velocity of a satellite

In summary, to determine the satellite's altitude above the Earth's surface, the equation used is r = GM/v^2, where G is the universal gravitational constant, m is the mass of the satellite, M is the mass of Earth, and v is the velocity. The result is then converted to the desired unit, which in this case is km. The incorrect answer obtained by the student was due to not using standard units in the equation.
  • #1
notsam
50
0

Homework Statement

A satellite moves in a circular orbit around
the Earth at a speed of 6.6 km/s.
Determine the satellite’s altitude above
the surface of the Earth. Assume the
Earth is a homogeneous sphere of radius
6370 km and mass 5.98 × 1024 kg. The
value of the universal gravitational constant
is 6.67259 × 10−11 N · m2/kg2.
Answer in units of km.



Homework Equations

m= mass of the satalite, M= mass of eart, G=gravitational constant, v= veolocity, r= radius of the entire orbit, and re= radius of the earth

The Attempt at a Solution

Ok so I start with GmM/r^2=mv^2/r, and then I simplify to r= GM/v^2, solving for r I get 916025899 km I then subtract the radius of the Earth "re" from it to get, 9160252629 km. This however is not the correct awnser. I can't figure what I am doing wrong I have already converted all of my units to km. I would REALLY REALLY appreciate step by step instructions on what I am doing wrong.
 
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  • #2
notsam said:
Ok so I start with GmM/r^2=mv^2/r, and then I simplify to r= GM/v^2, solving for r I get 916025899 km
Did you use correct units? That equation assumes standard units: v in m/s, r in meters, etc.

Use standard units, then convert to whatever you want at the end.
 
  • #3
You're a genius, I could'nt figure out what I was doing wrong thank you.
 

Related to Angular Velocity of a satellite

1. What is Angular Velocity of a satellite?

Angular Velocity of a satellite is the rate at which the satellite rotates around its axis. It is measured in radians per second and is an important factor in determining the satellite's orbit and trajectory.

2. How is Angular Velocity of a satellite calculated?

Angular Velocity of a satellite can be calculated by dividing the angle of rotation by the time taken for that rotation to occur. This can be expressed as ω = Δθ/Δt, where ω is the angular velocity, Δθ is the change in angle, and Δt is the time taken.

3. What factors affect the Angular Velocity of a satellite?

The Angular Velocity of a satellite is affected by its distance from the center of rotation, its mass, and the amount of force acting on it. Other factors such as the shape and composition of the satellite can also have an impact.

4. How does the Angular Velocity of a satellite impact its orbit?

The Angular Velocity of a satellite determines the speed at which it orbits around the body it is rotating around. A higher angular velocity means a faster orbit, while a lower angular velocity results in a slower orbit.

5. Can the Angular Velocity of a satellite change?

Yes, the Angular Velocity of a satellite can change due to various factors such as changes in gravitational force, collisions with other objects, and adjustments made by control systems on the satellite. These changes can affect the satellite's orbit and trajectory.

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