Physics satellite velocity and period

[astru025]

Homework Statement

a. What is the tangential velocity of a satellite in a circular orbit 300km above the surface of the Earth?

Homework Equations

Velocity of a satellite= v^2= G (Me/r)

The Attempt at a Solution

V^2= 6.67E-11 (5.98E24/6.37E6)
I calculated this and my answer proved incorrect. How do I incorporate the "300 km above Earth's surface" into this equation?.

 

[Doc Al]

How do I incorporate the "300 km above Earth's surface" into this equation?.

Use that to calculate the radius of the orbit, which will be "r".

 

[astru025]

I use 300km to calculate the radius of the orbit. What is the equation for the radius?

 

[Doc Al]

I use 300km to calculate the radius of the orbit. What is the equation for the radius?

In your calculation, you set r = radius of the earth. But that's not correct; r should be the radius of the orbit, which is bigger than the radius of the Earth (by the given amount).

First calculate the radius of the orbit, then use it in your formula to find the speed.

 

[astru025]

Okay thank you. Is there a special equation to find the radius of the orbit?

 

[Doc Al]

Is there a special equation to find the radius of the orbit?

Just add the altitude of the orbit, which was given, to the radius of the earth.

 

[astru025]

Okay so now I have : v^2= G (6.67E-11) x ((Me (5.98E24) / (r + 300 km. (6670 km))
Is this correct? So I got 244540.39.

 

[astru025]

That answer was incorrect. What am I doing wrong?

 

[SteamKing]

Did you check your units? Always check your units.

 

[Doc Al]

Okay so now I have : v^2= G (6.67E-11) x ((Me (5.98E24) / (r + 300 km. (6670 km))
Is this correct? So I got 244540.39.

I don't understand how you got that answer. Did you make sure to put the radius in meters, not km?

 

[nasu]

This must be it. You are off by a factor of about √1000. The radius should be in meters.

 

[astru025]

Okay I finally came up with 1768897.96 m/s

 

[astru025]

Okay now I came up with 7733.046. This must be correct. Miscalculation in my previous try.

 

[astru025]

This proved correct! Thanks so much. Always need to check my units :)