Calculating Geosynchronous Satellite Orbit and Velocity

[runningirl]

Homework Statement

Determine the radial orbit and velocity for a geosynchronous satellite in orbit around the earth. Remember that geosynchronous satellites are located directly above the equator and they remain above a fixed point on the equator as the Earth rotates

Homework Equations

The Attempt at a Solution

what does radial orbit mean?!
i guess i'd have to find the distance between Earth and the satellite which is 6.38(10^6)+a?
then i'd do F=GMm/r^2 to find F which i could then use for F=mv^2/r find velocity.

 

[LeonhardEuler]

Radial orbit probably just means circular orbit.

then i'd do F=GMm/r^2 to find F which i could then use for F=mv^2/r find velocity.

You are right to bring in these two equations, although it might be more useful to express the second one in terms of radial velocity, omega. I don't know what this means, by the way:
"i guess i'd have to find the distance between Earth and the satellite which is 6.38(10^6)+a?"

But you need to bring in the condition that the orbit is geosynchronous. What does that say about the radial velocity?

 

[gneill]

Probably just a typo for "orbital radius"

 

[runningirl]

Radial orbit probably just means circular orbit.

You are right to bring in these two equations, although it might be more useful to express the second one in terms of radial velocity, omega. I don't know what this means, by the way:
"i guess i'd have to find the distance between Earth and the satellite which is 6.38(10^6)+a?"

But you need to bring in the condition that the orbit is geosynchronous. What does that say about the radial velocity?

how would i find radial velocity??is it the same as the earth's?
because it says nothing about radial velocity on the problem.

 

[gneill]

how would i find radial velocity??is it the same as the earth's?
because it says nothing about radial velocity on the problem.

You are looking for the orbital radius and the angular velocity of the radius vector.

The radial velocity (the rate by which the *length* of the radius vector changes) of a circular orbit is zero.

 

[LeonhardEuler]

Thanks gneill, I meant angular velocity, omega.

how would i find radial velocity??is it the same as the earth's?
because it says nothing about radial velocity on the problem

You know that the satellite stays over the same point on the Earth's surface. What would the angular velocity have to be relative to the Earth to accomplish that?

 

[runningirl]

so, i took F=GMm/r^2 and F=mv^2/r and set them equal to each other to find r.
then i found the velocity using the T=2pi(r)/v equation (since T=86400 s).
is this method correct?!

 

[D H]

so, i took F=GMm/r^2 and F=mv^2/r and set them equal to each other to find r.
then i found the velocity using the T=2pi(r)/v equation (since T=86400 s).
is this method correct?!

Very close. You should be using the sidereal day as opposed to the mean solar day (86400 seconds) as the period.

 

[runningirl]

Very close. You should be using the sidereal day as opposed to the mean solar day (86400 seconds) as the period.

okay, i got something REALLY big.
r=6.67*10^-11(5.97*10^24)/v^2
86400=2*pi*(6.67*10^-11(5.97*10^24)/v^2)/v
v=3070.8 m/s
V=2pi*r/T
3070.8=2pi*r/86400
r=42226910.18m
circular orbit=2pi*r
=265319501.6m?

 

[D H]

Hidden somewhere amidst your answer is the correct answer, or something close to it.

Explain each step.

 

[runningirl]

i set F=GMm/r^2 and F=mv/r^2 equal to one another and found that r=GM/v^2...
i then took that r (r=6.67*10^-11(5.97*10^24)/v^2) and did T=2pi*r/V.
86400=2*pi*(6.67*10^-11(5.97*10^24)/v^2)/v
v=3070.8 m/s

V=2pi*r/T (i did this to find the radius)
3070.8=2pi*r/86400
r=42226910.18m

circular orbit=2pi*r
=265319501.6m?

 

[D H]

What question are you trying to answer with the last bit (the part starting with "circular orbit=2pi*r")?

 

[runningirl]

isn't circular orbit= 2*pi*r?

 

[D H]

The circumference is 2*pi*r. Were you ever asked to find the circumference?

 

[runningirl]

well then... how do i find the circular orbit?

 

[Redbelly98]

They probably just want the radius, r, also called the orbital radius. Calculating the circumference is not necessary.