Altitude of Satellite Orbit in 4.4 Hours

[Robertoalva]

1. At what altitude will a satellite complete a circular orbit of the Earth in 4.4 hours?

Homework Equations

T^2 = ((4π^2)(r^3))/GM

The Attempt at a Solution

Used the equation and plugged all the information, and solved, but for a weird reason it comes wrong, maybe I should convert the hours to minutes?

 

[SteamKing]

What units did you use for the quantities in your formula?

G = 6.674*10^-11 m^3/kg*s^2

so time may have to be in seconds rather than minutes.

I don't understand why folks think that the units will take care of themselves when making calculations.

 

[Robertoalva]

cuberoot((((15840seconds)^2)(6.67384E-11 N m^2 Kg^-2)(5.974E24Kg))/(4pi^2)) = r

is that correct?

 

[lep11]

cuberoot((((15840seconds)^2)(6.67384E-11 N m^2 Kg^-2)(5.974E24Kg))/(4pi^2)) = r

is that correct?

That formula looks good.

 

[haruspex]

That gives an answer in metres. What distance is that calculating, exactly? The question asks for altitude.

 

[Robertoalva]

I do it, but, the answer that it gives me is totally different from the answer that my practice problem gives

 

[Robertoalva]

the answer that this equation gives me is something like,13632 and the real answer should be 7260 or something approximated

 

[lep11]

the answer that this equation gives me is something like,13632 and the real answer should be 7260 or something approximated

That formula gives you the distance r between the center of the Earth and the satellite. To get the altitude of the satellite you have to subtract the Earth radius from r which gives you the correct answer.

 

[Robertoalva]

thank you!

 

[lep11]

thank you!

You're welcome.

 

[haruspex]

What distance is that calculating, exactly? The question asks for altitude.

the answer that this equation gives me is something like,13632 and the real answer should be 7260 or something approximated

No, I meant what distance does that number represent. I was trying to point out that you were not calculating altitude. Anyway, looks like you have it now.