Finding the distance a satellite travels. Help

[astru025]

Finding the distance a satellite travels. Help!

Homework Statement

A satellite orbits at a distance from the Earth's center of about 6.20 Earth radii and takes 21.7 hours to go around once. What distance (in meters) does the satellite travel in one day?

Homework Equations

Velocity will tell me m/s so I could find that and then translate it into just meters an get the distance the satellite travels.
V^2=G(Me/r)

The Attempt at a Solution

After using the equation above I came up with.
V^2= G (6.67E-11) * (Me (5.98E24) / r (6.2 *6370). I got 100498.75 m/s. I converted 21.7 hours to seconds and then multiplied it by 100498.75 m/s to come up with meters but my answer was incorrect. What am I doing wrong?

 

[Delphi51]

I used your formula to find velocity and got an answer more than ten times smaller! We could sort out our differences if you want to show the details of your calculation.

You can also find the number of circumferences traveled by using the 21.7 hours for one revolution and upping it proportionally to get the number of revolutions in 24 hours. Just a little more than one circumference, which is 2*pi*R. Don't forget to use the radius of the orbit, not the radius of the Earth in whichever method you choose.

 

[astru025]

Okay for velocity I did v^2= G* (Me/r)
For G I used 6.67E-11. For Me (Earth's mass) I used 5.98E24. For r I used 6.2 times the Earth radius which is 6370 km. and then I calculated that and took the square root of my answer to get V. Where did I mess up?

 

[Delphi51]

So you have v² = GM/R = 6.67E-11*5.93E24/(6.2*6.37E6) = 1 E 7
That makes v about 3 000 m/s, I think.

 

[astru025]

Yes I got 3162.27. Must have miscalculated somewhere. Thank you very much.

 

[astru025]

I did 6370 instead of 6.37 E6 . Thanks p!

 

[astru025]

So for the total distance traveled in one day I got 273220992 and that is the correct answer. Thank you very much.

 

[Delphi51]

Congrats!

 

[skeptic2]

A satellite orbits at a distance from the Earth's center of about 6.20 Earth radii and takes 21.7 hours to go around once.

What does "go around once" mean? Does it mean go around until it reaches the same point relative to the Earth or does it mean to go around until it reaches the same point relative to the sun?

 

[Delphi51]

Kind of a tough one. Go around once means going one circumference. Relative to the earth, without taking the rotation of the Earth into account. It goes one circumference in 21.7 hrs, so 24/21.7 circumferences in 24 hours.

 

[skeptic2]

Relative to the earth, without taking the rotation of the Earth into account.

This is the same as saying relative to the sun.

The period of the moon on the other hand is typically given relative to the Earth (29.5 days) as opposed to the period relative to the sun (27.3 days).

 

[gneill]

Usually when discussing the period of an orbiting object as calculated via Newtonian gravitation the period being referred to is the sidereal period. That is, the period with respect to the remote background stars. This is a good approximation of the inertial reference frame associated with Newton's absolute space.

The Sun's position against such a background moves perceptibly over the course of a day, and a period measured using it as a position marker would differ from the sidereal period you calculate using Newton's laws.