What is the formula for the radius of a satellite's orbit?

[jacob117]

Homework Statement

A 129 kg satellite experiences a gravitational force by the Earth of 790 N. What is the radius of the satellite's orbit?

Homework Equations

F=GM/R^2

The Attempt at a Solution

 

[RoyalCat]

For an object of mass m under the effect of Earth's gravitational pull, the force pulling it towards the center of the Earth is of a magnitude:

|F_gravity| = m((GM_earth)/r²)
where r is the distance of the object from the center of the earth.

Another formula you'll find helpful if there are any follow-up questions is the following:
An object in simple circular motion around a fixed point, is being pulled towards the center of its orbit by a force of magnitude:
|F_centripetal| = mv²/r
Where v is the tangential speed of the object, and r is the radius of its circular orbit.

Please make an attempt at the solution before asking us to help.

 

[jacob117]

r^2=G(m1m2)/F
r^2=6.67x10^-11(129x5.98x10^24)/790
r^2=6.67x10^-11(7.7142x10^26)/790
r^2=6.67x10^-11(9.764810127x10^23)
r^2=6.513128355x10^13
r=8070395.501

thats the answer i got but it is still wrong...i need some serious help...

 

[RoyalCat]

Final answer is 8068.29466 kilometers, according to Google calculator, so you're in the ball-park. Rounding errors could account for the difference in our answers.
Why do think you're wrong?

 

[jacob117]

so did i use the proper formula?

 

[RoyalCat]

Yes, I think so. But can you explain to me why that was the proper formula?

 

[jacob117]

hey guys i need some more opinions on this problem...and i just took a guess at the formula...

 

[ideasrule]

hey guys i need some more opinions on this problem...and i just took a guess at the formula...

Why do you need more opinions? You got the right answer.

As for why the formula is right, F=Gm1m2/r^2 is Newton's law of gravitation, relating gravitational force to mass and distance. You know F; that was given in the question. You know m1 and m2; one is the mass of the Earth and the other is the astronaut's mass. G is a constant. With one equation and one unknown (r), you can solve for r, which is what the question asks for.

 

[Redbelly98]

hey guys i need some more opinions on this problem...and i just took a guess at the formula...

Not to sound nitpicky, but RoyalCat gave you the correct formula in Post #2. Your formula in Post #1 was wrong.