Find the Ek of a satilite in orbit

[Format]

How do you find the Ek of a satilite in orbit with only its mass and acceleration due to gravity?

I did something like..

Fc = Fg
mv²/r = mg <-- g = the acceleration due to gravity

but then i don't have a radius...

How do i solve this?

 

[Justin Lazear]

Edit: After reading more carefully, you'll need to equate Newton's expression for gravitational force with the given mg force to determine the radius.

--J

 

[Format]

Mind elaborating on that?

 

[Format]

F = Gmm/r² ?

 

[Justin Lazear]

Yup.

--J

blah blah blah post too short my--

 

[Format]

I keep getting Ek = 7.44x10^10 but its 2.99x10^9

?

 

[quasar987]

Did you do this?

a = \frac{v^2}{R} \Rightarrow v^2 = aR

R = ?

F = ma \Rightarrow \frac{GM_{earth}m}{R^2} = ma \Rightarrow R = \sqrt{\frac{GM_{earth}}{a}}

\Rightarrow E_k = \frac{1}{2}ma\sqrt{\frac{GM_{earth}}{a}}

 

[Format]

Ah now i get it! Thanks for actually showing the steps it really helps lol.

 

[quasar987]

No problem. I guess it's okay for me to show you the steps after you've tried to do the problem on your own. But please make sure you understand each of these steps perfectly, otherwise you're not getting out smarter out of this.