What is the Kinetic Energy Formula for a Satellite Orbiting Earth?

[skiing4free]

Homework Statement

What is the Kinetic energy of a 180-kg satellite which circles the Earth (radius=6.4x10^6m, mass=6.0x10^24kg) with a period of 8.0 h?
a)2.2x10^9J
b)2.0x10^9J
c)1.8x10^9J
d)2.4x10^9J
e)3.6x10^9J

Homework Equations

Ep= GM1M2/r
Ek=.5Mv^2
Ac=(4\pi^2r)/T^2
v=-\omega^2r
Ep=Ek

The Attempt at a Solution

The radius that the satellite is orbiting is not given only Earth's radius, i tried to use ratios but this cannot work as the satellite is moving much faster than earth. Then i tried a guess and check method with the given options trying to cross check the speed. Eventually i got an answer of 1.8x10^9J which is correct. There must be a better method for calculating the radius of the satellite?

 

[lanedance]

not sure about your equations but hopefully this should help

Think about how the period & angular velocity are related

Then think about the force at work, ie the acceleration due to gravity causes the circular motion... can you equate something here to work toward a radius...

 

[skiing4free]

its sounds like an easy question and probably is but i keep getting confused with it, in answer to lanedance question, centripetal acceleration=angular velocity squared*radius

\omega=\Delta\theta/\DeltaT

maybe its just me but i keep going round in circles...
(terrible pun i know)

 

[lanedance]

so you have the angular velocity as you know it does 1 full revolution in 8hrs, centripetal accelaration equation looks good...

the key is the centripetal acceleration is the acceleration caused by gravity, so equate both terms and see what unknowns are left...

 

[selter01]

they told you time it takes for 1 rev, so if you know the distance [ circumference] and the time, you can find V, so just 1/2 mv^2

 

[lanedance]

the orbit radius is not given in the question

 

[selter01]

hm, then I guess use Gm(p)m(s)/r^2 = m(s)v^2/r
you know G, the gravitational constant, you know the mass of the Earth and satelite..
theen, since you don't know v OR r, you can use v = d/t, so
Gmp/r = (r/t)^2, solve for r. once you know r, find v, then KE.

 

[skiing4free]

OK i get where you're coming from, pity is that these multiple choice questions have to be answered in 1.5mins each or else u don't finish the paper in time, and this was an easy question from the extended paper grrrrr