# Kinetic Energy Of a Satellite

#### skiing4free

1. The problem statement, all variables and given/known data
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

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

3. The attempt at a solution
The radius that the satellite is orbiting is not given only earths 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

Homework Helper
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

$$\omega$$=$$\Delta$$$$\theta$$/$$\Delta$$T

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

Last edited:

#### lanedance

Homework Helper
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

Homework Helper
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

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