Cosmic Calculations and Kinetic Energy

[AClass]

Homework Statement

A satellite with a mass of 5.00 x 10^2kg is in a circular orbit, whose radius is 2(radius of the earth), around earth. Then it is moved to a circular orbit with a radius of 3(radius of the earth).

a) Determine the satellite's gravitational potential energy from the first orbit to the second orbit.
b) Determine the change in gravitational potential energy from the first orbit to the second orbit.
c) Determine the work done in moving the satellite from the first orbit to the second orbit. Apply energy conservation.
d) Calculate the speed it would need in order to maintain its new orbit.
e) Calculate the escape velocity for the satellite if it is on the Earth's surface.

mass of Earth : 5.98 x 10^24 kg
radius of the Earth : 6.38 x 10^6 m

Homework Equations

E_p = -1(G*m_1*m_2)/r
(delta)E_p = -((G*m_1*m_2)/r) - (-((G*m_1*m_2)/r))
v = sqrt((G*m_planet)/r)
v_escape = sqrt((2*G*m_planet)/r)

The Attempt at a Solution

a) Epi=[(-G)(5.98x10^24kg)(5.00x10^2kg)]/2(6.38x10^6m)
Epi=-1.5637x1010J

Epf=[(-G)(5.98x10^24kg)(5.00x10^2kg)]/3(6.38x10^6m)
Epf=-1.042x10^10J

b)

Change in Ep= Epf-Epi
Change in Ep= (-1.042x10^10J)-(-1.5637x1010J)
Change in Ep=5.20x10^9J

c)

This is where I'm having trouble, in this case does Changes in Ep= Work ?
Or is Change in Ep+ Ek = Work ?

d)

v=Sqr[ [(G)(5.98x10^24kg)]/3(6.38x10^6m)]
v=4566m/s

e)

Vesp = Sqr [ [(2G)(5.98x10^24 kg)] / (6.38x10^6m) ]
Vesp =111.84.48 m/s

Could some verify my solutions, and shed some light on my problems in c)

 

[hy23]

work is simply the change in potential energy, so final PE - initial PE, which should work out to be a positive value

 

[cupid.callin]

hy23 is right ...

and more precisely ...

W(internel conservative forces) = -(Uf - Ui) = Ui - Uf

dont think that work can only be positive ... negative work do exist!

 

[hy23]

yes negative work do exist, I meant in his case, since he's going from a very negative potential energy to a not so negative PE, positive W is done

 

[rwisz]

and d)?


Hello, great job on your attempt at the solution! Your calculations for parts a, b, d, and e are all correct. For part c, you are correct in thinking that the change in gravitational potential energy is equal to the work done on the satellite. This is because energy is conserved in this system, meaning that the change in potential energy is equal to the work done on the satellite. Therefore, the work done in moving the satellite from the first orbit to the second orbit would be equal to the change in gravitational potential energy, which you have already calculated to be 5.20x10^9J. Keep up the good work!