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Satellite orbits and energy 
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#1
Feb1107, 12:27 PM

P: 62

Can't really figure out where to start. Any help would be appreciated.
1. The problem statement, all variables and given/known data A 575 kg satellite is in a circular orbit at an altitude of 550 km above the Earth's surface. Because of air friction, the satellite eventually falls to the Earth's surface, where it hits the ground with a speed of 2.10 km/s. How much energy was transformed to internal energy by means of friction? 2. Relevant equations E = 1/2 G Ms Me / r v = 2 pi r / T E =  G Me Ms / Re + d M = mass R = radius 3. The attempt at a solution ok so 575kg, 550000 m above earths surface, falls at 2100 m/s 5.97 x 10^24 kg is earths mass (Me) 6378100 for earth radius (Re) Ms is mass of satelite G is constant so for Ek = 1/2mv^2 = 0.5*575*2100^2 = 1267875 kJ E =  G Me Ms / Re + d = (6.67 x 10^11)(5.97 x 10^24)(575) / (6378100 + 550000) = 3.305 x 10^10 so do I substract E in orbit by Ek at crash (E  Ek)?? 


#2
Feb1107, 01:45 PM

P: 1,351

Well we know energy in these situations is conserved, except that lost to drag and heating of the satellite.
So the initial energy in orbit equals the final energy at impact plus that lost due to drag. So see if you can set up some equations for the situation based on that. Since it was in orbit, there may be way to simplify the kinetic energy of the satellite. 


#3
Feb1107, 02:44 PM

P: 62

ok, yeah i agree, but im not sure if im using the right equations



#4
Feb1107, 03:10 PM

P: 1,351

Satellite orbits and energy
well at least take a stab, post what is the total energy in orbit, then what you compute for the potential energy plus kinetic at impact. From there we can help.



#5
Feb1107, 03:12 PM

P: 62




#6
Feb1107, 03:19 PM

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PF Gold
P: 2,361

All right let's see if some pointers help
You've got the formula for finding the total energy in orbit and you've found the kinetic energy at impact. You just need to find the potential energy at impact to complete the picture. 


#7
Feb1107, 03:34 PM

P: 62

wow thank you,
so if im understanding correctly E = 1/2 G Ms Me / r (total energy in orbit) Ek = 1/2mv^2 (kinetic on ground) Ep = mgh (potential on ground) and therefore E = Ek + Ep + Elost Elost =  0.5(6.67x10^11)(575)(5.97x10^24) / (6378100 + 550000)  0.5(575)(2100)^2  (575)(9.8)(6378100) = 5.37 x 10^10 Im pretty sure thats not right so i probably screwed up sumwhere in my understanding. 


#8
Feb1107, 04:28 PM

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Sci Advisor
PF Gold
P: 2,361

Instead, go back and look at the equation that gives the potential energy for the Satellite in orbit. Can you see a way of modifying it so that it gives the potential energy at the surface? 


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