# Satellite in circular orbit with friction

1. Apr 19, 2016

### reminiscent

1. The problem statement, all variables and given/known data
A satellite with mass 848 kg is in a circular orbit with an orbital speed of 9640 m/s around the earth. What is the new orbital speed after friction from the earth’s upper atmosphere has done -7.50·109 J of work on the satellite? Does the speed increase or decrease?

2. Relevant equations
K1+U1+Wfriction=K2+U2

3. The attempt at a solution
I have a hard time setting this problem up. Will gravitational PE stay the same, so K1=K2?

2. Apr 19, 2016

### drvrm

suppose you are rotating a stone tied to a string at some velocity/speed v.
some air friction due to wind is doing -ve work on your stone . what will happen ?
try to set up a diagram .... show frictional force against the displacement and try to visualize ....
if the speed decreases what will happen to radius of rotation path?

3. Apr 19, 2016

### reminiscent

Will it decrease as well? But we don't know how far away the satellite is from the Earth.

4. Apr 19, 2016

### drvrm

one can assume a value of radius say r and see what happens .

some body said
.. A satellite orbiting in motion will speed up as its height (or distance from the earth) is decreasing and slow down as its height (or distance from the earth) is increasing .
is it true ..check

5. Apr 19, 2016

### reminiscent

I see. But I don't understand still because there are 2 unknown variables to find then.

6. Apr 19, 2016

### drvrm

first you may find the the argument on the basis of energy whether its speed decreases/increases.

what are the other variable to find.

7. Apr 19, 2016

### reminiscent

I am getting confused because there is a distance that needs to be accounted for - the one from the Earth to the satellite. When you say "one can assume a value of radius say r and see what happens," do you mean keep R the same when calculating the change in gravitational potential energy? But wouldn't that make gravitational PE = 0?

8. Apr 19, 2016

### haruspex

No, drvrm means assume a stable orbit at a new r. What is the relationship between orbital radius and orbital speed?

9. Apr 19, 2016

### reminiscent

Is it v=√GM/r?

10. Apr 19, 2016

### reminiscent

For circular orbit though.

11. Apr 19, 2016

### reminiscent

Do I solve for R by using v=√GM/r, using the initial velocity given?

12. Apr 19, 2016

### haruspex

No,both v and r change. The new v and r are related by that equation, as were the original v and r. In each case, you can express the total energy in terms of the v and r. So you know the original total energy and the energy lost. That gives you a second equation relating the new v and r to the new energy. Solve the pair of simultaneous equations.

13. Apr 20, 2016

### drvrm

i think i will again quote my post number 3 in which i asked you to rotate a stone in circular orbit by tying a string- go back to doing that little experiment.
what we do -we pull on the string and the stone rotates with a radius say r1. suppose one wants to decrease the radius a further pull on the stone is required - the stone moves with a constant speed during circular path. if one releases /reduces the pull the stone takes a path of larger radius.
In satellite motion the pull is given by earths gravitational field -which is smaller as radius increases- and larger as radius decreases-
think about the force required for circular motion- it has a special name -and earths gravitational pull provides that.
another feeling with stone the speed of rotation increases as the radius is shortened and decreases as the radius is longer.
that is being done on the satellite by the gravitational attraction- working in the above manner.

now i think we are in a better situation to judge as to what will happen if the frictional force has reduced the kinetic energy of satellite-
so the speed must have reduced and now the satellite can rotate in a larger orbit -having increased radius and that will be provided by the gravitational pull -which is reduced by the distance/radius increase.

so the new radius is different or larger -and try to calculate the change in the radius .
think how one can do the numbers!