So here's an interesting thought experiment. Does the rotation rate of the Earth about its spin axis slow down when an artificial satellite is launched into orbit around the planet?
I would argue yes because in the post-launch state, the new system's moment of inertia is greater and so to conserve energy, Earth must rotate at a slower rate.
launching, not maintaining it's orbit.
I think I did not get the point across. My argument is that by putting a satellite in orbit around the Earth, the Earth's rotation rate (about it's axis) will slow down very slightly because the moment of inertia of the entire system will be slightly larger. As an analogy, imagine an ice skater who is spinning in place - when she pulls her arms in she spins faster and when she lets her arms out, she spins more slowly.
Well, your argument is based on the Law of Conservation of Angular Momentum, isn't it?
Note that angular momentum is conserved if no "EXTERNAL TORQUE IS APPLIED ON THE SYSTEM". Thus, this quantity is only conserved under ideal conditions.
In this case, one could argue that the satellite has "left" the system in which the earth rotates.
You could also argue that the system we are talking about is the entire universe as the earth isn't a closed system. So, even if the moment of inertia increases, one could say that the angular momentum is conserved in the universe.
You could also consider isolating the satellite as a unique system. If you imagine the satellite when it was on earth, it was rotating at the same speed as the earth. So, once it got into orbit outside the earth, in order to conserve angular momentum, its rate of revolution slowed down as compared to the rate of rotation of the earth.
And even if your argument is correct, won't the slow down be highly negligible owing to the negligible mass of the satellite as compared to the earth?
I'm still a bit unsure of this issue as you could have a valid argument for both sides.
