Re: VRD: Variations in the path of the space shuttle?

Hello Randal & Philip,

I've got a map here in my office showing the path of shuttle flight STS-91, which carried my group's cosmic ray experiment AMS aloft for ten days back in 1998. The map shows orbits 80 through 154 overlaid on a Defense Department world map. You're right, the path flies over a different spot on the earth on every orbit. Maybe a detailed look at how the orbit changes will suggest what is going on. Let's ask, for example, at what longitude does the Shuttle cross the equator (heading north, say) on successive orbits?

Reading off the map (the equator-crossing times are printed in the corner fortunately), we see

orbit (number) time (since launch)    longitude
82		5d 3h 45m 51s     	168.5 E
83              5d 5h 17m 49s	 	145.1 E 
84              5d 6h 49m 47s		121.7 E
85              5d 8h 21m 44s		98.3 E
86              5d 9h 53m 42s 		74.9 E

So how fast is the orbit changing? It's steadily shifting west at about 15 degrees longitude every 60 minutes. Hmm, that adds up to 360 degrees every 24 hours. Does that suggest something?

Indeed, the orbiter - and all spacecraft, satellites, moons, etc. - is moving in a fixed plane in space. The orbit is an ellipse of some sort, possibly a circle, moving in a plane which slices through the Earth at some angle. However, as the shuttle makes these circles, the Earth rotates beneath it. When the shuttle reaches "the same point" in space every hour and a half, the Earth has rotated a bit and a new city finds itself underneath the flight path. So the orbit appears to move around the Earth at exactly the speed at which the Earth rotates.

There's another explanation - or rather the same explanation from a different point of view. If we didn't know that the Earth was rotating, we would have to explain the Shuttle's motion by saying that some sort of strange forces were acting on it. There are names for these "apparent forces": the centrifugal force and the Coriolis force. They are used by people in a rotating reference frame to explain motion in that frame. Someone hovering far away in space sees the Shuttle making perfect circles around a (rotating) Earth. But someone standing on the rotating Earth sees more complicated motions, and postulates new forces to explain them. The centrifugal force appears to push things away from the Earth's axis, while the Coriolis force pushes sideways on anything that moves in a in the north-south direction. Applying these "forces" also should give an accurate description of orbits as viewed from the ground. But that's complicated and rather inelegant, I think.

Sorry I can't find one of these orbit-maps on the Web; I suspect that you can get one from NASA. You can read about Coriolis forces in a classical mechanics textbook (like Marion & Thornton), and a bit at the Treasure Trove of Physics.

Sincerely,

-Ben Monreal