THE SLOWER THE FASTER

Now for a more pleasant aspect of satellites. Kosmos 1402 was intended to orbit at 150 miles above the earth; as we go to press, it has sunk to some 135 miles, entering the outermost layers of the atmosphere (there is no sharp boundary, only a region where the density begins to rise from zero). The atmosphere brakes the satellite, reducing its speed and turning its energy of motion into heat (which means imparting high velocities to air molecules as they bounce off the metal). As a result, the satellite sinks deeper, into denser parts of the atmosphere, is braked still further, its speed increases (yes, increases), until it goes so fast that it turns red-hot. A few days after you get this issue, you will know whether all of Kosmos 1402 burned up, or whether its 4-ton mass and other factors allowed larger chunks to survive to hit the earth's surface.

But there seems to be something wrong here. The atmosphere brakes the satellite so that it goes faster?

Yes: a simple case of the result overpowering the cause.

A satellite is in stable orbit when two opposing forces are in exact balance: the centripetal force ("center-seeking," i.e. the earth's gravitational attraction), and the centrifugal force ("center-fleeing," the one that seeks to throw the satellite out of the curve as its inertia wants it to continue along a straight line). When so balanced, the satellite will move round a circle with constant radius (gourmets and snobs will correct that to a conic section with constant semi-latus rectum).

When now an external force such as atmospheric friction reduces the velocity of the satellite, the centrifugal force will diminish (for it is proportional to the square of velocity), but the gravitational attraction will remain unchanged. The satellite will therefore be pulled in closer to the earth until the balance between the two is restored.

But as any schoolboy who has twirled a chestnut at the end of a string knows, the shorter the string, the faster the chestnut; similarly, the smaller the height of the satellite, the greater its velocity. Thus there is no paradox: the satellite starts by being braked and ends up by going faster.

[More: Isaac Newton, Philosophiae Naturalis Principia, London, 1687.]