That's a completely different scenario. Satellites in decaying orbits are descending due to atmospheric drag. Atmospheric drag is difficult to predict because it depends on the precise shape of the satellite, the precise orientation, and atmospheric conditions at each moment.
If you're dropping an interplanetary asteroid on an enemy, it won't be in a slowly decaying orbit. It'll spend a few seconds within the atmosphere, which won't mess up predictions that much.
It occurs to me that we just had a great example of the ability to predict where big rocks will be in space long in advance. People were able to predict that the Moon's shadow would cross from Oregon to South Carolina decades ago, and of course the predictions were spot on.
You underestimate the difficulty. For example the asteroid could break up, which would move the trajectory. If the asteroid is not round it will tumble and shift. Uneven heating would cause a "jet" of hot air to act like a rocket and move the asteroid.
Don't forget that it's very unlikely you will be able to guide an asteroid perpendicular to the earth (which would give you the most accuracy, and the most velocity, which also helps with accuracy). Most of the asteroids obit more or less in the same plane as the earth, so you will have to settle for a more shallow impact, which will magnify atmospheric effects.
> example ... moon
We have had thousands of years to precisely record the orbits of the moon and earth [sun]. That is the only reason we are able to predict it. And despite that, past a few hundred years accuracy goes down, and past 1 thousand or so it's mostly impossible to predict eclipses.
And that's for bodies we have very accurate data on, and who have no atmospheric drag.
The inaccuracy for eclipses is because we can't predict how fast the earth will turn (to an accuracy of a ppm) more than a few months out, and because of tidal effects changing the orbit of the moon.
If you're dropping an interplanetary asteroid on an enemy, it won't be in a slowly decaying orbit. It'll spend a few seconds within the atmosphere, which won't mess up predictions that much.
It occurs to me that we just had a great example of the ability to predict where big rocks will be in space long in advance. People were able to predict that the Moon's shadow would cross from Oregon to South Carolina decades ago, and of course the predictions were spot on.