Well, I was going to anticipate that point, but I was too lazy to at the time.
If two equivalent asteroids were held above earth and mars and dropped form the same height, it would be as you said.
But the asteroid and the planet already have some very high relative speed. Their orbits are (we can assume) not common. So, while the gravity of the planet will have some definite effect, I would estimate it to minimally alter the existing speed difference as the two bodies come together. I suppose some fairly simple calculations could settle how much additional delta V the gravity of earth vs mars gives the asteroid (assuming all other trajectory parameters are the same) that is already closing at some tens of km/sec.
This is my physical intuition talking here. No doubt the respective gravities of earth and mars will "suck" the asteroid in and add additional speed. It's just the magnitude of the additional delta V vs the already existing speed that I suspect is not that significant.
I'd love to be proven wrong here if someone was willing to do the calculations?
I also suspect that the earths atmosphere, for a good sized asteroid moving at 17 to 20 km/sec would not be "noticed" much by the asteroid in the 1 to 2 seconds it took to pass through the dense portion of the atmosphere.
Thanks for pointing out my SMALL oversight. I did a rough calculation which suggests that from a distance of 1 mile above earth and mars respectively the addition velocities would be about 392 mph and 218 mph. As you say small beer compared to the original velocity of the asteroid . I estimate , using 1/2 m V^2 that the kinetic energy in both cases would be increased byabout 8K M and 2.4K M respectively.
For the sake of comparison with your figures, I have translated the velocities into metric measure on the basis of 1m=3'. They work out as 191m/sec and 106m/sec respectively. Obviously. these value will be larger if we were to calculate them from the time the asteroid enters earth's atmosphere as opposed to my values based on a height of 1 mile. They would, however, still be insignificant , in relation to 17-20km/sec.
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