Help With Conservation Of Energy Concept
just a though to put out there ( Im not a maths guy )
you havent given an example of the size/mass of an asteroid for your calcs
I would consider that the difference in size of say an asteroid up to ~ 1km across compared to the size of the earth, the gravitational PE may not be a large factor compared to the KE of the incoming asteroid.
average incoming velocity of a meteor/asteroid ..... 30 - 40 km / sec
acceleration due to gravity 9.81m/s2 .... big difference, orders of magnitude
some one more knowledgeable than me will hopefully clarify more