Calculating Semimajor Axis of Meteor Orbit

[crystalplane]

if i know a meter is observed at an altitude of 6km, to be traveling with an initial velocity of 20 km/s and the decelerating at a rate dv/dt=0.2km/s^2, which formula i should use to get the length of the semimajor axis of the meteor'orbit?

 

[Jenab2]

if i know a meter is observed at an altitude of 6km, to be traveling with an initial velocity of 20 km/s and the decelerating at a rate dv/dt=0.2km/s^2, which formula i should use to get the length of the semimajor axis of the meteor'orbit?

You would have to estimate the speed the meteor would have at Earth's position if Earth had not been in the way to accelerate it with gravity and then decelerate it with atmosphere. Probably you'd want multiple observers with multiple exposures on film so that you could know the direction of meteor flight and deduce the speed of the meteor between each observed position. Then use Runga-Kutta to back out the velocity before it hit the atmosphere. Then apply the conservation of energy to get the speed in the absence of Earth's gravitational acceleration. Then you can infer what the hypothetical unperturbed state vector of the meteor would have been, and from there you can derive the elements of the meteor's former orbit.