Thursday, January 10, 2013

Tracking an Object in 3D

Suppose that the two observers in the last blog take a second sighting on the 1° parallax object an hour after the first and calculate a new position for it. (To simplify the problem the Earth's rotation has been neglected.)

The new position can be used to determine how much the object has moved relative to the Earth in the elapsed time. They will find that it has moved 0.8 Earth radii so its speed relative to the Earth will be 0.80 RE/hour.

Once our observers have the geocentric position and velocity relative to the Earth they can make predictions about where it will be at future times and will be in a better position to track the object as it moves across the night sky. Taking into account the Earth's motion relative to the Sun the data from the observations could also be used to determine object's motion under the influence of the local gravitational field. When sighting a distant NEO our two observers could make two sets of observations exactly one Earth rotation apart so that the calculations can be done in the Earth's reference frame. A more practical approach would be to do everything in the geocentric celestial reference frame and adjust the observers positions for the Earth's rotation since photographis observations are done relative to the background stars.