I am hoping for a math genius to help me with a certain problem. Now, I am not that advanced in mathematics at all and only know certain very basic things, and I hope that the following problem is quite simple, or that the solution can be relayed to me in simple terms if there is one.
I am trying to model a gravitational field (acceleration values) about a celestial body that does NOT extend away from the centre of the body in accordance with a general inverse square law.
Now, in astronomy, I am aware that on the issue of deriving the curvature of an elliptical body in orbit, of say the sun, you only need 3 points, and that a unique curve will pass through all 3 points to give the total ellipse. I am hoping for something similar by way of a solution to my problem.
I have 3 distance measures from the centre of an ‘experimental’ celestial body, with the centripetal gravitational values at those points. What I want to know is, is there a way to determine the unique curvature of the field from just this data? I am hoping for a general method so I could experiment with different values. Any help would be appreciated.
Distance from centre of body = 238857.528 Miles
Centripetal (Gravity) Acceleration = 0.000000020633339375 Miles/Second^2
Distance from centre of body = 1114.118548 Miles
Centripetal (Gravity) Acceleration = 0.0009483872877 Miles/Second^2
Distance from centre of body = 1079.943132 Miles
Centripetal (Gravity) Acceleration = 0.006093296399 Miles/Second^2