GodThingFormerly
A Different Kind of Asshole
Well, the other planet had exactly the same distance from the sun as the Earth did, didn't it? So where does the Third Law come in?
"Suppose that the Earth is represented as a point of mass m revolving in a circular orbit of radius a around a center of force (the Sun) of mass M. Increase the usual Newtonian attraction of the Sun by the attraction of the hidden Anti-Earth and compute the change in length of the Earth year under the new central force. (How many seconds longer or shorter will the year be under the Anti-Earthian influence than the 'real' year is?)
The presence of the Anti-Earth would be seen as an increase in the constant GM, and that changed constant would then change the periods of the other planets when calculated from Kepler's Third Law. But those periods are observed to be in harmony with the period of Earth when it is calculated by Kepler's Third Law. Conclusion: no Anti-Earth." - The Sheer Joy of Celestial Mechanics by Nathaniel Grossman (Birkhäuser Boston, 1996).
TGT