23
edits
Changes
Jump to navigation
Jump to search
Line 61:
Line 61: + + + + + + + + + + + + +
Simple rebuttal to Aschlafly's Moon point #4
: Errors explained and supported are corrected. Ideologically motivated claims of error are not. All I see here so far are the latter.--[[User:Aschlafly|Aschlafly]] 12:33, 17 March 2007 (EDT)
: Errors explained and supported are corrected. Ideologically motivated claims of error are not. All I see here so far are the latter.--[[User:Aschlafly|Aschlafly]] 12:33, 17 March 2007 (EDT)
== Simple rebuttal to Aschlafly's Moon point #4 ==
Your Moon point #4 that the Moon must have been receeding faster in the past can easily shown to be false in three lines. First, write the total angular momentum (L) for the Earth+Moon system. It consists of three parts: the Earth's rotation on its axis, the Moon's rotation on its axis, and the Moon's revolution about the Earth:
L = Ie We + Im Wm + r^2 Mm Wm
where Ie and Im are the momen of inertias of the Earth and Moon, We and Wm are the angular rotations of the Earth and Moon, Mm is the mass of the Moon and r is the Earth-Moon radius.
Second, since angular momentum is conserved, take the time derivative dL/dt, set it to zero, and solve for dr/dt. For brevity, I'll denote the time derivate with a D, so dr/dt = Dr. This gives:
Dr = -(DWe + DWm(1 + Mm r^2)) / (2 r Wm Mm)
Third, both the numerator and denominator in this expression are positive, since We and Wm are negative (both the Moon and Earth rotate slower, that is We and Wm are less than zero, as energy is lost due to tidal friction). This means that Dr is positive. So the rate of change in the Earth-Moon distance is increasing with time, so it was slower in the past. This refutes your claim that the Moon must have been receeding faster in the past.--[[User:Macronking|Macronking]] 12:58, 17 March 2007 (EDT)