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Motion of the Moon

computing the true longitude of the Moon:

True longitude of Moon = mean longitude + mean anomaly + evection + variation + annual inequality (+ ...)

Select "Orbit" instead of "Diagram" to watch the geocentric motion of the Moon.

 mean longitude of the Moon: measured from the mean position of the perigee L0 = 218.31617 + 481267.88088*T - 4.06*T*T/3600.0 the Moon's mean anomaly: M = 134.96292 + 477198.86753*T + 33.25*T*T/3600.0 the Sun's mean anomaly: MSun = 357.52543 + 35999.04944*T - 0.58*T*T/3600.0 the mean distance of the Moon from the ascending node F = 93.27283 + 483202.01873*T - 11.56*T*T/3600.0 the difference between the mean longitudes of the Sun and the Moon D = 297.85027 + 445267.11135*T - 5.15*T*T/3600.0 Time T = (JD - 2451545)/36525

True longitude of Moon = mean longitude + major inequality + evection + variation + annual inequality

L = L0 + ...

 Period (1) Major Inequality = 22640"*sin(M) + 769*sin(2M) 31.8 d (2) Evection = -4586"*sin(M-2D) 14.7 d (3) Variation = 2370"*sin(2D) (4) Annual Inequality = -668"*sin(MSun) 1 y (5) Reduction to the Ecliptic = -412"*sin(2F) (6) Parallactic Inequality = -125"*sin(D) term1 term2 term3 term4 term4 term5 term6 = -212"*sin(2*M-2D) = -206"*sin(M+MSun-2D) = +192"*sin(M+2D) = -165"*sin(MSun-2D) = +148"*sin(L-MSun) = -110"*Math.sin(M+MSun) = - 55"*Math.sin(2F-2D) E The eccentric anomaly (a parameterization of polar angle) ν The true anomaly specifies the position along the orbit. M The mean anomaly is the angle of the line joining the focus (Earth) to a hypothetical body that has the same orbital period but travels at a uniform angular speed: M = n·(t - T)

Kepler's Equation for a body orbiting on an ellipse with eccentricity e:

M = E - e·sin(E)

Instructions: Choose or hide the terms of interest. The value of a term is red if active, otherwise black. The values for the annual inequality, the reduction to the ecliptic, the parallactic inequality, and the additional terms are magnified by a factor of 10.  You may use the keys d or m to increase the date, or month, or Shift key and d or m to decrease the date or month ! Click the applet first !  Click the diagram to get the coordinates of a point. Click a point and a second point holding down the Alt key to get a (horizontal) time intervall. Click a point and a second point holding down the Shiftkey to get a (vertical) angular difference.  Select "Orbit" to see the orbit of the Moon for the month selected.  You may use the keys d, m or h to increase the date, month, or hour, or Shift key and d, m or h to decrease the date, month, or hour ! Click the applet first !

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