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 GeoAstro Applets |
 Astronomy |
 Chaos Game |
 Java |
 Miscel- laneous |
Motion of the Moon
Computing the true longitude of the Moon:
True longitude of Moon = mean longitude + major inequality + evection + variation + annual inequality + reduction to ecliptic + parallactic inequality + more terms
Select
"Orbit"
instead
of
"Diagram" to watch the geocentric motion of the Moon.
mean longitude of the Moon: 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
measured from the mean position of the perigee
Source: Montenbruck, Pfleger: Astronomy on the Personal Computer
True longitude of Moon = mean longitude + major inequality + evection + variation + annual inequality + reduction to ecliptic + parallactic inequality + more terms
L = L0 + ...
(1) Major Inequality
(equation of center) = 22640"*sin(M) + 769*sin(2M)
(2) Evection = -4586"*sin(M-2D)
(3) Variation = 2370"*sin(2D) (4) Annual Inequality
= -668"*sin(MSun)
(5) Reduction to the Ecliptic
= -412"*sin(2F) (6) Parallactic Inequality
= -125"*sin(D) 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)
(7) More terms
term1
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E |
The eccentric anomaly (a parameterization of polar angle) |
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ν |
The true anomaly specifies the position along the orbit. |
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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, 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. You may use the
keys d, m or h to
increase the date, month, or hour,
or Shift
key and d or m to decrease the date or month !
Click the
applet first !
or Shift key and d, m or h to decrease the date, month,
or hour !
Click the applet first !
More applets:
More details:
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Last update: 2023, Oct 05
