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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

Source: Montenbruck, Pfleger: Astronomy on the Personal Computer

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 - esin(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.

keys 

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.

Details of the Moon's orbit

keys 

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 !

Books

More applets:

Moon Data

Moon Phase

Moon Phases for a Year

Sun & Moon Polar Applet

Azimuth of the Sun and the Moon at rise or set

Longitude of the Moon

Moon Light

More details:

Blue Moon

Full Moon distance

Lunar Perigee and Apogee Calculator

Web Links

http://www.dang.se/texter/moon.txt

Keplers Equation (MathWorld)

Last update: 2014 Mar 17