Wish to track an orbit and rotation?

Question

I wish to find a way to track the orbit of the moon in conjunction with the earth. I also want to check the earth's rotation, using the moon as a reference

Answer 1

comparing the moon's position with respect to teh stars from night to night should do it...

Answer 2

Determining the Geocentric Position of the Moon.

Let's suppose that you haven't been paying attention to the sky for a while, and you're not sure where the moon will be tonight. You don't want to go to all the trouble of leaving your comfortable living room unless you know that your efforts to see the moon will be rewarded. This is the math you need!

Step 1. Choose a calendar date for your observation.

Y = the number of the year (four digits)

M = the number of the month (1-12)

D = the day of the month

d = 367*Y - (7*(Y + ((M+9)/12)))/4 + (275*M)/9 + D - 730530

d = the number of days since midnight UT beginning January 0, 2000 (also known as 31 December 1999).

c = d / 36525

c = the number of Julian centuries since midnight beginning January 0, 2000.

J = d + 2451543.5

J = the Julian date of the prediction.

The numbers d, c, and J are merely alternative ways of expressing the date you chose. In the steps below, I'll use (d) most of the time, except when figuring the Earth's obliquity I'll use (J).

If you want a short cut, here's a web page that converts from calendar date/time to decimal Julian date.

http://wwwmacho.mcmaster.ca/JAVA/JD.html

Step 2. The first approximation to the moon's position.

a = 60.2666

e = 0.0549

i = 5.1454 * pi/180

L = ( 125.1228 - 0.0529538083 d ) * pi/180

w = ( 318.0634 + 0.1643573223 d ) * pi/180

Mm = ( 115.3654 + 13.0649929509 d ) * pi/180

Adjust L, w, and Mm to the interval [0, 2pi).

u1 = Mm

Repeat...

.   u0=u1

.   F0 = u0 - e sin u0 - Mm

.   F1 = 1 - e cos u0

.   F2 = e sin u0

.   F3 = e cos u0

.   D1 = -F0 / F1

.   D2 = -F0 / [ F1 + D1 F2 / 2 ]

.   D3 = -F0 / [ F1 + D1 F2 / 2 + (D2)^2 F3 / 6 ]

.   u1 = u0 + D3

Until |u1-u0| < 1E-15

Um = u1

x = a [cos(Um) - e]

y = a sin(Um) sqrt(1-e^2)

R = sqrt( x^2 + y^2 )

v' = Arctan(y / x)

If x < 0 then v = v' + pi

if x > 0 and y < 0 then v = v' + 2 pi

Xm' = cos L cos(v+w) - sin L sin(v+w) cos i

Ym' = sin L cos (v+w) + cos L sin(v+w) cos i

Zm' = sin(v+w) sin i

Step 3. Improving the first approximation by accounting for various gravitational perturbations.

Ls = ( 638.9875 + 0.985647352 d ) * pi/180

Ms = ( 356.047 + 0.9856002585 d ) * pi/180

Lm = L + w + Mm

D = Lm - Ls

F = Lm - L

Adjust Ls, Ms, Lm, D, F to the interval [0, 2pi).

Finding the moon's geocentric ecliptic longitude.

Lonm' = Arctan(Ym'/Xm')

If Xm'<0 then Lonm=Lonm' + pi

If Xm'>0 and Ym'<0 then Lonm=Lonm' + 2 pi

Lonm = Lonm - 1.274 (pi/180) sin(Mm - 2D)

Lonm = Lonm + 0.658 (pi/180) sin(2D)

Lonm = Lonm - 0.186 (pi/180) sin(Ms)

Lonm = Lonm - 0.059 (pi/180) sin(2 Mm - 2D)

Lonm = Lonm - 0.057 (pi/180) sin(Mm - 2D + Ms)

Lonm = Lonm + 0.053 (pi/180) sin(Mm + 2D)

Lonm = Lonm + 0.046 (pi/180) sin(2D - Ms)

Lonm = Lonm + 0.041 (pi/180) sin(Mm - Ms)

Lonm = Lonm - 0.035 (pi/180) sin(D)

Lonm = Lonm - 0.031 (pi/180) sin(Mm + Ms)

Lonm = Lonm - 0.015 (pi/180) sin(2F - 2D)

Lonm = Lonm + 0.011 (pi/180) sin(Mm - 4D)

Finding the Moon's geocentric ecliptic latitude.

Latm = Arcsin( Zm' )

Latm = Latm - 0.173 (pi/180) sin(F - 2D)

Latm = Latm - 0.055 (pi/180) sin(Mm - F - 2D)

Latm = Latm - 0.046 (pi/180) sin(Mm + F - 2D)

Latm = Latm + 0.033 (pi/180) sin(F + 2D)

Latm = Latm + 0.017 (pi/180) sin(2 Mm + F)

The geocentric direction of the moon, unit vector in ecliptic coordinates.

Xm = cos(Lonm) cos(Latm)

Ym = sin(Lonm) cos(Latm)

Zm = sin(Latm)

[Xm, Ym, Zm] is a unit vector from the center of Earth toward the center of the moon's disk, in ecliptic coordinates.

Correcting the moon's geocentric distance.

R = R - 0.58 cos(Mm - 2D)

R = R - 0.46 cos(2D)

The geocentric position vector of the moon, in ecliptic coordinates:

X' = R Xm

Y' = R Ym

Z' = R Zm

Earth's obliquity is found to facilitate a rotation from the ecliptic coordinate system to the celestial coordinate system.

phi = 23.439282 - 3.563E-7 ( J - 2451543.5 )

This equation gives the obliquity in degrees. If you need to have it in radians, multiply by pi/180.

X = X'

Y = Y' cos(phi) - Z' sin(phi)

Z = Y' sin(phi) + Z' cos(phi)

if X = 0 and Y > 0 then RA = 6 hours

if X = 0 and Y < 0 then RA = 18 hours

if X = 0 and Y = 0 then RA = 0 hours

if X > 0 and Y > 0 then RA = Arctan( Y / X ) / 15

if X < 0 then RA = Arctan( Y / X ) / 15 + 12 hours

if X > 0 and Y< 0 then RA = Arctan( Y / X ) / 15 + 24 hours

The above compound equation assumes that the Arctan function will return the angle in degrees.

dec = Arcsin ( Z / R )

R is the distance in Earth radii between the Earth and the moon at time d.

RA is the moon's geocentric right ascension in decimal hours at time d.

dec is the moon's geocentric declination in decimal degrees at time d.