Planet movements?

Question

Does anyone know a website which shows the movements of the planets through the constellations over the next few years?

Answer 1

You don't even need a planetarium program. You can learn to do the math for yourself. I'll show it to you.

Here are the orbital elements for the planets.

Mercury
a = 0.387099 au
e = 0.205620
i = 7.0048 deg
L = 48.183 deg
w = 29.079 deg
T = JD 2447015.85

Venus
a = 0.723326 au
e = 0.006738
i = 3.3946 deg
L = 76.566 deg
w = 54.844 deg
T = JD 2447019.52

Earth
a = 1.0000001124 au
e = 0.0167102192
i = 0.0
L = 0.0
w = 103.078101 deg
T = JD 2454468.667

Mars
a = 1.523668 au
e = 0.093405
i = 1.8498 deg
L = 49.463 deg
w = 286.318 deg
T = JD 2447385.90

Jupiter
a = 5.202880 au
e = 0.048138
i = 1.3051 deg
L = 100.362 deg
w = 275.118 deg
T = JD 2446986.77

Saturn
a = 9.534190 au
e = 0.053477
i = 2.4861 deg
L = 113.556 deg
w = 337.857 deg
T = JD 2442029.95

Uranus
a = 19.2024 au
e = 0.045693
i = 0.7734 deg
L = 73.991 deg
w = 97.398 deg
T = JD 2439440.74

Neptune
a = 30.1219 au
e = 0.009569
i = 1.7696 deg
L = 131.683 deg
w = 258.417 deg
T = JD 2405459.79

Pluto
a = 39.3636 au
e = 0.246694
i = 17.1394 deg
L = 110.164 deg
w = 114.084 deg
T = JD 2447859.10

a = semimajor axis (au)
e = eccentricity
i = inclination
L = longitude of the ascending node
w = argument of the perihelion
T = time of perihelion passage (Julian date)

Here's the procedure by which you find the heliocentric position of the planet, in ecliptic coordinates, from the orbital elements for that planet and a selected time of observation, t.

M = 2 pi (t - T) / { 365.256898326 a^(3/2) }
Adjust M to the interval [0, 2 pi).
u(0)=M
REPEAT
u(i+1) = { M + e [sin u(i) - u(i) cos u(i)] } / [1 - e cos u(i)]
UNTIL | u(i+1) - u(i) | < 1E-12
u = u(i+1)
x''' = a [(cos u) - e]
y''' = a sin u sqrt(1-e^2)
Q' = arctan(y'''/x''')
if x'''<0 then Q = Q' + pi
if x'''>0 and y'''<0 then Q = Q' + 2 pi
r = a (1-e^2) / (1+e cos Q)
x'' = x''' cos w - y''' sin w
y'' = x''' sin w + y''' cos w
x' = x''
y' = y'' cos i
z' = y'' sin i
x = x' cos L - y' sin L
y = x' sin L + y' cos L
z = z'

t = time of observation (Julian date)
M = mean anomaly (radians)
u = eccentric anomaly (radians)
[x''',y'''] = canonical heliocentric position of planet
Q = true anomaly (radians)
r = heliocentric distance (au)
[x,y,z] = position of the planet in heliocentric ecliptic coordinates

For the same time of observation, t, you will do all the above math, and thereby get heliocentric position vectors [x,y,z] for both Earth and the other planet. Then you translate the ecliptic coordinate system from the sun to the Earth, with a vector subtraction.

Xge = x(planet) - x(earth)
Yge = y(planet) - y(earth)
Zge = z(planet) - z(earth)

Then you rotate the geocentric position vector for the planet from ecliptic coordinates to celestial coordinates.

tilt = 23.438 deg

(Where tilt is the Earth's obliquity.)

Xgc = Xge
Ygc = Yge cos(tilt) - Zge sin(tilt)
Zgc = Yge sin(tilt) + Zge cos(tilt)

Finally, you calculate the distance, the right ascension and the declination of the planet, in geocentric celestial coordinates.

Rgc = sqrt(Xgc^2 + Ygc^2 + Zgc^2)

RA' = arctan(Ygc/Xgc)
If Xgc<0 then RA = RA' + pi radians
If Xgc>0 and Ygc<0 then RA = RA' + 2 pi radians
RAhrs = 12 RA / pi
DEC = arcsin(Zgc/Rgc)
DECdeg = 180 DEC / pi

The right ascension of the planet is RAhrs (in decimal hours), and its declination is DECdeg (in decimal degrees). You can use a star atlas to see where the planet would appear in Earth's sky at the time of observation you used.

Answer 2

This site
http://www.fourmilab.ch/yoursky/
lets you create star charts from any location and includes all planets.
And it allows you to publish ephemerides (tables) that can span long time periods.

However, it is not very user friendly for what you may want to do: You'd have to do each planet separately and interpret the date (planet position) in order to determine the constellation it is in.

Answer 3

You can do this with any planetarium program. There are a few free ones and one I know of is called Stellarium. I am listing the website so you can look at it and download it.

Answer 4

Wow looks like jena just went through orbital mechanics in physics. SHOW OFF! :)

Answer 5

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Answer 6

This site might. Hope it helps. Not sure how to use it that much.