last updated 02/14/10

EMBOSS position calculation using mean orbital elements

Modified by Joey Chatelain

Mostly stolen from Stephen R. Schmitt

Enter your location:
latitude ° ' North South
longitude ° ' East West
Object H a e i O w T

today:

Enter the date and time:
mm/dd/yyyy hr:min:sec
/ /      : :

Computation steps

The main steps in calculating the RA and DEC of a planet from the mean elements are:

  1. Find the day number or time since the date of the elements
  2. Find the average (or mean) orbital elements of the planet
  3. Find the true anomaly, the angle to the planet from perihelion
    (helio means Sun)
  4. Find the heliocentric radius, distance to planet from sun
  5. Find the heliocentric ecliptic rectangular coordinates of the planet
  6. Find the heliocentric ecliptic rectangular coordinates of the Earth
  7. Transform the heliocentric coordinates to geocentric coordinates
    (geo means Earth)
  8. Transform the geocentric ecliptic coordinates to equatorial coordinates
  9. Calculate the RA and DEC and the distance to the planet from Earth

Notation

Parameters

H - Absolute MAgnitude (Mag), Magnitude of object if it were at 0 phase angle and 1 AU from both sun and Observer
a - mean distance (AU), the value of the semi-major axis of the orbit (AU - Astronomical Unit - average Sun to Earth distance)
e - eccentricity of the ellipse which describes the orbit (dimensionless)
i - inclination (degrees), angle between the plane of the ecliptic (the plane of Earth's orbit about the Sun) and the plane of the planets orbit
O - longitude of ascending node (degrees), the position in the orbit where the elliptical path of the planet passes through the plane of the ecliptic, from below the plane to above the plane
w - Argument of perihelion (degrees), the position in the orbit where the planet is closest to the Sun
T - Time of Periapsis(days), the last time the object was at periapsis in Julian Days

Calculated quantities

M - mean anomaly (degrees)
V - true anomaly (degrees)
R - heliocentric radius (AU)
X,Y,Z - rectangular coordinates (AU)
RA - right ascension (hour angle)
DEC - declination (degrees)
hmag - apparent brightness (mag) in whatever filter used for H
note: hmag for planets is for H at that planet's position

Coming soon?

printing object name in output
moon distance-to-planet calculator Right here!

References

  1. origional site http://home.att.net/~srschmitt/script_planet_orbits.html,