Object
Coordinates and Phenomena Calculation


Star Data Matrix

This is a convenient place to enter frequently
required star locations. Each row contains the following data going
across: Star name, Year epoch of data, 3 columns of RA (hr, min,
sec), 3 columns of DEC (deg, min, sec), Proper motion in RA in
arcsec/yr (not RA seconds), Proper motion in DEC arcsec/yr. Rows
can be inserted at the end as needed to accommodate new stars. 
Star Data Extraction 
Notes: The
following functions are used to extract data from the STARMAT
table. 
Input for all
functions: Star Number in table. Header row is zero so first
star is one. 

Retrieve Star Name 
Output: Star name
from table. 


Retrieve Epoch Year 
Output: Epoch year
from table may be integer or floating. 


Retrieve RA of Star in
Decimal Degrees 
Output: RA of star
in decimal degrees. 


Retrieve DEC of Star
in Decimal Degrees 
Output: DEC of
star in decimal degrees. 


Retrieve Yearly Proper
Motion in RA 
Output: Proper
motion in seconds of arc (same scale as DEC) per year. 


Retrieve Yearly Proper
Motion in DEC 
Output: Proper
motion in seconds of DEC per year. 



Example: Retrieve
star data. 
Row of star to find data
for: 
Name: 

Year: 

RA: 

DEC: 

Proper Motion in RA in
seconds of arc per year: 

Proper Motion in DEC in
seconds of arc per year: 

Planet Data Matrix

The planet matrix is
arranged by planet (missing Pluto) in order from the sun  Earth
data is the 3rd row after the headers. Data here assumes the
standard epoch J2000. Each row contains: Mean heliocentric longitude
at epoch, first order change in longitude per century and semimajor
axis in AU. Dividing the values in the second column by the number
of days in a Julian Century (36525) yields the mean daily motion of
the planet in degrees at epoch J2000. 



Pluto is absent because of its great inclination
and eccentricity. Only enough data is included to perform low
precision position calculations with the equations that follow the
matrix. Minor planets can be added to the end of the table as long
as their orbits have low eccentricity and inclination.
Resources: [AA: p. 141, pp. 2002]
[ESAA: p. 704] 
Planet Data Functions 
Low Precision Helio and Geocentric Longitudes of
the Planets 

Notes: As Johannes Kepler could attest,
calculating planetary positions would be a lot easier if the planets
in our solar system traveled in purely circular orbits entirely in
the plane of the ecliptic. With respect to the central sun
(heliocentric) the daily motion would be a constant number of
degrees per day. Calculating a planet's Earth centered (geocentric)
location would take a little trigonometry once you knew the daily
motion and distance from the sun for the Earth and planet in
question. While not very exact, a ballpark estimate of planetary
location can be made with the following equations if the above is
assumed true. Accuracy falls off as the orbit deviates from a circle
(eccentricity), increases in inclination to the ecliptic and is
modified by perturbations. Therefore you should not use these
equations to calculate comet orbits. 

The first equation calculates heliocentric
positions of a planet. This data is generated for the Earth and
another planet for input into either of the three geocentric
position equations that follow. The first geocentric equation
handles the geometry for outer planets (Mars and outward) and the
second for the inner (Mercury and Venus). The final geocentric
equation (LONGe()) wraps the functionality of the prior two
equations by using the semimajor axis parameter to determine if an
inner or outer planet is in question. 
Resources: [PAC: p. 72]
Low Precision Mean Heliocentric Longitude of
Planet Equation 
Input: Date of interest in Julian
centuries from J2000, Planet number 1 = Mercury, ..., 8 = Neptune. 
Output: Heliocentric longitude in degrees
normalized to 0  360. 

Low Precision Geocentric Longitude of Outer
Planets 
Input: Heliocentric longitudes of planet
and Earth and semimajor axis of planet. 
Output: Geocentric longitude of planet in
degrees normalized to 0360. 

Low Precision Geocentric Longitude of Inner
Planets 
Input: Heliocentric longitudes of planet
and Earth and semimajor axis of planet. 
Output: Geocentric longitude of planet in
degrees normalized to 0360. 

Low Precision Geocentric Longitude for Outer
and Inner Planets Based on Semimajor Axis 
Input: Heliocentric longitudes of planet
and Earth and semimajor axis of planet. 
Output: Geocentric longitude of planet in
degrees normalized to 0360. 

Example: Low precision heliocentric
longitude of the Earth when Spring begins. 

Date of vernal equinox: 
Low precision heliocentric longitude of Earth on
above date: 

By definition the geocentric longitude of the Sun
at this instant is 0degrees. The geocentric longitude of the sun
always differs by 180degrees from the heliocentric longitude of
the Earth. So compare the result with the exact answer of
180degrees. 

Example: Low precision geocentric
longitude at conjunction. 

On Feb. 23, 1999 Venus and Jupiter were separated
by a mere 1/3degree  able to fit together in a lowpower
telescopic field of view. It figures their geocentric longitudes
must have been similar 

Conjunction date: 
Low precision geocentric longitude of Venus on
above date: 
Low precision geocentric longitude of Jupiter on
above date: 

The calculations place the planets in the area of
the vernal equinox. 
Rising and Setting

Sidereal Time of Rising and Setting 

Notes: These calculations can determine the
approximate sidereal time that an object is on the horizon. Sidereal
time can be translated to UT to determine civil time of the event.
The calculation here are an approximation based on a spherical Earth
and do not take into account other factors like object motion,
altitude and atmosphere refraction. These two factors alone can
affect setting and rising time by several minutes. 

From a particular location objects may be in the
sky all the time or not at all. For such an object the rise and set
functions will show an error. The WillRiseSet() function below can
assist in determining if the error can be explained by an object
that does not rise or set. 
Resources: [PAC p. 36]; [TAA p. A12] 
Core Function for Rise and Set 
Used by the functions that follow. 
Input: Latitude of observer and
declination of object in degrees. 
Output: Sidereal time in degrees. 

Rise and Set Test Function 
Determines if object will have a rising and
setting. 
Input: Latitude of observer and
declination of object in degrees. 
Output: String indicating if the phenomena
can occur. 

Sidereal Times of Rising and Setting 
The first function determines rise time and the
second set. The results are in degrees of sidereal time. Note that
if these functions are used for objects with a large apparent motion
against the background stars (moon, sun, comets, mercury, etc.) that
the DEC and RA should be for the time close to the rising or
setting. If you have a method of determining these coordinates for a
set time you can determine rising and setting iteratively as
follows:
 Take the DEC and RA values for some point during the day in
question and determine sidereal rise and set time using the
functions below.
 Use your method of determining the object DEC and RA for these
times and substitute back into the rise and set equations.
 Repeating this will yield better results until a point is
reached where the values do not change.


Input: Latitude of
observer, declination of object in degrees, right ascension of object
in degrees. 
Output: Sidereal
time in degrees. 


Example: Determine time of
rising for Leonid meteor shower radiant. 


Position of radiant in
RA: 

and DEC: 

Position of observer in
LAT: 

and LONG: 

Date of observation: 



Will the radiant rise
at all?: 

Sidereal time of rise: 

Universal Time of rise: 


Astro
Utilities Electronic Book Copyright ©
1999 Pietro Carboni. All rights reserved. 
