## Astronomical Computing

## Calculation of Apparent Orbit of Binary Star

Written by Toshimi Taki

January 21, 2007

### 1. Spreadsheet

I made a spreadsheet to calculate apparent orbit of a binary star. The speadsheet uses the equations in Reference [1]. The calculation is straight forward. The spreadsheet also outputs a figure of apprarent orbit.

The orbital elements of visual binary stars are found in Reference [2].

Click here to download "binary_form.xls".

### 2. References

[1] Jean Meeus, "Astronomical Algorithms," Willmann-Bell, Inc., 1991.

[2] C. E. Worley and W. D. Heintz, "The Fourth Catalog of Orbits of Visual Binary Stars," Publ. U.S. Naval Obs. (2) 24, part VII (1983).

### 3. Example of Calculation Result --- Apparent Orbit - Zeta Her

(1) Input Data

- Name of Binary Star: Zeta Her
- Position, R.A.: 16h37.5m
Declination: +31 47'
- Period of Revolution, P: 34.487 year
- Time of Perhrlion Passage, T: 1967.8 year
- Eccentricity of True Orbit, e: 0.46
- Semimajor Axis, a: 1.355 arc second
- Inclination of Plane of True Orbit to
the Plane at Right Angle to the Line of Sight, i: 132.9 degree
- Position Angle of Ascending Node, Omega: 229.2 degree
- Longitude of Perihelion, omega: 290.9 degree
- Primary - Magnitude: 2.9
- Spectral Type: G0IV
- Secondary - Magnitude: 5.53
- Spectral Type: G7V

(2) Result

Time Position Angle Separation
(year) (degree) (arc sencond)
============================================
2000.0 12.69 0.747
2001.0 344.77 0.565
2002.0 302.14 0.512
2003.0 265.13 0.634
2004.0 242.37 0.801
2005.0 227.06 0.936
2006.0 215.10 1.028
2007.0 204.78 1.087
2008.0 195.32 1.124
2009.0 186.36 1.148
2010.0 177.72 1.167

(3) Figure