Department of Physics User's Guide to the Night Sky

## How to estimate the opposition position of a planet

The orbits of the planets are only moderately inclined (i.e. a few degrees) to the ecliptic plane and hence the planets are seen to roughly track along the ecliptic. A good approximation to the Sun's (RA, Dec) position is given by

RA [deg] = λ + 2.45 sin 2λ        sin Dec [deg] = 0.4 × sin λ   ( or Dec [deg] = 23.5 × sin λ ) ,

where λ is the Sun's ecliptic longitude. &lambda can be estimated by assuming that the Earth's orbit is circular with the Sun observed at λ = 0° on 21st March, λ = 30° on 21st April, λ = 60° on 21st May, λ = 90° on 21st June, etc.

We can use these two formulae to make a rough estimate of a planet's (RA, Dec) position at the time of opposition. Jupiter was at opposition on 9th July 2008. So if we estimate the Sun's (RA, Dec) position at a date six months eariler (or later), e.g. 9th January, then this position will be approximately where Jupiter will be at opposition.

On the 9th January the Sun's ecliptic longitude is about 288° (on 21st January the Sun's λ = 300° and hence 12 days eariler will be about 300° − 12° ). Using the above formulae, we find RA = 287.0° and Dec = −22.4°. Jupiter's actual position at opposition in 2009 was RA = 289° (19h 16m) and Dec = −22.5°.

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