# How to calculate the angle formed between 2 planets?

I am interested in calculating the angles formed between planets like Saturn opposite to Neptune - 180 degrees, PlanetX opposite/trine/square to PlanetY. How to find such degrees?

I use Stellarium software to find positions of planets. Here I am adding positions of Saturn, Jupiter and Sun.   Stellarium shows information about selected objects, can it be used to calculate angle formed, for example, angle formed between Saturn and Jupiter taking Sun as reference point?

• What's your third reference point, and have you seen a sextant? – Carl Witthoft Jun 13 '18 at 15:09
• If the vertex of the angle is the Sun, please edit your question to say so. – Mike G Jun 13 '18 at 15:52
• I think this could be a valid question (even though it seems to be about astrology, not astronomy), but with significantly more detail. planetwatcher.com may or may not be of more use to you (also googling "astrology planet positions" (no quotes)). – user21 Jun 13 '18 at 15:52
• @CarlWitthoft I am not sure about 3rd reference point, the place where I read it doesn't mention anything about 3rd reference point so my assumption would be sun but I am not sure what reference point to use when sun itself is involved, for example sun square pluto - forming 90 degrees. – Chinmay Sarupria Jun 14 '18 at 6:09

## 1 Answer

The planets are moving along elliptical paths, and we are viewing them from another planet that is also moving along an elliptical path, this makes the motion that the planets make in the sky (relative to distant stars) seem to loop and move with an inconsistent rate. The planets don't all orbit in the same plane, and so may be above or below the ecliptic (the apparent path in the sky of the sun)

So there is no shortcut to finding the angle between two planets: You have to calculate the sky position of the planets and then find the angle between those positions.

The first step is called calculating an ephemeris. The details are beyond the scope of this answer, but NASA have a good ephemeris calculator at https://ssd.jpl.nasa.gov/horizons.cgi. Alternatively, software like Stellarium will be able to calculate the position of a planet on any given date in the near future or past.

When you have the position of the planets as RA and Dec, and you have converted the units to decimal degrees, you can calculate the angle $A$ between them using

$$\cos(A) = \sin(\mathrm{Dec_1})\sin(\mathrm{Dec_2}) + \cos(\mathrm{Dec_1})\cos(\mathrm{Dec_2})\cos(\mathrm{RA_1} - \mathrm{RA_2})$$

Further details and a calculator is found at http://www.gyes.eu/calculator/calculator_page1.htm

• I use Stellarium software, I've updated the question with screenshots taken from it, please take a look. – Chinmay Sarupria Jun 14 '18 at 16:48
• This answer is exactly correct: if you know the position of two objects on the unit sphere, you can use spherical geometry to compute the angle between them as above. – user21 Jun 14 '18 at 16:52
• To calculate the angle between two objects as seen from the Sun, you need those positions as seen from the Sun. The positions given in the images you added to the question are positions as seen from the Earth. If you can change Stellarium to show the "sky" as seen from the Sun, you should be able to get the heliocentric ecliptic latitude and longitude (or find these values from JPL's Horizon). Then replace RA in Jame's formula with longitude and Dec with latitude and the calculation will give you the angle between the objects as seen from the Sun. – JohnHoltz Jun 14 '18 at 16:58
• @JohnHoltz Thanks, just to understand the calculator, I would like to use the current values in the question which are relative to Earth. In Saturn screenshot above, you can see there are 2 Ecliptic latitude and longitude per selected object, which one to use? Also James gave a calculator link, that calculator says enter RA and Dec in decimal hours but the latitude and longitude available are in degree form, what to enter? I would be grateful if you could help me a bit with the calculator. – Chinmay Sarupria Jun 14 '18 at 17:44
• @JohnHoltz I was able to figure out the values required in the calculator. It requires J2000 RA and Dec values not Ecl. Longtiude and Latitude. – Chinmay Sarupria Jun 15 '18 at 3:52