I wanted to point at the L4 and L5 of Sun-Jupiter to find Trojan asteroids but I don't know how to calculate the RA and Dec of these. Do you know of any software that does it for you or how to calculate them?
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2 Answers
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The L4 and L5 points are unstable orbits. The Trojans move in perturbed (ie slightly non-keplerian) orbits that move them around the L4 and L5 points. At any time you will find Trojans in a pair of lobes between about 30 and 90 degrees ahead of Jupiter.
You can find individual asteroids using NASA Horizons ephemeris For example 624 Hektor, the largest Trojan (and placed in the Greek Camp around L4) will be found at RA 20 47 54.08, Dec -28 04 20.1 on Feb 10 2018. And 884 Piramus (in the Trojan Camp, L5) will be at RA 10 43 51.39 Dec +01 04 11.3.
(Jupiter is between them at RA 15 18 55.32 Dec -17 07 47.1)
Neither are easy to find, with a Magnitude of 15 or 16, due to their greater distance than main belt asteroids, and very dark colour. The image below shows the distribution of Trojans around Jupiter.
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In order to find the rather large extent of space where Jupiter's Trojan asteroids can remain, one would use a map of the Celestial sphere, and look at the long stretch of points that happen to be +/- sixty degrees of wherever Jupiter happens to be at the moment. I show a screen shot from in-the-sky.org's Star Atlas page. The purple dot in the center next to the constellation name Libra is Jupiter, but because of some glitch it is not showing right now. Holding a cursor over the dot shows its name. The yellow diagonal line is the Ecliptic, and the +/- 60 degree regions will be at either end of the box. It's really really huge, there are no specific coordinates, and the only way to know an extremely faint dot would be an asteroid rather than a star would be an extremely detailed star map, or a series of exposures over hours or days showing the motion relative to the other objects.
EDIT: You can use any similar mapping program or website. You've asked about December, the programs can usually be walked backwards or forwards in time to whichever date you are interested in. The figure below is for mid-February, when I posted the answer.
You can also enjoy Scott Manleys YouTube Videos:
- Asteroids In Resonance With Jupiter (First 3:2 resonances, then Trojans are shown separately)
- Asteroid Discovery - 1980-2012 - UHDTV (several versions on this YouTube channel)
