The Star Next to the Moon

A tool and the count behind it. The tool is Which light is that?, Sky Now run backwards: say where you are, when, and where the light is (or that it is next to the Moon), and it ranks every planet and bright star in that part of your sky by how bright each looks from where you stand. This page is what it stands on, and a count of what the light beside the Moon turns out to be.

Only ten things

The Moon goes round the sky close to the ecliptic, the line the Sun follows through the stars over a year, because its orbit is tilted to the Earth’s by only about five degrees: NASA’s fact sheet gives the inclination to the ecliptic as 5.145 degrees. The planets keep close to the same line, their orbits tilted to the Earth’s by no more than about seven degrees (Mercury’s). So the lights that can ever sit beside the Moon are the planets and whichever bright stars happen to lie near that line, and there are not many of those.

Among the stars of magnitude 1.5 or brighter (on the magnitude scale lower is brighter, and 1.5 takes in the 22 brightest points among the stars, Alpha Centauri’s close pair counted as one), five lie within seven degrees of the ecliptic, as the Hipparcos positions put them: Regulus (0.47 degrees from it), Spica (2.05), Antares (4.57), Aldebaran (5.47) and Pollux (6.68). The next nearest bright ones, Procyon and Betelgeuse, are 16 degrees off. The cut at 1.5 decides the list: Castor (1.58), Shaula (1.62) and Elnath (1.65) lie near the line just below it, and they come back further down.

That is the reasoning. Here is the count. For every night from 1 January 2020 to 31 December 2038, nineteen years (longer than the 18.6 years in which the line where the Moon’s orbit crosses the ecliptic turns once round the Earth, shifting the Moon’s monthly path among the stars), at eight latitudes from 45 degrees south to 55 degrees north, I took every whole hour after civil twilight (the Sun more than 6 degrees below the horizon) when the Moon was more than 5 degrees up, and listed every planet, and every star of magnitude 1.5 or brighter, that was itself more than 5 degrees up and within 10 degrees of the Moon. Ten degrees is about the width of a fist held at arm’s length.

The list of everything that ever turned up, at all eight latitudes together, is the five planets and those five stars, and Betelgeuse once.

latitude	nights the Moon was up after dusk	nights a light that bright was within 10° of it	with a planet among them	with only stars
45° S	5,722	2,069 (36%)	956 (46%)	1,113 (54%)
30° S	5,979	2,249 (38%)	1,079 (48%)	1,170 (52%)
15° S	6,035	2,260 (37%)	1,090 (48%)	1,170 (52%)
0° (equator)	6,036	2,280 (38%)	1,091 (48%)	1,189 (52%)
15° N	6,128	2,343 (38%)	1,144 (49%)	1,199 (51%)
30° N	5,973	2,239 (37%)	1,053 (47%)	1,186 (53%)
45° N	5,719	2,140 (37%)	960 (45%)	1,180 (55%)
55° N	5,226	1,895 (36%)	855 (45%)	1,040 (55%)

So on a little over a third of the nights the Moon is up, a light that bright is close beside it, and it is only stars slightly more often than it is a planet, at every latitude counted.

The cut at magnitude 1.5 is a choice. Lower it to everything the tool carries (stars brighter than magnitude 2.15) and nine fainter stars join the list, every one of them within 14 degrees of the ecliptic: Nunki, Elnath, Alhena, Algieba, Castor, Hamal, Kaus Australis, Denebola and Shaula, in order of how many nights they spent beside the Moon. On 25 to 28 per cent of the nights when anything the tool carries was within 10 degrees of the Moon, the only thing there was one of these nine. So a light beside the Moon that is noticeable but not dazzling may well be one of them; the tool names it either way.

When more than one of the ten is near the Moon on the same night, the one a person asks about is most likely the brightest. Counting only the brightest of each night’s lights, by the light’s own magnitude before the air dims it:

latitude	Jupiter	Saturn	Mars	Venus	Mercury	Spica	Regulus	Antares	Aldebaran	Pollux
45° S	283	264	189	149	50	290	255	254	171	164
30° S	297	276	199	215	65	295	277	264	181	180
15° S	295	278	206	224	64	297	274	264	184	174
0° (equator)	299	278	211	226	51	296	284	267	193	175
15° N	305	286	219	239	73	295	280	267	202	177
30° N	299	287	208	206	32	297	278	267	200	165
45° N	282	286	200	163	10	281	276	253	216	173
55° N	263	267	179	118	11	238	259	186	205	168

(Plus Betelgeuse, once, at 55° N.) Nothing dominates. Jupiter, Saturn, Spica and Regulus each take a similar share, and Venus is rarer than its fame suggests. It never gets more than about 47 degrees from the Sun (47.2 at its farthest in these nineteen years, by this engine), so when the Moon is beside it the Moon is a crescent near the Sun too, often low in a twilit sky where this count’s limits (5 degrees up, the Sun 6 degrees down) leave the pair out. Over a different nineteen years the counts would shift a little, because Jupiter and Saturn spend years at a time in particular stretches of the ecliptic.

The one that got in sideways

On the night of 22 April 2034, seen from 55 degrees north on the Greenwich meridian, the Moon came to 9.96 degrees from Betelgeuse at 22:00 UT, with the Moon 13 degrees up and Betelgeuse 5 degrees up in the west. From the centre of the Earth the same Moon would have been 10.75 degrees away. The difference is parallax: you stand about 6,400 km from the Earth’s centre, the Moon is only about 60 Earth radii away, and from the surface it sits up to about a degree lower in the sky than it would from the centre. That night the degree pointed at Betelgeuse. JPL Horizons’ own position for the Moon at that minute puts it 9.958 degrees from the star, so the near miss is the sky’s, not this engine’s.

The evening’s brightest light

The other half of the question has no Moon in it: what is the bright light in the evening sky? At the moment civil twilight ends each evening, the brightest-looking light more than 5 degrees up (the Moon left out), counted the same way over the same nineteen years:

latitude	evenings	a planet	most often
45° S	6,940	59%	Venus 33%, Sirius 29%, Jupiter 25%, Alpha Centauri 9%
30° S	6,940	65%	Venus 38%, Jupiter 26%, Sirius 21%, Alpha Centauri 11%
15° S	6,940	68%	Venus 39%, Jupiter 27%, Sirius 18%, Alpha Centauri 10%
0° (equator)	6,940	69%	Venus 40%, Jupiter 27%, Sirius 15%, Arcturus 8%
15° N	6,940	69%	Venus 39%, Jupiter 27%, Sirius 13%, Arcturus 9%
30° N	6,940	68%	Venus 38%, Jupiter 28%, Vega 11%, Sirius 10%
45° N	6,940	65%	Venus 33%, Jupiter 29%, Vega 16%, Arcturus 10%
55° N	6,940	54%	Jupiter 31%, Vega 29%, Venus 21%, Arcturus 9%

Here a planet does win, on 54 to 69 per cent of evenings, and Venus or Jupiter is the answer on more than half of them everywhere counted. “Brightest-looking” includes the air: a planet low in the west is dimmed by the long path through the atmosphere, so a high bright star can beat it.

How the tool decides, and how sure it is

It works out the Sun, the Moon, the five planets and the 62 brightest points among the stars (the 63 Hipparcos stars brighter than magnitude 2.15, with Alpha Centauri’s two stars counted as the one light they are to an eye) for your place and moment. Positions come from Sky Now’s engine, which was checked against JPL Horizons when it shipped; this tool adds the Moon’s parallax. Each planet’s brightness comes from the equations Mallama and Hilton published in 2018 for The Astronomical Almanac. Then every light is dimmed by the air it crosses: the airmass (about 2 at 30 degrees up, 5.6 at 10, 38 at the horizon) times an extinction coefficient from Green’s 1992 model, 0.28 magnitude per airmass at sea level.

It never gives a probability. It knows nothing about your eyes, your weather or what else is in your sky, and a remembered direction is rough. Instead it ranks the lights in the region you name and states the gap, with words fixed in advance: almost certainly when the brightest outshines the next by at least 1.5 magnitudes (four times the light) and nothing else there is within one magnitude of it; most likely at 0.75 magnitude (twice the light) or more; otherwise it says brightness alone cannot decide, and tells you what to check: which one is higher, when it will set, what binoculars would show.

It refuses anything that moves across the sky in a minute or two. Planets and stars keep their places among each other; a light that slides past them is an aircraft, a satellite, a drone or a meteor, none of which it computes. For satellites, past ones included, it sends you to tools that do: azmth, Heavens-Above and Astroviewer.

The check

research/bright-light/verify.mjs runs offline against values kept from JPL Horizons and passes 90 checks, then breaks the engine five ways and requires each break to be caught:

• Brightness. Run on Sky Now’s own positions, the magnitude equations reproduce Horizons’ values every five days from 2020 to 2032 to within 0.0025 magnitude for Mercury, 0.0014 for Venus, 0.0033 for Jupiter and 0.0089 for Saturn (rings included). Mars differs by up to 0.126, because it is computed without the paper’s two small terms for its rotation and season, which the paper’s own table puts at 0.11 and 0.15 magnitude across their full range.
• Direction. At five sites over two days, every position more than 3 degrees up matches Horizons’ refracted altitude and azimuth to within 0.074 degrees for Saturn, 0.025 for Jupiter and under 0.02 for the rest, the Moon included once its parallax is applied.
• The air. The airmass matches Horizons’ to a median 0.03 per cent, and the dimming to a median 0.0003 magnitude. The extinction coefficient Horizons uses at each site’s height is Green’s: 0.2811 at sea level, 0.1761 at 1,600 metres, 0.1719 at 1,700.
• Rising and setting. Venus, Jupiter and Saturn at two sites reach the horizon within a minute of Horizons’ own times, every one of 24 events.
• The count. One latitude of the nineteen-year run is recomputed from scratch and must equal the saved file, the list of lights ever near the Moon must be exactly the eleven above and the nine fainter ones, and the page’s tables must match the file row for row.
• The controls. A Venus constant moved by a tenth of a magnitude, a Moon without parallax, air that dims nothing, a wording rule fed half of each real gap, and Betelgeuse moved a degree on the 2034 night must each turn their family red, and do.

What it does not check: whether you will see any of this through cloud, haze or city light; whether your horizon is open; and anything faint. The magnitudes are for a clear night at sea level, and a hazy one dims low lights more.

Who else answers this

While building it I checked what already exists, and the honest answer was: most of it, apart from the Moon. That changed what it became. Two free pages already name the bright lights in the direction you are looking: CycleCalcs’ “What Is That in the Sky?”, which takes a height as well and works for an earlier night, and LiveEarthViewer’s “What’s That in the Sky?”, whose city pages take an earlier time too. Both carry advertising, neither takes “next to the Moon” as the question, and neither opens from a link on an answer for a given place, time and direction. Stellarium Web draws the whole sky for any place and moment from a link, and leaves the identifying to you. For moving lights, azmth, Heavens-Above, Astroviewer and NASA’s Spot the Station app all answer “was that the Space Station?” for times in the past. So this was built as a mode of an existing tool rather than a new one, it leads with the Moon, and it adds what none of them had: a link an assistant can hand you that opens on the answer, the same answer as a call (which_light, on this site’s MCP server), the dimming of the air, and a margin stated instead of a confidence invented.