Wikipedia:Reference desk/Archives/Science/2023 June 23

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June 23

Twin bore

This [1] (posted 11 PM yesterday) appears to show the moon very close to Venus. How often does she actually occult Venus from a particular location on the Earth's surface? 80.43.83.113 (talk) 16:25, 23 June 2023 (UTC)

The relevant article should be Lunar occultation of Venus but that's terrible. Let's say "once every few years" until a better reference has been found. I only vaguely remember having seen or having tried to see such an event in 2001. Didn't leave much of an impression, which seems a bit surprising. --Wrongfilter (talk) 16:59, 23 June 2023 (UTC)

The next one is on 9 November this year, visible from Europe, albeit in day time. [2]. --Wrongfilter (talk) 17:04, 23 June 2023 (UTC)

In 1959 the planet Venus went over a bright star. That is amazing. Sagittarian Milky Way (talk) 18:15, 23 June 2023 (UTC)

That would be normal. If a star (other than the sun) goes over Venus, that would be trouble. ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:47, 23 June 2023 (UTC)

Still pretty rare. A planet won't superimpose a planet even slightly from the 1810s to the 2060s though I think that's longer than average. Almost every time it happens it's hard or impossible to see from mid-northern latitudes it seems cause the faster the planet moves the more likely it is to be involved and Mercury is only erect from these latitudes when it's on the 18 degree from the Sun part of its elliptical orbit or when it's less than 2 hours before sunrise (Venus can reach 46 degrees from the Sun and is brighter, especially when the Mercury crescent gets too thin it gets very dim, Mars is never very bright when it's behind Mercury). Only like 1 or 2 times has anyone ever saw one of these events, mentioned it in some kind of writing and the writing is known about. A European in the 1100s saw one and said it briefly looked like a single star. Sagittarian Milky Way (talk) 21:11, 24 June 2023 (UTC)

Here is an attempt at a back-of-the-envelope calculation. For simplicity, assume the Moon's orbit is circular, so that its angular diameter is an unwavering $D=31.7',$ and that Venus, in comparison of a negligible angular diameter, orbits in the plane of the ecliptic. The Moon crosses the ecliptic twice every (synodic) month of $m=29.53\,{\text{days}}$ at an angle $\alpha =5.15^{\circ }.$ It then occludes a segment of the ecliptic of length $L=D\,{\text{cosec}}\,\alpha .$ Since there is no synchrony relation between the Moon's and Venus's orbital periods, the likelihood that Venus is at that time in the occluded segment equals $p=L/360^{\circ }.$ So on the average an observer has to wait a time ${\tfrac {1}{2}}m/p.$ This comes out at about $903\,{\text{days}}.$ However, the Earth is not transparent, and if the observer is on the hemisphere away from the Moon, they may be unable to observe the occultation, so the actual average time between occultations observed from a fixed spot may be about twice that.  --Lambiam 22:30, 23 June 2023 (UTC)

Small nitpick: the moon crosses the ecliptic twice a month, once at the ascending and once at the descending node. The nodes are not fixed in space, but rotate in a retrograde direction, completing one circuit in 18.61 years. The time from new moon to new ("synodic month" - think of church leaders meeting at the General Synod) is longer than the time the moon takes to repass a fixed star because there is continual eastward movement of the sun and moon against the stars. The time from one node to the same node on the next orbit is shorter because of the node's westward motion. The relevant "draconic month" is 2d 7h 42m shorter than the time from new moon to new. 2A00:23C3:FB81:A501:753B:8542:37AF:9712 (talk) 13:17, 24 June 2023 (UTC)

Redoing the calculation with a draconic month of $27.21\,{\text{days}}$ results in an average time between successive occultations of $832\,{\text{days}}.$  --Lambiam 20:00, 26 June 2023 (UTC)

Yes not sure why I said equator, ecliptic thus draconic month. Venus can get more than 8 degrees from the ecliptic however it isn't above 5.15 that often (by percent of a full ~quarter millennium Venus cycle) and being away from the ecliptic (up to a point) makes it get occulted more often I wonder how this affects the numbers. Sagittarian Milky Way (talk) 22:19, 26 June 2023 (UTC)

The value used for $\alpha$ above should be the angle between the orbital planes of the Moon and Venus. But if that angle varies considerably in time and can get close to $0^{\circ }\!,$ you cannot just take the average.  --Lambiam 11:29, 27 June 2023 (UTC)

The orbit planes of Venus and Earth are a 3.39 degree angle while Luna's orbit around Earth is ~4.995 to ~5.295 degrees (it varies ~0.3 degrees) from Earth's orbit around Sun. However the mean nodes circumnavigate the entire sky every 18.61 years as IP noted and the true nodes are never more than a few degrees from the mean nodes in the forwards-backwards direction while the Venus nodes take thousands of years to circumnavigate so when the nodes align the planes could be less than 2 degrees apart and roughly 1 decade later over 8 degrees apart. Due to Earth being very far from Sun (well outside Venus' orbit in fact, in various directions (towards Aries, away from Aries etc) it's actual track doesn't closely follow the "fairly steady "from Sun path" translated to "from Earth" without rotation". Venus can even do a loop that goes backwards for weeks (backwards in the rugby sense) or sometimes it halts while "returning to plane" balances "approaching Earth" so it looks like it braked and reversed instead of slowly turning. Sagittarian Milky Way (talk) 17:07, 27 June 2023 (UTC)

31.7 minutes is a bit too big. The Moon crosses the equator twice every tropical month (less than 27 1/3rd days). Sagittarian Milky Way (talk) 21:44, 24 June 2023 (UTC)

The Moon's average angular diameter is 0.52° close to 31 arcminutes and it wavers because the Earth-Moon distance varies from 356,400 to 406,700 km. Philvoids (talk) 02:44, 25 June 2023 (UTC)

The angular diameter varies between 29.3 and 34.1 arcminutes. For a back-of-the-envelope calculation, it is entirely acceptable to estimate its average as the average of the extremes.  --Lambiam 08:24, 25 June 2023 (UTC)

Oh I see where that weird number came from (bigger than "center of Earth at semi-major axis" and probably even bigger than "nearest part of Earth at semi-major axis in a jet at 36,000 feet at semi-major axis taking into account Moon mountains, the adjacent of the right triangle being 4-5 miles shorter than the Moon center to observer distance and the diameter of the horizon of the Moon sphere at Moonar sea level being extremely slightly less than the diameter of the Moonar sea level"). It orbits faster the closer it is and "halfway between km extremes" isn't the semi-major axis like it is in unperturbed 2-body ellipses but closer cause the combined gravitation effect's stronger/more perturbing for 356,000 km than 407,000 km (mostly Sun at Full and New Moon effects) and 10,000 km from inner extreme changes minutes of arc more than 10,000 km from outer extreme so halfway between extremes is too big. Good enough for back-of-the-envelope though of course. Sagittarian Milky Way (talk) 17:11, 25 June 2023 (UTC)

The Astronomical Almanac for the year 1983 includes the following note:

The most interesting event is an occultation of the naked-eye star 1 Vulpeculae by 2 Pallas on 1983 May 29^d 05^h. Preliminary predictions indicate a track 550 km wide, with the central line crossing the USA from W 78°, N 34° to W 100°, N 37° to W 124°, N 35°. The maximum duration will be 46 seconds.

For interest, such occultations can be used to measure the approximate size and shape of the occulting body. If a number of observers are spread across the width of the track, and each accurately times how long they see the star occulted, a rough outline of the body can be drawn. {The poster formerly known as 87.81.230.195} 90.197.177.243 (talk) 15:04, 26 June 2023 (UTC)

163 Erigone covered the 15th brightest star (besides 6 that never rise north of 38) halfway up New York City's sky on 3/20/2014 but it was so cloudy no one on Earth said they saw it. It wasn't even uncomfortably cold or windy or anywhere near the blocked by Earth part of the asteroids, just rainy or cloudy. Sagittarian Milky Way (talk) 18:48, 26 June 2023 (UTC)

For a list of occultations over the next millennium see list of future astronomical events. 80.43.83.113 (talk) 16:13, 27 June 2023 (UTC)