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[Centaur]

Here is a planetary trivia quiz. It's open-book - research is allowed. Don’t be afraid to guess - bonus points will be given for bravery. The first one to answer all five questions correctly earns the right to pose the next question or pass that right to someone else. Good Luck.


1) How many years are there between inferior conjunctions of Venus?
--A. 0.6
--B. 1.6
--C. 3.6
--D. 8.6
--E. 121.6

2) When is the earliest year in which Mars will approach closer to Earth than in 2003?
--A. 2005
--B. 2082
--C. 2287
--D. 7233
--E. 62101

3) Which of these is a triple conjunction?
--A. 3 planets sharing the same right ascension
--B. 3 planets sharing the same ecliptical longitude
--C. 2 planets and a fixed star sharing the same right ascension
--D. 2 planets and the Sun sharing the same ecliptical longitude
--E. 2 planets sharing the same ecliptical longitude thrice in less than a year

4) How many times during 1900-1999 did Mercury transit the Sun?
--A. 0
--B. 2
--C. 5
--D. 14
--E. 46

5) When is the last time that there was a transit or occultation between two planets?
--A. 1818
--B. 1940
--C. 1959
--D. 1984
--E. 2003

[Centaur]

My fellow Chicagoans embarrass me. Is no one here ambitious enough to attempt to provide answers? On two other astronomical message boards members actually participated until someone answered all questions correctly. Everyone had a good time. A more difficult bonus question was added, but folks applied logic and figured out the solution. I suppose that my neighbors simply want the answers.

OK, here they are with commentary:


1) How many years are there between inferior conjunctions of Venus?
--B. 1.6

This is the synodic period of Venus – the time it takes to lap the Earth in its race around the Sun. Venus' last inferior conjunction was the much heralded transit of 2004 JUN 08. The next IC will be on 2006 JAN 13. In the meantime there will be a greatest eastern elongation of 47°06' on 2005 NOV 03. During 8 years, Venus orbits the Sun approximately 13 times producing about 5 synodic periods. That is the famous 8-year cycle during which the dates of conjunctions and greatest elongations nearly repeat.


2) When is the earliest year in which Mars will approach closer to Earth than in 2003?
--C. 2287

It may have been more than 60,000 years since Mars was closer than in 2003, but it will take only 284 years to get even nearer. Actually, it was only slightly further in 1924 than in 2003. As Mars’ orbital eccentricity experiences a cyclical increase, it will periodically make even closer approaches until around the year 25000.

3) Which of these is a triple conjunction?
--E. 2 planets sharing the same ecliptical longitude thrice in less than a year

Occasionally one planet will appear to pass another - turn retrograde moving by the second planet again in the reverse direction - then resume direct motion for a third passage. The probability of any of the other four choices ever occurring is zero if the conjunctions must be precise.

4) How many times during 1900-1999 did Mercury transit the Sun?
--D. 14

That’s close to the average of about 13 per century. The last one occurred on 2003 MAY 07. The next one will occur on 2006 NOV 08.

5) When is the last time that there was a transit or occultation between two planets?
--A. 1818

On 1818 JAN 03 Venus transited across Jupiter. There is no record of an observation. The only recorded event since the invention of the telescope was the occultation of Mercury by Venus on 1737 MAY 28 witnessed by a lone English amateur astronomer. The next event will be a partial transit of Venus over Jupiter on 2065 NOV 22, but it will occur only 8° from the Sun making it difficult to observe.

[Rocketman]

Well darn, I just saw it. I'll participate next time, that is, if you post another.

[Centaur]

rocketman2 said:

Well darn, I just saw it. I'll participate next time, that is, if you post another.

OK then, I'll post a bonus question:


6) Whenever the shadows of three of the four Galilean satellites appear simultaneously on Jupiter, which satellite's shadow is always involved? Why?

A. Io - I
B. Europa - II
C. Ganymede - III
D. Callisto - IV
E. No satellite's shadow is always involved.

[Rocketman]

Callisto. (cheated)

I vaguely remember reading something about this...

[Chicago Astronomer - Astro Joe]

Callisto eh?

I would provided a wild guess in IO, because it's so close and revolves quicky.

The occultation of planets is a very interesting one to ponder about. One would think that this type of event would occur more often.

Hmmm.

[Centaur]

rocketman2 said:

Callisto. (cheated)

I vaguely remember reading something about this...

I can't say whether you're right or not until you answer the most important part of the question: Why?

[Centaur]

admin said:

Callisto eh?

I would provided a wild guess in IO, because it's so close and revolves quicky.

A reasonable guess and explanation. Next please.

[Centaur]

admin said:

The occultation of planets is a very interesting one to ponder about. One would think that this type of event would occur more often.

Actually, we're living during a long and unsual drought for the mutual transits or occultations between planets. There were 2 each in 1477 and 1708. In fact, there were 4 from 1702 to 1708. There will be 6 from 2065 to 2104. Either get a time machine or take good care of your body. ;D

[Rocketman]

Well I would say Callisto because it orbits slower, thus casting a shadow on Jupiter longer...


Seeing three shadows on Jupiter happens only about once or twice a decade. Io, Ganymede, and Callisto orbit Jupiter at different rates. Their shadows likewise cross Jupiter's face at different rates. For example, the outermost moon Callisto orbits the slowest of the three satellites. Callisto's shadow moves across the planet once for every 20 shadow crossings of Io. Add the crossing rate of Ganymede's shadow, and the possibility of a triple eclipse becomes even more rare.

Gravitational perturbation?


Ok.

[Centaur]

rocketman2 said:

Well I would say Callisto because it orbits slower, thus casting a shadow on Jupiter longer...


Seeing three shadows on Jupiter happens only about once or twice a decade. Io, Ganymede, and Callisto orbit Jupiter at different rates. Their shadows likewise cross Jupiter's face at different rates. For example, the outermost moon Callisto orbits the slowest of the three satellites. Callisto's shadow moves across the planet once for every 20 shadow crossings of Io. Add the crossing rate of Ganymede's shadow and the possibility of a triple eclipse becomes even more rare.

Ok.

Nice try, but the speed of crossing is irrelevant. And rarity is not the concern. One of the four is always involved in a triple shadow transit. None of the others is always involved. That is not merely true over a period of centuries, but over millions or perhaps billions of years.

[Centaur]

Obviously, my previous post eliminated choice "E". I will provide another hint and say that a quadruple shadow transit is absolutely impossible. There is a logical explanation for all of this. It does not have to do with probabilities.

[Centaur]

OK, it's been over 24 hours since I gave the last hint, so everyone must be stumped. Kudos to Joe and Grady for giving it the old college try. Yes, Grady was right; the answer was Callisto, and he was hinting at the reason when he added mention of gravitational perturbation. Here's the explanation:

The orbital periods of the inner three Galilean satellites are locked into an harmonic resonance due to gravitational interactions with each other. If you were a fictional observer with X-ray vision located at the center of Jupiter, whenever two of the inner three satellites appeared in conjunction with each other, the other one would be far from the vicinity of the paired satellites. It's the only known case of precise synchronization in the solar family involving more than two orbiting bodies. Callisto (IV) does not join in that relationship. Of course, due to the harmonics there can never be a quadruple shadow event.

The last triple shadow event occurred on 2004 MAR 28, involving I, III & IV. The next three will be:

2013 OCT 12 - I, II & IV

2014 JUN 03 - II, III & IV

2015 JAN 24 - I, II & IV

Then a break until 2032.

[Chicago Astronomer - Astro Joe]

Quite an interesting factoid. Now considering harmonics, why couldn't the 4th moon join in on a shadow event?

At one time or another, I would think that all four meet up on one side of the planet, transit the sun, (from Jupiters perspective), at the same time, and ergo...cast shadows.

[Centaur]

admin said:

Quite an interesting factoid. Now considering harmonics, why couldn't the 4th moon join in on a shadow event?

At one time or another, I would think that all four meet up on one side of the planet, transit the sun, (from Jupiters perspective), at the same time, and ergo...cast shadows.

Yes, it's interesting, but not a "factoid" - it's actually true. The suffix "oid" means "resembling in appearance but not genuine", e.g. an asteroid resembles a star in a telescope but is not a star, or an android is a robot and not a man ("andr" being the prefix meaning man.) Something resembling a fact, but is not actually one must be a myth or lie. I believe CNN stopped using the term to mean a brief fact after enough linguists had complained. Forgive me for harping on that, but while working in the news media it became one of my pet peeves. dictionary.reference.com/search?q=factoid

Returning to your actual question, Joe, please re-read my explanation of why the inner three Galilean satellites can never appear near conjunction together for a Jovian observer. If those three cannot ever appear together, then it follows that four cannot appear together. If you would like a deeper analysis, I'll provide it. But be prepared for something long-winded when diagrams can't be drawn.

[Chicago Astronomer - Astro Joe]

"it became one of my pet peeves"

Oh Curt....hee hee.

This will be an interesting dip into celestial mechanics and bring Newton, Brahe and Kepler into the conversation. If you have links with pics to demonstrate the motion of bodies, then I'll post them.

I'll be playing Holst's "The Planets" while I read your explanation...

[Centaur]

Factoid in the dictionary: dictionary.reference.com/search?q=factoid

If you have access to Mathematical Astronomy Morsels by Jean Meeus, check out chapters 43 and 44. I checked the Amazon site and they won't let you search inside that book the way you can with mine. But great diagrams are on pages 272 and 274. If you can't find a copy, then I'll provide a long prose narrative if what I stated four posts above is insufficient.

[Centaur]

OK, here's the long version.

For this explanation let’s define a chron as a unit of time equal to 1.175154518 dynamical days. The Galilean satellites, Io, Europa, Ganymede and Callisto will be referred to as #1, #2, #3 and #4 respectively. The synodic period between any pair of Jovian satellites is the average time it takes one to lap the other as they revolve around Jupiter.

The synodic period between #1 and #3 is precisely 2 chrons.
The synodic period between #1 and #2 is precisely 3 chrons.
The synodic period between #2 and #3 is precisely 6 chrons.
The synodic period between #4 and any of the others is not an integer number of chrons.

Our observer is located at Jupiter’s center viewing the satellites by X-ray vision.

Whenever #2 and #3 appear in conjunction with each other, #1 is always in opposition (180°) to them.

Whenever #1 and #2 appear in conjunction with each other, #3 is always either 90° ahead of them or 90° behind them.

Whenever #1 and #3 appear in conjunction with each other, #2 is always either 60° ahead of them, 60° behind them or in opposition to them.

Never will #1, #2, and #3 all appear close to being in simultaneous conjunction with each other. Whenever two of them are in conjunction with each other, the third is always at least 60° away. This being true, it follows logically that all four Galilean satellites can never appear close to being in simultaneous conjunction with each other.

#4 could conceivably be at any point in its orbit whenever any of the above configurations occur. Therefore, it is the only one that always participates whenever three Galilean satellites appear close to being in simultaneous conjunction with each other. If the Sun were also to appear to be close to conjunction with them and Jupiter's tilt toward Earth were small, then we might have a triple shadow event.

[Rocketman]

Centaur sure knows his stuff ;D