I am reading a fiction book that involves two planets called Blue and Green that orbit the same sun. Every 20 years there is something called “the conjunction”, which is when the two worlds are the least distance from eachother. During this time, while gazing at the sky, the protagonist mentions that Green is “as big as a man’s thumb”.
Is such a thing possible? Could they be closer? What’s the limit?
I don’t see why not, but it’s hard to judge, since “big as a man’s thumb” isn’t very precise, and no mention is made of the relative sizes. If we assume that the two worlds are about the same size and density, and further that they are about the size of the Earth, then they can approximately approach to within the so-called Roche limit (actual objects are held together by more than just gravity, so can actually approcah even closer, but this is back-of-the-envelope stuff here), which for a pair of Earth-sized bodies, would be about 2.423 times their radius, or about 15,450 km. An Earth-sized object 15,000 km from us would appear HUGE in the sky–it would have an angular diameter of about 24 degrees. The full Moon subtends about one degree.
Wow.
That should be one half a degree.
Quite so.
The other one is fairly easy. The moon is just about the size of your outstretched thumb (meaning the tip of your thumb can just barely cover it). It’s about 240,000 miles away. From the moon, the Earth subtends something like 2 degrees of arc, I believe, or about four times the size. So double the distance, and an object the size of the earth would look about as big as the moon does now.
I’m sure a body the size of the earth could pass that close, but I don’t think those orbits would be stable over time.
Two of Saturn’s moons, Epimetheus and Janus, regularly come close enough to each other to “exchange momentum” and trade orbits. I can imagine scaling this phenomenon up to planets orbiting a star, though I expect there would be some serious climate changes preceding and following each transition. That might make life as we know it highly unlikely.
While we’re on this subject, can we take it in the opposite direction?
Ignoring transient comets, the only two astronomical phenomena which appear to the naked eye as anything other than points (or occasionally tiny smudges) of light are the Sun and Moon.
What is the distance an object of a given size would need to be to be resolved as a small circle rather than a point of light with the naked eye? It’s probably simple trig to figure this, but I’m not skilled at how one might determine it. I’m not sure what would qualify as “a small circle” either – based on the Moon, perhaps 1 or 2 minutes of arc subtended would be on target. (Anyone who wants to refine that better knowing human optical behavior and trig is welcome to do so.)
For purposes of this question, let’s set up a list of a dozen objects:
[ul][li]A typical “small moon” of say 50 km diameter[/li][li]Our own moon[/li][li]An Earth/Venus-sized planet[/li][li]A Jovian planet – use Jupiter itself?[/li][li]A brown dwarf[/li][li]A white dwarf star[/li][li]A typical M star[/li][li]A typical Sunlike G star[/li][li]Sirius[/li][li]An O-type main sequence star[/li][li]A typical Red Giant[/li]A supergiant – Betelgeuse?[/ul]
Poly, you can use our own wolfmeister’s handy Angular Size Calculator. It tells me that an Earth-sized body would have to be about 21,919,000 km away to appear as a disc of one minute of arc, for example.
Clarifying: that’s for a disc of radius 1’, not diameter 1’; an Earth-sized body about 44 000 000 km away (twice as far) will have angular diameter 1’. Venus gets about this close to Earth at conjunction; sadly, at conjunction it is close to the Sun in the sky (and new) and so it is not easily observed then. Here’s a chart of approximate angular diameters (from this page) for the planets for 2004. This doesn’t cover an entire synodic period but gives an idea of the sizes of the planetary discs.
As I can recall a couple of years back in a Sky and Telescope article, that some people with excellent eyesight can make out the crescent of Venus when it is approaching/departing inferior conjunction with the Sun (but still have enough angular distance from the Sun’s glare). As I hopefully can recall, I believe that Venus can approach close to one arcminute in angular size.
I can use my pinky at arm’s length to cover the full moon completely. It’s surprising how little of the sky the moon really does cover, once you compare it to something you know is small.
Doesn’t speed come into effect here? I am thinking that two large bodies would be able to come closer to each other the faster they were going. If the moon was going slower, it would not be able to be so close, right?
If these two planets in the book were passing each other pretty fast, they could get pretty close. If they were going even faster, they could pass by even closer. Right?
Robert Forward, a physicist, has written a series of books that deal with two planets so close to each other that they share the same atmosphere- starting with the book Flight of the Dragonfly. Roche is a rocky, dry world, while Eau is primarily a water planet. They orbit about the center of their combined mass, and, will occasionally come so close together (it’s not a perfectly circular orbit) that water will “slosh” from Eau to Roche, and then back.
The water will slosh
From Eau to Roche,
But never the twain
Shall meet.
From Roche to Eau
They orbit just so,
One ocean, one desert,
Repeat.
Nor do I, but I’m not going to run the simulator. For those who are interested, here’s where you can find out for yourself:
Q.E.D. Posting #9
That’s the first time an SDMB member (other than myself) has referenced my website.
Thanks.
The original post regarded two planets orbiting a sun in such a way that they come into conjunction once every 20 years. Taking “year” in this case to be one revolution of the inner planet, the outer planet will have completed 19/20 of a revolution in one spin of the inner planet, so it’s period is 20/19 inner-planet-years.
Kepler’s third law tells us the ratio of the cube of the planets’ mean distance from the sun (Ro/Ri) is equal to the ratio of the square of their periods (To/Ti), making Ro/Ri = 1.0348 (approx.). If the inner planet were about the same distance from the Sun as Earth (~93M miles), it’s outer neighbor would be at 96.2M miles, or about 13 times further away than the moon is from the Earth. If the outer planet is about the size of the earth, it would appear to subtend ~1/6 of a degree in the sky, or a little less than 1/3 the size of the full moon, on a par with the separation between the naked-eye double star at the crook of the handle in the big dipper.
The gravitational force between the two planets at conjunction would be about 1/3 of 1% of the Sun’s influence–enough to perturb the orbits but hardly enough to assume they will be unstable.
Not that anyone asked…
