Planetary Orbits

[SixSixSix]

A couple of questions for any amateur (or professional) astronomers out there.

Would it be possible for an Earth like planet (ie roughly Earth's size, with an Earth like moon, about the same distance as Earth from a Sun-like star) to have a rotation period equal to its revolution period? In other words, it would effectively have a day the same length as its year. I believe the Moon more or less has this, and there are planets that have a longer day than their year, but I'm not sure what factors influence rotation speed.

Another question: how big can comets get? Could you have a planet sized comet with a highly elliptical orbit, such that it spends a short amount of time very close to the star and a much longer time very far away? Or would a celestial body of that size decay fairly rapidly into a more stable orbit?

Answers such as, "Try this website" etc will be fine.

Incidentally - this isn't a homework assignment or the like. I'm considering a few ideas for a new roleplaying game setting I'm planning on starting soon, and the gaming possibilities of this options appeals to me (of course, it's a game - I can say that things are however I wish - but I like my games to at least have a moderately believable basis).

 

[Dilb]

Fortunately, these are fairly easy questions, so I'll try answering them.

To answer your first questions: Yes. The distance from the sun to the earth determines the time it takes to revolve around the sun, so the year would be the same, but nothing stops a planet from simply having less spin to it. Day length is mostly due to how the earth was formed.

Day length is affected by tidal forces (gravity pulling the closer part of the planet slightly more than the further part), which streches the earth and causes some rotational energy to be lost. I believe this slowed the moon's day. The moon also has a heavy side, which caused the rotation to be locked into the same period as it's rotation around the earth.

As to the second question: I don't know if things that should be called comets would ever be planet sized, but a planet could be in as large an elliptical orbit as you like and be stable. Really circles are just a special case of ellipses. As long as nothing significantly pulls it other than the sun (like a planet in a closer orbit might) or it doesn't hit anything, (also like a planet in a closer orbit), it's angular momentum and energy can't change, so it stays in the same orbit.

You might want to look at Kepler's Laws. In particular, I'd recommend seeing how the 3rd law discribes the period of an orbit.

 

[pauldmin]

Mercury has an orbit similar to what you are talking about, although it is on a 3:2 ratio, so it has a very long solar day ( about 176 earth days ).

Certainly, the Earth and Moon could have a similar orbit, although our moon is unusually large for a normally created satellite and was probably formed as the result of a collision with another planetoid. This may or may not produce the required rotation.

The more important consideration is what would happen to the weather systems in such a scenario? With one side being heated constantly, you would get some very strong winds being generated, transferring hot air to the dark side and cold air the opposite direction. I presume this would result in a constant cold wind at the dark/light interface, where most life would have to congregate in order to survive.

 

[Beady]

Would it be possible for an Earth like planet (ie roughly Earth's size, with an Earth like moon, about the same distance as Earth from a Sun-like star) to have a rotation period equal to its revolution period?

AIUI, earth's rotation on its axis is slowing because of gravitational interaction with the moon, and there may well come a time when it always presents the same face to the moon, as the moon does to earth (I *think* this has already happened with Pluto/Chiron). Somewhere in here (haven't done the math), the earth's rotation may well match its revolution. So, yes, it's possible, by demonstration.

Could you have a planet sized comet with a highly elliptical orbit, such that it spends a short amount of time very close to the star and a much longer time very far away?

Again, haven't done the math, but I would think that anything having the mass of a planet would have enough internal gravitational interaction to pull the individual pieces together into an actual planet. As Dilb noted, there's no reason a large object can't have an eliptical orbit, an elipse is just a funny circle. Also, as Dilb touched on, the really interesting part comes when you consider the interaction of such a body in such an orbit with other bodies in that same star system. You might want to investigate the role of Jupiter in deflecting comets, for example.

 

[SixSixSix]

Thanks for the responses, guys! I think I'm going to use both ideas; the comet might serve as the home for some nasty guys that only come around every few centuries (ripped off from Anne McCaffery, I guess), while the "Dark Side of the Earth" planet will serve as the main campaign setting. Good point about the weather systems as well; I'll keep that in mind (although I plan on having some life on both the light and the dark side - though fairly different from each other).

One further question: let's suppose I give this planet-with-a-year-long-day a moon as well. Are solar eclipses pretty much inevitable for a three-body system like this, or would there be possible orbits where they would never occur? I'm thinking it could be interesting if there was a solar eclipse on (say) an annual or semi-annual basis, where all sorts of mayhem can occur.

 

[Earthborn]

The National Geographic Channel series "Extraterrestrial" had exactly such a planet, called Aurelia. Here's more on this hypothetical planet and its weird atmospheric conditions.

 

[Earthborn]

Are solar eclipses pretty much inevitable for a three-body system like this, or would there be possible orbits where they would never occur?

That depends on what angle the orbit of the moon is to the orbit of the planet around its sun. If the moon orbits along the planet's equator, there will be solar eclipses very often. If it orbits over the poles, there never will be.

I'm thinking it could be interesting if there was a solar eclipse on (say) an annual or semi-annual basis, where all sorts of mayhem can occur.

Solar eclipses on Earth happen on a semi-annual basis. They are only visible within a narrow band on the ground, which is why most people miss them most of the time. On another planet that won't be any different, although the band may be wider if the moon is much bigger or closer than Earth's moon is.

 

[Yllanes]

To add to the replies above, a year-long day is not only possible, but also the stable configuration. If your day is not as long as your year, you will have tidal forces, etc., so a system were the revolution and rotation take the same time is in its state of minimum energy. Because of this, all planets are slowly matching their rotation and revolution periods (very slowly, it would certainly take much more time than what our Solar System has left).

 

[wollery]

These pages may help.

 

[Earthborn]

If it orbits over the poles, there never will be.

That's not true. The orbit of the moon does not rotate together with the planet, therefore a polar orbit will still appear above different parts of the planet and a solar eclips may still be possible.

 

[wollery]

Also a polar orbit would cause all sorts of weird effects on the body being orbited. Tidal dragging works on both bodies.

 

[Cuddles]

One further question: let's suppose I give this planet-with-a-year-long-day a moon as well. Are solar eclipses pretty much inevitable for a three-body system like this, or would there be possible orbits where they would never occur? I'm thinking it could be interesting if there was a solar eclipse on (say) an annual or semi-annual basis, where all sorts of mayhem can occur.

Solar eclipses would actually be very unlikely. At the moment the Moon is just the right distance from Earth to just cover the Sun. In thousands of years (not much time astronomically speaking) it will be too far away and only annular eclipses will be possible, where the Moon only partially covers the Sun. If you take a planet, whatever it's day length, and give it a randomly sized and placed moon it is very unlikely that total eclipses will occur.

Of course, this assumes an Earth-like orbit. If a planet orbits much further away from the star then total eclipses are much more likely, but since the star will appear so much smaller the most likely case here would be for the moon to completely obscure the star, including the corona which is the signature of eclipses as we know them. As stated by Earthborn, the frequency depends on the angle of the moon's orbit.

 

[CaveDave]

Wierder yet...

Imagine an Earth-sized planet with a Terran-sized moon (ie, like Earth's moon) but the moon "counterrotates" to the planet's rotation, but on the equatorial plane.
Now, to to get jiggy wid it, the planet's axis is tilted 90 degrees to the star system's main axis, so that the planet's rotational axis lies in the ecliptic and the year involves one point when the "south" pole faces the star, another, 1/4 year later, when the star moves east-to-west, 1/4 year later the "north" pole faces the star, and 1/4 year later the star moves west-to-east.
Seasons and weather would be remarkable, at least.

Any reason TLOP won't allow this?

-----------

Also, you should read "Nightfall" by Isaac Asimov for a wierd scenario.

Cheers and happy gaming,
Dave

 

[Dilb]

Wierder yet...

Imagine an Earth-sized planet with a Terran-sized moon (ie, like Earth's moon) but the moon "counterrotates" to the planet's rotation, but on the equatorial plane.
Now, to to get jiggy wid it, the planet's axis is tilted 90 degrees to the star system's main axis, so that the planet's rotational axis lies in the ecliptic and the year involves one point when the "south" pole faces the star, another, 1/4 year later, when the star moves east-to-west, 1/4 year later the "north" pole faces the star, and 1/4 year later the star moves west-to-east.
Seasons and weather would be remarkable, at least.

Any reason TLOP won't allow this?

As far as I know it should be possible, unless you get into planetary formation physics. If you suppose a planet that is rotating like that, nothing should cause it to shift into some other configuration.

Sixsixsix, with 3 bodies, the results are almost impossible to predict. As a physics student (hopefully the pickiest sort of person to question the physics undermining an RPG), I wouldn't fault anyone who invents a solar system where such a thing happens. The 3 body problem is an example of where the math is so complicated it's not possible to come up with exact solutions, except in a few (and I do mean few, like 8 or so) special cases. Unless you happen to be roleplaying a group of astrophysicists (as in the people and the characters are astrophysicists) I wouldn't worry about eclipses, regardless of whether they occur or don't. As an example, I'm pretty sure you could have a moon that orbits perpendicular to the sun and never crosses in front of the planet.

Beady, you're right that the earth is slowing down due to the moon. It's fairly intuitive that anything that causes the water level to rise and fall (such that work can be extracted, like with tidal generators) is wasting energy, so the earth is slowing down. There's also the idea that the tidal forces raise a bulge in the planet, and the rotation shifts the bulge so it's not directly facing the sun, and as a result there's a torque on the planet that causes it to slow it's rotation. I don't think the earth will tidally lock to the moon before the sun runs down, but it's at least neat to consider. IIRC dinosaurs had an 18 hour day.