Effects of *adding* another planet to the inner solar system?

Factual Questions
#1

OK, time for me to post a question that reveals my sheer ignorance of astrophysics, but that’s still been preying on my mind for awhile…

Here’s the setup: I want to add a second Earth-type planet in our solar system. It’d be the same size, density, ecosphere, etc. as the first Earth. But I’m not going to have it suddenly enter the solar system from the outside, like a comet or anything…I’m going to have it suddenly appear in place, like magic. But otherwise, there’d be nothing supernatural about the way it interacted with the rest of the universe from that point on. (But I would make sure it started out moving at the proper speed so it’d maintain it’s orbit around the sun.)

(For the sake of clarity, I’ll just call this new planet “Deuce” from now on.)

My question is…how close could I put planet Deuce to Earth, without screwing up Earth’s orbit? Could the two planets “share” the same orbit around the sun, but still remain constantly visible to each other, or could Deuce have a slightly wider or smaller orbit than Earth, (Say, a little more or a little elss than 1 AU) but still be able to “keep pace” with Earth as it orbited the sun? I’d want to have Deuce look about as big in Earth’s sky as our moon does, for most or all of the year…would that be possible, without bringing around disastrous side effects (Like the moon being ripped out of it’s orbit; or Deuce and Earth drawing each other into a collision; or Earth getting it’s rotation or axial tilt changed, bad stuff like that.)? How close could you put Deuce to Earth, without any major ill effects?

Well, thanks for your time,
Ranchoth
(::Walks off, muttering something about cutting back on watching “Escaflowne”::slight_smile:

#2

IANAn astrophysicist, but I think the biggest barrier to this is making Deuce the same physical size as Earth, while appearing to be the same size of the Moon from Earth. Remember, the Sun and the Moon, though vastly different in size, appear to be the same size from Earth. Since we know how big we want to make Deuce, we can approximate how far away from Earth it must be.

First, some facts (all gathered from Wikipedia.com):

Diameter of Moon - 3,474.8 km
Diameter of Sun - 1,392,000 km
Diameter of Earth/Deuce - 12,756.3 km

Average distance (Earth to Moon) - 384,400 km
Average distance (Earth to Sun) - 150,000,000 km

Now, since both Moon and Sun are about the same size (from Earth), the following should hold:

Moon’s diameter / Moon’s distance ≈ Sun’s diameter / Sun’s distance

3,474.8 km / 384,400 km ≈ 1,392,000 km / 150,000,000 km

0.0090 ≈ 0.0093

Approximately equal, as we could expect. Now, we’ll split the difference to get a constant of 0.00915. Using this, we can approximate how far away Deuce must be:

Deuce’s diameter / Deuce’s distance ≈ 0.00915

12,756.3 km / Deuce’s distance ≈ 0.00915

Deuce’s distance ≈ 12,756.3 km / 0.00915 ≈ 1,394,000 km

So, it would have to be about 4 times further away than the moon - spitting distance, really. I’ll leave it to the real rocket scientists to tell you what effects this would have on Earth. My guess: not good.

#3

I would say it’s impossible for the planet to appear the size of the moon/sun and have both it and Earth in stable orbit around the sun. (I assume No matter how it would be arranged, the Earth and Deuce would pull on eachother and eventually collide. The only way to prevent this would be to have them in orbit around eachother, but that would be difficult, and would screw up everything with the moon and day/night cycles on Earth.

#4

If the planet were at one of the stable Lagrangian Points, it would be in the same orbit as the Earth, but it would be at 150 000 000 km from Earth and would seem much smaller than the Moon.
If the orbit was smaller or greater than the Earth’s, the apparent size would vary, since different orbits take different times to be completed.

#5

Couldn’t we just pull a (reading too many comics here) stick Deuce right behind the sun? That is, position Deuce so it’s always “opposite” earth? Am I making sense!? I guess the OP called for more of a brotherly Deuce, rather than an elusive one that couldn’t be visited, but I think maaaybe this is the only way it would work.

-S&S

#6

The other side of the sun will work only in a comic book. That’s not a Lagrangian point, so it’s unstable.

#7

Could we remove the moon and have it and earth orbit mutually at a slightly greater distance? Wouldn’t be perfect but couldn’t you at least get a stable orbit like that?

#8

The other side of the sun is a Lagrangian point! But you are partially right, it is unstable and could not maintain a planet in orbit.
See http://www.physics.montana.edu/faculty/cornish/lagrange.html for a simple explanation of stable and unstable Lagrangian points.

#9

The moon does not revolve around the earth. The earth and moon both revolve around the center of mass of the earth-moon system.

Replace the moon with earth[sub]2[/sub] and it and earth[sub]1[/sub] will revolve around the center of mass of the earth[sub]1[/sub]/earth[sub]2[/sub] system, which will be halfway between the two bodies, and not stable.

And yes, I do know that L3 is one of the unstable Lagrangian points, and that was supposed to be my point too. I don’t know why it didn’t come out that way. Sorry for any confusion.

#10

You can say that about any system–the Earth and the Sun also mutually orbit about a common center. But that starts to get silly. The common point in the Earth-Moon system is well below the surface of the Earth, so for all practical purposes, the Moon does orbit the Earth.

#11

There’s pretty much no way to tell, as this definitely becomes a chaotic system. Technically, we don’t know that the solar system as it’s set up now won’t “eject” (as is the technical term) Earth at some point in the future. Most of the reason we feel secure for the time being is that other planets are far enough away from Earth’s path, but there’s no telling what will happen even if you put Deuce on the opposite side of the sun. As an example, Deuce and Earth passing by now twice as fast might be enough to tug Mars out of its orbit to come crashing into one or the other. How long will it take until a catastrophe? No way to tell.

#12

Well, obviously they would orbit the centre of mass which would obviously be in the middle. I said as much in my post (“it and the earth orbit mutually”). I had had the impression that the moon was too massive to be stable due to Lagrange point reasoning, and that two bodies of comparable mass mutually orbiting each other, and together going round a bigger one, would be stable, but apparently not.

I had a go at doing the physics but it’s been too long since I’ve done anything like vector calculus. Could you explain why this is unstable, or point me at a cite? I know it’s in general chaotic, but aren’t there some stable things, like lagrange points and kemplerer rosettes?

#13

Technically, there may not be any Lagrange points in the real solar system. There are five Lagrange points in the reduced 3-body system where a very small particle interacts with two very large particles. A satellite added to the Earth-Moon system, for instance, is close enough as long as you ignore all the other planets and the sun.

Basically, in grossly oversimplified systems you can find some stable solutions, but when you’re talking about the Sun-Earth-Deuce system plus the nudges from Venus, Mercury, and the moon, it’s really too complicated to make any decent predictions.

#14

IIRC there are stable points at 1/3 and 2/3 around the orbit (i.e 3 earths could share the earth orbit is equally spaced.

#15

But hey, I was close, right?

Guys?

#16

If there is some orbital momentum for which this configuration is a solution of the equations of motion, it’s certainly not a stable solution.

#17

Ok then. Let’s do it.
Somebody call GWB.
Peace,
mangeorge

#18

Isn’t one of those stable triangle points (L4 or L5?) where Cruithne is?

#19

Nope. From this page

See the nifty applets mapping the orbit on that page and you’ll notice that it’s no where near the L4 or L5 points.

This has little to do with the OP, but they’ve discovered a large object (almost as large as Pluto) that appears to be in the Oort Cloud. At least it’s further out than the Kuiper Belt. Tentatively, it’s named Sedna