Negative Mass

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AlternateGravity
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Negative Mass

Post by AlternateGravity »

I was running some simulations with negative mass and found some interesting properties regarding negative mass. I found that negative mass is attracted to positive mass but positive mass is repelled by negative mass. When I made two objects of equal and opposite mass that initially weren't moving the object with the two objects would accelerate with the positive mass in front and the negative mass and positive mass remaining an equal distance apart. Eventually a negative and positive mass planet would be going very fast even if at first they weren't moving. I found that if I removed a negative mass planet the positive mass planet would continue moving very fast and if the planet collided with a star at the right speed the star would absorb the planet and the motion of the planet would get transferred to the star that absorbed it. I also found that it was hard to get a planet to touch a negative mass star as when it would get close it would be repelled by the negative mass. When I moved a planet towards a negative mass star it would curve away from the negative mass. I also found that if I created a cluster of fixed stars with a negative mass star surrounded by some positive mass stars and with the mass of the negative mass star equal to the positive mass star planets could not have stable orbits and would either spiral into the group of stars or spiral away from the group of stars. When the planets spiraled into the group of stars they would be repelled by the negative mass and would move away from the negative mass star.
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robly18
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Re: Negative Mass

Post by robly18 »

Yeah, negative mass has some pretty neat properties.
Something else we found about the whole 2 objects with opposite mass thing is that it actually doesn't break conservation of momentum: since the net mass is zero, the energy needed to move it is null!
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A Random Player
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Re: Negative Mass

Post by A Random Player »

Here's some more stuff about it. Really cool, despite it being unrealistic (for now?)
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AlternateGravity
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Re: Negative Mass

Post by AlternateGravity »

I found that if I put a negative mass planet in orbit around a positive mass star the system did not seem to accelerate.
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robly18
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Re: Negative Mass

Post by robly18 »

Unless the total mass is 0, then the system stays where it is.
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testtubegames
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Re: Negative Mass

Post by testtubegames »

AlternateGravity wrote:I found that if I put a negative mass planet in orbit around a positive mass star the system did not seem to accelerate.
Huh, I hadn't noticed that before. And confused me for a bit, too.

At first, I thought it might be what robly said... where unless the total mass is 0, you don't get acceleration. (If I understood you correctly.) But I put a 1000 mass star next to a -1030 mass star, and they still accelerated. The non-acceleration just happened when you set up an orbit.

When I looked closer, though, I noticed that the whole system is still accelerating. (Setting up a -10 planet around a 1000 star, say) It's acceleration just changes direction as the planet orbits. So the net effect each orbit is a displacement... but you end up with the same velocity as you started with. Seems to happen any time you set up an orbit. Pretty neat -- kinematics in action!
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robly18
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Re: Negative Mass

Post by robly18 »

testtubegames wrote:At first, I thought it might be what robly said... where unless the total mass is 0, you don't get acceleration. (If I understood you correctly.) But I put a 1000 mass star next to a -1030 mass star, and they still accelerated. The non-acceleration just happened when you set up an orbit.

Actually, if you'll notice: The negative star gets closer and closer to the other one, approaching it and eventually getting past it, reversing direction; and acting like a pendulum of sorts.

The only event in which this does not happen is if their masses are exactly the opposite of one another.

Because the CoM always stays in the same place; it's just that if the total mass is zero, then there is none.
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exfret
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Re: Negative Mass

Post by exfret »

I've always seen cycloids going on when I put a negative-mass planet around a positive-mass sun. So, I guess if you balance the starting velocities, you could end up with a perfectly stationary (CoM-wise) system. When the masses are equal, I don't really know what happens, but if the negative-mass planet has less mass than the positive mass star has positive mass, then I'd expect acceleration to occur (total mass of 0 could be like a parabola and negative might be like a hyperbola in the escape behaviors).

Edit: I was right. If total mass is positive, the negative planet can orbit the negative planet. If the total mass is zero, the negative mass *just barely* can't make a full orbit, just like in a parabolic-escape-trajectory situation. If the total mass is negative, then the smaller the ratio of the negative mass to the positive mass (smaller, cuz it's negative), the less the negative mass can go around the positive mass, just like how in a hyperbolic escape situation, the escaping body only reaches a certain angle to the mass it's escaping from.
Last edited by exfret on Mon Jul 07, 2014 9:21 pm, edited 1 time in total.
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testtubegames
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Re: Negative Mass

Post by testtubegames »

Now I'm all turned around. Man, negative masses are cooler than I thought.

Well it's true that if the two planets' masses don't add up to zero, there's a center of mass that needs to stay stationary. (Assuming we're in the center of mass frame)

Strangely, though, the center of mass tends not to lie between the two objects anymore. Which means the two objects can indeed accelerate away from their center of mass. :shock:

Let's confine everything to a 1D problem. The center of mass is generally: Xc = (m1*x1+m2*x2)/(m1+m2). A weighted average of the location of the two objects. If their masses are equal, it's directly in the middle. And for positive masses, it will always be between them.

But suppose the two planets have mass 100 and -110. Then (doing a bit o' math), if planet 1 is at x=1, and planet 2 is at x=-1... the the center of mass is at Xc = 21. (Plus or minus, depending on which had the negative mass). Moral of the story: it's waaay far away. And the further apart the two planets get, the further away their center of mass is from them. (Generally, if the distance between them is 2a, the distance from their midpoint to the center of mass is 21*a)

So, as the two planets drift apart from one another, they'll be zipping away from their center of mass. If they get closer together, they'll move back towards it. So you can get everything accelerating still, without violating conservation of momentum. Crazy.
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robly18
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Re: Negative Mass

Post by robly18 »

Interesting. Didn't consider the fact that they might diverge, accelerating.

Let's see: F = G*m1*m2*f(r). If m1 or m2 is negative, then m1*m2 < 0, making F negative. This tells us:

The positive planet is the one getting away from the negative
The negative planet is attracted nonetheless, because it cancels out when doing the math from F to v.

So if the positive one is on the right, the system accelerates right, at first at least.

If their masses are the negative of one another (i.e. 10, -10) they accelerate at a constant rate and stay at the same distance

If the positive mass is greater, then the negative one accelerates faster than it, eventually outrunning it, and thus the system starts accelerating in the opposite direction, thus orbiting around the CoM

And finally, if the negative mass is greater... Again, we get the case where infinite motion. The positive planet outruns the negative, which never reaches it, so they keep accelerating from each other. However, in this case the acceleration decreases as they diverge.
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