I know it might be too soon to talk about some of the details in Star Wars: The Force Awakens, so you might want to wait on this blog post. This is your warning. You still have time to leave.
While you consider your decision, here is a random picture.
OK. You're still here. I guess that means we can talk about Star Wars. Specifically, the physics of the awesome Starkiller Base.
Yes, everyone knows the physics of Starkiller Base isn't perfect. It doesn't have to be. That doesn't mean we can't have a discussion about the science of a star-sucking planet killer. Before we get to the questions, though, let me start with my basic assumptions about some of the parameters of the First Order's weapon of mass destruction. I've seen the movie just once (so far), but here's what I can guess.
- The Starkiller gets its power by sucking out a star. I am going to say the base draws all of the star's mass into the weapon, leaving nothing behind. Clearly scholars could debate the mechanics of a star suck for decades without really deciding how it works.
- This mass-sucking process is quick. Let's say it takes 10 hours. Really, it doesn't matter if it is just one hour or 48 hours. Either way, that's really fast in terms of astronomical processes.
- The Starkiller fires something at other planets. I have no idea what it is, but it can reach another star system and destroy planets.
This is what I'll start with. Now I will also use two physics principles (other than saying mass is conserved). First, I will assume that momentum is conserved during the star sucking. This means that if the center of mass of the star-planet system is stationary, the center of mass will be in the same location after suckage.
Second, angular momentum will be conserved. If there are no external torques on the planet-star system, then the total angular momentum should be the same both before and after the planet absorbs the mass of the star. If I assume the star is much more massive than the planet, then just about all the angular momentum before the weapon charges is due to the orbital motion of the planet. However, there also is a component of angular momentum due to the rotation of the planet. If the rotation of the planet is the same direction as the orbit, then the total angular momentum can be written as:
I will use this expression to answer one of the following questions.
Since the center of mass of the Starkiller Base plus the star would remain the same, as the base accumulated mass and the star lost mass the base would move to the center of mass. Assuming a star like our sun and a planet like Earth, the center of mass starts inside the sun. This means that at the end of the suck, there would be a planet where the star used to be.
What would this do to the rest of the planets in the star system? Nothing significant, actually. The primary interaction for the orbit of a planet is the gravitational interaction with the star. Now that the star is replaced with a planet with approximately the same mass as the star, nothing really changes.
OK, technically the planet-planet gravitational interaction would change since one of the planets moved. However, this is so small a force compared to the pull from the star that you could ignore it. In the long term it might cause a slight shift in orbits---but who cares, the star just disappeared. That's a much bigger problem.
Let's start with some numbers. Assuming a planet like Earth and a star like our sun, we have the following two masses:
- Mass of star = 2 x 1030 kg
- Mass of Starkiller Base = 6 x 1024 kg
The mass of the star is 300,000 times greater than the base. If all this mass is now inside the planet, then the gravitational field on the surface of the base would increase. Again, assuming an Earth-like planet the starting surface gravitational field would be 9.8 N/kg. If the radius of the base is the same as the Earth, increasing the mass by a factor of 300,000 would put the surface field at about 3 million N/kg. No one would be able to move. The would all be squashed on the surface of the planet---which also would be crushed.
If the Starkiller base maintained its size, it wouldn't be quite small enough to turn into a black hole---but it's close. If the radius decreased to 3 x 103 m, it would be a black hole.
But wait! There's more. Remember what I said about angular momentum? As the Starkiller moves from its orbit to the new center of mass, it will no longer be moving around in a circle. Instead it will only be spinning. To conserve angular momentum, the planet-base must increase its rotational angular velocity. But by how much? Let's say that the Earth is the Starkiller base so that I can use known mass and orbital data. Before the star-sucking takes place, I will assume all of the angular momentum is in the orbit (neglecting the rotation of both the sun and Earth). After sucking, it's all angular momentum due to rotation.
Putting in values for our Earth-sun, I get a final planet rotation rate of 43.7 revolutions per second. Earth, of course, has a rotation rate of one revolution per day. This rotation rate is fast enough to fling everyone off the planet---or is it? What about the increased gravitational force from the extra mass? Would that be enough to keep a person on the surface of the planet?
Let's assume a human is standing on the equator of this spinning planet. In the accelerating reference frame of the human, there are two forces: the downward gravitational force and the fake force pushing away from the center of rotation (centrifugal force). The centrifugal force depends on the mass of the human, the angular velocity and the radius of rotation. For the gravitational force, it depends also on the radius of the planet, but also the mass of the planet. Setting these two forces equal to each other I can solve for the mass of the planet needed to hold people down.
In order for the human to stay on the surface, the mass of the planet would have to be greater than 2.9 x 1035 kg---which is quite a bit smaller than the mass of the star. These guys are going to fly off the planet. They're doomed.
I don't know how the Starkiller Base moves, but it must have something like a hyperdrive to get it to the next star. But when it jumps out of the system, what happens to the planets left behind? Obviously, they will be literally "in the dark," but they will also be without a star to exert gravitational forces. Just for fun, I made a quick model that shows two planets with a star that goes away.
Without a gravitational force to make planets follow a circular orbit, they would move off in a straight line. OK, technically the two planets would still interact, but this is a very small effect. But really, you could say Starkiller Base kills a bunch of planets---the ones it targets and the ones it leaves behind.
If you want something to calculate on your own, here are some suggestions:
- Suppose you build a super awesome Starkiller Base that can shoot at stuff in another star system. How hard would it be to aim this weapon? Estimate the angular accuracy you would need to hit just one planet in a star system one lightyear away. Make a comparison to shooting something with a gun.
- If momentum is conserved during the firing of this Starkiller, what is the recoil velocity of the planet? You will need to estimate the speed of the stuff fired from the weapon (I assume it is all the mass of the absorbed star).
- Pretend you are a writer for Star Wars. Come up with a plausible method for Starkiller Base to shoot vast distances in just a few hours.
- Would the process of a Starkiller Base sucking up a star create gravitational waves? Would they be detectable at Earth's position? Is this the rumored gravitational wave detected by LIGO?
