h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

This is one of those questions that keeps me awake at night:

If a planet orbited a sun at near the speed of light, what would its inhabitants experience of reality be? For instance, how would they experience time - would they be constantly travelling in time relative to the rest of the universe, and what would they see if they gazed out at the universe?

I imagine the angular momentum would either chuck them out to visit the rest of the universe, or squash them flat, before being inside the sun could cook them.

Now for the (not) science bit... (c)Jennifer Anniston.

I think, from their viewpoint, the rest of the universe would be moving at close to lightspeed, and would therefore experience time dilation.

I thought it might be unlikely for anyone or anything to live on a planet orbiting so fast, so the question was really hyperthetical, (the scenario is presumably at least hyperthetically possible).

Assuming it was possible and that the planet spun on its axis at about the same rate as the Earth, it occured to me that whilst a day may last 24 hours, a year may last possibly just a few minutes.

Also, if someone on the planet surface, facing the direction of the planet's orbit were to fire a bullet from a gun, what would happen to the bullet? Combined with the speed of orbit the bullet would theoretically be travelling faster than light.

The first thing I'll say is that this situation is much more complicated than people think, and lots of people who know a small amount of physics, including myself, are likely to get the wrong answer. So treat all answers with suspicion.

What would happen to the bulllet? That's an easy one. We're used to working out relative speeds by adding them. If you're driving a car at 60 miles an hour and you shoot a bullet out the front at 1000 miles per hour, the speed of the bullet relative to the ground is 1060. But this simple addition rule doesn't apply as you get closer to the speed of light.

If you are travelling at, say half the speed of light and the bullet is travelling relative to you are half the speed of light in the same direction, the bullet is not travelling at the speed of light relative to the stationary viewer. There's a more complicated formula for calculating the relative speed, and it ensures that the combined result is never greater than the speed of light. In the extreme case, it the bullet is travelling at almost the speed of light (0.9999c) relative to you on the planet, then it will also be travelling at almost the speed of light relative to the stationary viewers.

If the planet spun once a day and went around the sun once a minute, then a year would indeed be much shorter than a day. Venus has the situation where a year is shorter than a day, although not by that much.

There's only two ways you could get a planet to stay in an orbit like that - shoot a giant rocket outwards away from the sun, pushing the planet in towards the sun. This would provide the centripetal acceleration needed to stay in a circle, rather than shooting off in a straight line into space. The other way is to have a very powerful gravity source and to orbit very close to it. If this was a normal star, then the orbital distance from the centre would probably put you inside the star which would slow down the planet. You could probably do it around a black hole, though.

There are now two views of what is happening to the planet. According to Einstein, the physics of what happens should come up with the same results whether the universe is stationary and the planet moving or vice versa. In the traditional stationary universe view, the planet is speeding around and the gravity of the black hole is pulling it inward into a circle. In the more unusual 'planet stationary, universe moving' view, the planet is fixed above the black hole, and the universe is rotation rapidly around the planet. A rotating mass generates a gravity field by the laws of General Relativity. And the entire universe rotating around the planet generates a sufficient gravity field to pull on the planet and counteract the gravity of the black hole.

Time dilation is the next problem and I'll need to think about that one.

Assuming orbiting a black hole of some chosen mass, how tight would an orbit need to be to enable a body to orbit at close to lightspeed, compared with the event horizon of the black hole?

I think the orbiting speed at the event horizon would be the speed of light, so just outside the event horizon, it would be just less than the speed of light.

The photon sphere where photons theoretically orbit the hole is 1.5 times bigger than the Event horizon, unless the hole is spinning, which complicates matters.

Zube

I think that the people on the planet would see their stars being both blue and redshifted. So if you were looking up at the sky one night, on one half the stars would have a blueish colur and the other half a reddish colour. Though which side would depend on the direction of your orbit. It would then change when you reached the opposite end of your orbit.