Zompist Bboard Again

What would the night sky of such a planet be like to intelligent life on such a planet? Would they be seeing the universe evolve super fast?

An Earth-like planet with an orbital speed of 0.99c would have an orbital distance of around five millimetres, so it'd be dominated by being inside a star in the moments after you start the simulation but before it stops being a planet.

Ketsuban wrote: ↑Sat May 18, 2024 11:51 am An Earth-like planet with an orbital speed of 0.99c would have an orbital distance of around five millimetres, so it'd be dominated by being inside a star in the moments after you start the simulation but before it stops being a planet.

It's really interesting how an object's orbital speed is governed by its distance from a central object.

One would think it were possible for an object to orbit faster than another object at the same distance around a central object.

Ahzoh wrote: ↑Sat May 18, 2024 2:46 pm It's really interesting how an object's orbital speed is governed by its distance from a central object.

One would think it were possible for an object to orbit faster than another object at the same distance around a central object.

You can be going at any speed in any location, but then your orbit isn't necessarily circular. A comet with a periapsis of about five millimetres theoretically hits 0.99c at closest approach, but I don't think a solar impactor really fits the criterion of "a planet [moving] around its star". You could also have a rogue planet travelling at 0.99c, but that's not really moving around the star in any sense since it has well above hyperbolic escape velocity.

Of course, any physical object aside from an elementary particle at a 0.99c speed in an orbit would not be able to maintain any kind of structural integrity and would rapidly disintegrate as it approached the object it was orbiting around.

You could get a more reasonable distance if you're orbiting something really massive. Say you're orbiting a supermassive black hole of 500,000 solar masses at a distance of 0.005 au (460 thousand miles); your speed will approach the speed of light. And that is (self-evidently) outside the event horizon so I guess it's theoretically stable until you take Roche limits into account.

The fastest orbital velocity I can think of would be S62 around Sgr A* (the supermassive black hole at the centre of the Milky Way) which approaches the 4927000-solar-masses object at a distance of 16 AU, which implies a velocity at periapsis of 13,000 mi/s, or 0.07c. There's probably some rough limit which I might try and work out later.

If I remember special relativity correctly, if we watch a spaceship going at .99c, we see it slowed down by a factor of 7. However, the people on the spaceship see us (and the whole universe) flying past them at .99c, so they see the universe as slowed down.

The planet doesn't work like this, because it's constantly accelerating. (Motion on a curve, like an orbit, is acceleration.) Therefore you have to bring in general relativity. I don't know the details, but I think Space60's intuition is correct (except that a factor of 7 is not super fast). After all we've tested this with (say) planes and spacecraft, to say nothing of particles circling accelerators: they all go slower from our perspective.

zompist wrote: ↑Sat May 18, 2024 4:24 pm After all we've tested this with (say) planes and spacecraft, to say nothing of particles circling accelerators: they all go slower from our perspective.

We even have tested that the speed of particles affects their decay times. For instance, this is why muons can reach the Earth's surface ─ from our perspective their decay is slowed down by their speed as they go through the Earth's atmosphere.

Subbing the Roche limit into the equation for orbital velocity, you get

v = sqrt(GM/(r(cbrt(2M/m)))

v = orbital velocity
G = 6.67 × 10^(−11)
M = mass of primary
r = radius of satellite
m = mass of satellite

To maximise the orbital velocity, we need big M and m, and small everything else (could also do with a big universal gravitational constant but it's unfortunately a constant). For a planet orbiting a star, the best we can do is probably a massive neutron star with M = 2.4 solar masses, r = 150,000km, m = 2*10^28 kg, maximal v = 530 km/s or 300 mi/s, roughly 0.2% the speed of light. You could increase this by making the radius of the planet smaller, but you also don't want to make its mass smaller. If you use Earth's values you only get 80 km/s.

We could imagine a white dwarf orbiting a neutron star, using m = 1.4 solar masses and r = 1800 km, and you get a more respectable 11,000 km/s ~ 7,000 mi/s ~ 4% c.

The only scenario where you could get speeds approaching c would be something like a small black hole orbiting a supermassive black hole. Of course your aliens couldn't be on the black hole because then they couldn't see anything – they'd have to be in orbit of it. And I think there's an equation for the minimum orbit for a satellite (the small black hole) to possess a sub-satellite (the planet with the aliens) which would probably be much much further out than the Schwarzschild radius of the supermassive black hole, which would slow you down a lot.

If you're orbiting a black hole, avoid the plunging region:

https://www.cnn.com/2024/05/17/world/bl ... index.html

Responsible black hole owners will put up warning tape, but this is not always present.

zompist wrote: ↑Sun May 19, 2024 5:13 pm If you're orbiting a black hole, avoid the plunging region:

https://www.cnn.com/2024/05/17/world/bl ... index.html

Responsible black hole owners will put up warning tape, but this is not always present.

Standards have really deteriorated since we were young, haven't they?