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SciFi movies and pathetic misconceptions of tech failing for the story line.

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vad:
If the elevator were tall enough, you could surpass the speed of light. Or could you?

rdl:

--- Quote from: Kim Christensen on April 18, 2023, 05:09:56 pm ---Since the the angular velocity of the Earth's rotation at the equator is 465.1m/s, if you launched a rocket straight up (And managed to maintain that angular velocity) you could reach an altitude where 465.1m/s of orbital speed was sufficient to prevent you from reentering Earth's atmosphere
....

--- End quote ---

I think your decimal point is in the wrong place.


--- Quote from: vad on April 18, 2023, 07:15:53 pm ---If the elevator were tall enough, you could surpass the speed of light. Or could you?

--- End quote ---

In theory. At least I think so. In reality  probably no material would ever be strong enough and you would have problems with it colliding with the Moon.

After writing that I found a calculator and if I used it right, the height would be a bit over 4 billion kilometers. It would reach out past Pluto.

Kim Christensen:

--- Quote from: rdl on April 18, 2023, 08:17:34 pm ---
--- Quote from: Kim Christensen on April 18, 2023, 05:09:56 pm ---Since the the angular velocity of the Earth's rotation at the equator is 465.1m/s, if you launched a rocket straight up (And managed to maintain that angular velocity) you could reach an altitude where 465.1m/s of orbital speed was sufficient to prevent you from reentering Earth's atmosphere
....

--- End quote ---
I think your decimal point is in the wrong place.

--- End quote ---

There are 86,400 seconds in a day. Therefore at 465.1m/s, a single point on the equator would have moved 40,184,640 meters (40,185 km in 24 hours) which is approximately the circumference of the Earth at the equator.


--- Quote ---After writing that I found a calculator and if I used it right, the height would be a bit over 4 billion kilometers. It would reach out past Pluto.

--- End quote ---

Most of these calculators only take a single body into account to keep the math simple. I think you had the Sun selected as the primary SOI instead of the Earth.
Oopps. I see you're talking about the speed of light here...

But you got me thinking... A little research turned up the term Hill Sphere which is basically the highest orbit that could be maintained, at least temporarily, around a body. For the Earth, this is 1.47 million Km, so my theoretical orbit at 1.84 million Km from Earth would be impossible because an object that far from Earth would end up in orbit around the Sun instead of the Earth.

tszaboo:

--- Quote from: Kim Christensen on April 18, 2023, 05:09:56 pm ---
--- Quote from: rdl on April 18, 2023, 04:30:15 pm ---
--- Quote from: BrianHG on April 18, 2023, 02:24:37 pm ---My meaning 'straight up' as in keeping a relative stationary position above the ground.  This means if the ground is rotating, you do have some orbital speed, it's just at low orbits like 408km up, it is not enough to stop you from falling back down like a rock.

--- End quote ---
It's not enough at any orbit.

--- End quote ---

If you had a 35,786 km tall space-elevator at Earth's equator, and rode it all the way to the top and stepped off, you'd stay where you were relative to the elevator and the ground. (More or less)
This is because the elevator is rotating at 1 RPD (1 revolution per day) with the Earth. ie: The top of the elevator would have an angular velocity of apx 3.07km/sec due to it being affixed to the ground.

Since the the angular velocity of the Earth's rotation at the equator is 465.1m/s, if you launched a rocket straight up (And managed to maintain that angular velocity) you could reach an altitude where 465.1m/s of orbital speed was sufficient to prevent you from reentering Earth's atmosphere. Around 1.84 million Km altitude.. Not sure if this would be a stable Earth orbit due to influences from the Sun and Moon. It would probably end up in solar orbit soon enough.

--- End quote ---
I've been cracking my head about this for an hour now. It didn't feel right, and this was contrary to the fact what I knew about orbital mechanism. So if you just burn radial out, this doesn't work at all, and you fall back to earth, quite fast. The only way to "carry" your prograde velocity  to that high orbit is to add more speed prograde. It's because while you are going to that 1.84M km point, the direction of that vector changes, because you move and the earth moves.
But I'm going to try this tomorrow, because it's an interesting proposition nonetheless.

Kim Christensen:

--- Quote from: tszaboo on April 18, 2023, 10:03:59 pm ---So if you just burn radial out, this doesn't work at all, and you fall back to earth, quite fast.
--- End quote ---

You can, if you reach escape velocity, then you won't fall back to Earth. Less than escape velocity, then yes, you'll fall back.
So as long as you are traveling at more than 11.2 km/s away from Earth, it doesn't matter which direction you are going*. But this is not what we do when launching a satellite which we want to orbit the Earth. Then we need to lean the rocket into a gravity turn to give it horizontal velocity in addition to getting it out of the atmosphere. Ideally a satellite, in a perfectly circular orbit around a perfectly spherical Earth, has zero vertical velocity relative to the surface of the Earth.

*  Well, you might come back in a few years if your new solar orbit intersects that of Earth's orbit around the Sun. (That's why Elon's Tesla will pay us a visit sometime in the future)

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