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# Does more ground move underneath you the further away you are from earth? watch

1. Another discussion in the office from humanities educated CT.

We're talking about a super fast hypothetical plane developed which can get to Sydney from London in four hours.

One of us reckons he read somewhere that it goes straight up into space from London, waits for the earth to move underneath it, then comes down and lands in Australia (hypothetically, let's leave accuracy problems aside).

Intuitively this makes no sense to me - would more ground really pass underneath you just because you're far away? Why would it make a difference being 10 ft, 10,000ft or right up on the edge of space? The earth still moved at the same speed, right...?

If someone could explain this I'd be really grateful
2. (Original post by Puddles the Monkey)

Intuitively this makes no sense to me - would more ground really pass underneath you just because you're far away? Why would it make a difference being 10 ft, 10,000ft or right up on the edge of space? The earth still moved at the same speed, right...?
I don't think it would make a difference. Ultimately it becomes a question of gravity the further out you get (which gets exponentially weaker). The lack of gravity and resistance forces would mean the slightest force like a tiny bit of thrust would have a big impact, which might be where the idea comes from in order to move around the earth super fast. But if you didn't expericne any other force acting on you you would eventually float back down to the same spot on earth that you left. Of course this is all a very Newtonian view, how you would explain it in general relativity I do not know

When you jump you don't smack into the wall. When you jump on a train you don't go flying into the front (unless the frame of reference is accelerating, which is key to this, a force has to be provided somewhere in order to move in relation to the earth frame of reference). When in super Mario you jump on moving platform and the platform moves beneath Mario, the mushroom kingdom has different laws of physics to us. When you hover in a helicopter the Earth's surface doesn't move beneath you.

When you are stood on surface of the earth you have the same angular velocity of the earth. So when you jump you move with it. You need to burn energy to change your angular velocity relative to the earth's reference frame to move to a different spot on the earth's surface. You can't just move directly upwards and let the earth's surface move beneath you. The only time that kind of thing would happen is if either you accelerate or the earth accelerates (if thye earth suddenly stopped rotating we would all go flying )

If you want to go to a different part of the the earth you have to put in the Force in order to create the acceleration. No free lunches.
3. (Original post by ChaoticButterfly)
No for the same reason when you jump you don't smack into the wall. When you jump on a train you don't go flying into the front (unless the frame of reference is accelerating). When in super Mario you jump on moving platform and the platform moves beneath Mario, the mushroom kingdom has different laws of physics to us. When you hover in a helicopter the Earth's surface doesn't move beneath you.
Doesn't it?

When you are stood on surface of the earth you have the same angular velocity of the earth. So when you jump you move with it. I imagine it is the same for planes. You need to burn energy to change your angular velocity relative to the earth's reference frame to move to a different spot on the earth's surface. You can't just move directly upwards and let the earth's surface move beneath you. The only time that kind of thing would happen is if either you accelerate or the earth accelerates (if thye earth suddenly stopped rotating we would all go flying )

shooks read about it, he should have a link to something He says it was on horizon or something like that.

I'd say no though. If you want to go to a different part of the the earth you have to put in the Force in order to create the acceleration. No free lunches.
4. (Original post by Puddles the Monkey)
Doesn't it?

shooks read about it, he should have a link to something He says it was on horizon or something like that.

I edited in some stuff to try and explain it better
5. [QUOTE=Puddles the Monkey;60368409]Doesn't it?
/QUOTE]

Well it does if the helicopter provides force to change it's angular velocity in relation to the surface of the earth.
6. (Original post by Puddles the Monkey)
Another discussion in the office from humanities educated CT.

We're talking about a super fast hypothetical plane developed which can get to Sydney from London in four hours.

One of us reckons he read somewhere that it goes straight up into space from London, waits for the earth to move underneath it, then comes down and lands in Australia (hypothetically, let's leave accuracy problems aside).

Intuitively this makes no sense to me - would more ground really pass underneath you just because you're far away? Why would it make a difference being 10 ft, 10,000ft or right up on the edge of space? The earth still moved at the same speed, right...?

If someone could explain this I'd be really grateful
No it doesn't "wait" for earth's rotation.

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7. (Original post by jneill)
No it doesn't "wait" for earth's rotation.
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To confuse matters...

Once it reaches it';s top velocity and travels at uniform speed it can be said to be 'waiting' for the Earths rotation
8. (Original post by jneill)
No it doesn't "wait" for earth's rotation.
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So it is just a super fast plane? Or it needs to go up that high in order to work?
9. (Original post by Puddles the Monkey)
Another discussion in the office from humanities educated CT.

We're talking about a super fast hypothetical plane developed which can get to Sydney from London in four hours.

One of us reckons he read somewhere that it goes straight up into space from London, waits for the earth to move underneath it, then comes down and lands in Australia (hypothetically, let's leave accuracy problems aside).

Intuitively this makes no sense to me - would more ground really pass underneath you just because you're far away? Why would it make a difference being 10 ft, 10,000ft or right up on the edge of space? The earth still moved at the same speed, right...?

If someone could explain this I'd be really grateful
Well sort of... if we're talking about sub orbital spaceflight, the higher your apogee is, the longer it'll take to fall back into earth's atmosphere... the earth is constantly turning so the more time you spend in space, the further the earth will have turned by the time you reenter the atmosphere. This means you'd have to aim your reentry at where australia will be by the time you get there (rather than where it is when you launch.)

going straight up is a non-starter though as you'll come back down at the same lattitude... probably somewhere in the north Atlantic if your flight time is 4 hours... back to london if it's ~24 hours.
10. It would work, it's just silly compared to a normal suborbital flight. When a rocket or plane takes off, it takes off already with the momentum because of the spinning earths surface.

This is the reason rockets always take off pointing east, they get a "boost" from the earths rotation that makes it more efficient to get into an orbit speed, if they took off west they'd have to counteract that energy, and use a lot more fuel to get into the same orbit.

However, as you go "up" you don't just keep "in sync" with the earth surface. Say the earth's surface is spinning at 10m/s, and you launch upwards. You're distance from the surface increase, but you are still only travling 10m/s laterally. But because you're further from the "center", in order to "keep up" with where you were on the surface from this greater hight, you'd actually need to be traveling something like 15m/s. The further away from the center of the rotating object, the faster things have to go (to all keep in line/together).

Does this increase as you get further and further out? Yes. But it increases by less and less the further you go, and get's closer and closer to if you simply had "no" lateral velocity, so if you were completely stationary and earth was spinning below you. The fastest way to travel via this method would be at the speed of the surface of the earth's rotation. If you rocket up high enough only upwards, you can only get closer and closer to this "speed".

Does more ground move underneath you the further away you are from earth?
Yes! It's something that can be helpful in sub-orbital or to-orbit flights, but it's not something you'd rely on completely, and it can also be a hindrance.
11. (Original post by Puddles the Monkey)
So it is just a super fast plane? Or it needs to go up that high in order to work?
Yes. It goes that high mostly because the air density is much lower, therefore less drag, therefore more speed (for the same amount of propulsion).

Also the sonic boom won't be so noticeable if it's up high. That was a big problem for Concorde.

Edit to add: in space no one can hear you boom. . (Sound needs a medium, eg air, to propogate.)

How does Puddles the Geek sound

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12. (Original post by Joinedup)
Well sort of... if we're talking about sub orbital spaceflight, the higher your apogee is, the longer it'll take to fall back into earth's atmosphere... the earth is constantly turning so the more time you spend in space, the further the earth will have turned by the time you reenter the atmosphere. This means you'd have to aim your reentry at where australia will be by the time you get there (rather than where it is when you launch.)

going straight up is a non-starter though as you'll come back down at the same lattitude... probably somewhere in the north Atlantic if your flight time is 4 hours... back to london if it's ~24 hours.
What about if you just hover above earth? You'd still need ~11/12 hours for Australia to roll around underneath you, right?

Or do you need to be out of the atmosphere to get the Earth turning benefit?

Edit: I've just realised that the further away you get from earth the quicker you have to travel to keep in line because you've got a bigger circle to cover.
13. (Original post by Puddles the Monkey)
What about if you just hover above earth? You'd still need ~11/12 hours for Australia to roll around underneath you, right?

Or do you need to be out of the atmosphere to get the Earth turning benefit?

I think you are still failing to grasp the concept of relative angular velocities. You need to understand that in order to grasp everything else.Hovering above earth means remain stationary relative to the surface of the earth. You move with the surface of the earth and do not travel to a different part of the surface of the earth.

Have you played Kerbal Space Program?
14. (Original post by Puddles the Monkey)
What about if you just hover above earth? You'd still need ~11/12 hours for Australia to roll around underneath you, right?

Or do you need to be out of the atmosphere to get the Earth turning benefit?
If you go vertically up you would still be moving laterally in the direction of the earth's rotation, unless you also applied a horizontal force in the opposite direction. Newtons laws apply.

It's because the earth is applying a lateral force (it's rotation under you) to you when you took off. Even if you ignore air resistance etc.

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15. (Original post by Puddles the Monkey)
Edit: I've just realised that the further away you get from earth the quicker you have to travel to keep in line because you've got a bigger circle to cover.
Exactly!

And you'd need to get mostly out of the atmosphere, as it's spinning with the earth and would drag you to a speed synchronous with the surface.

Also, it's really really thin (a hundred miles at most for low earth orbit, which is almost no atmosphere) which isn't going to give you much of a difference in speeds - it's only 2.5% further up than the surface-center.

You'd need to go significant distances to get any significant lag from the earth's surface.
16. (Original post by ChaoticButterfly)
I think you are still failing to grasp the concept of relative angular velocities. You need to understand that in order to grasp everything else.Hovering above earth means remain stationary relative to the surface of the earth. You move with the surface of the earth and do not travel to a different part of the surface of the earth.
Does this remain the same however far away from the surface of the earth you go? I think that's the question I'm trying to ask.

Have you played Kerbal Space Program?
Yes, but I never managed to launch a spaceship
17. (Original post by Puddles the Monkey)
Does this remain the same however far away from the surface of the earth you go? I think that's the question I'm trying to ask.

Yes, but I never managed to launch a spaceship
Hovering above earth means remain stationary relative to the surface of the earth. You move with the surface of the earth and do not travel to a different part of the surface of the earth.

In order for the earth surface to move beneath you, you yourself have to exert a force that gives you angular velocity change. Lets say earths angular velocity is 10. If you go directly 'upwards' and 'hover' your angular velocity will also be 10. You are moving with the surface of the earth. So when you come back down you have not traveled anyway in relation to the surface of the earth. You have traveled with the surface of the earth through space but not in relation to the earth's surface.

If once you move directly upwards you switch on your rocket boosters and create force that accelerates you to an angular velocity of 15 compared to the earth's angular velocity of 10. 15 - 10 = 5. So there is a 5 difference in angular velocity between the surface of the earths reference frame and the ships reference frame. So now when the ship 'hovers' the earth's surface does indeed move beneath it at an angular velocity of 5. Or you can equally say the ship moves over the 'hovering' earth surface. Both statements are true since it is relative and the point of reference is arbitrary.

This 'hovering' at 5 requires the constant thrust of the engines of the ship, since otherwise the ship will slow down due to the forces of propulsion being outweighed by other forces such as friction. So it costs energy to do this and get to a different part of the earth's surface.

What this super plane is doing is no different than a normal plain except it is going much higher where there is less friction from a thinner atmosphere (and maybe other factors I don;t know about) so we can get more thrust, which creates a high angular velocity per consumption of unit energy. So say now the ship can get to an angular velocity of 100 compared to earth's 10. 100-10 = 90 90> 5. We can go faster and do it more efficiently resulting in getting to Australia much faster than normal. But no free lunches! Which is what your humanities friend was alluding to

I have no idea if any if that helped you but ti took a long time to write
18. (Original post by ChaoticButterfly)
x
I think I get all this.

Let's pretend for a second that angular velocity doesn't exist and you could ignore the laws of physics and float above the Earth without being affected by the rotation of the earth or the atmosphere. In that situation, the earth would move at the same pace beneath you regardless of far away from it you are?

On another slightly unrelated subject, this is all helping me understand the dark matter thing a bit better.
19. (Original post by Puddles the Monkey)
I think I get all this.

Let's pretend for a second that angular velocity doesn't exist and you could ignore the laws of physics and float above the Earth without being affected by the rotation of the earth or the atmosphere. In that situation, the earth would move at the same pace beneath you regardless of far away from it you are?

On another slightly unrelated subject, this is all helping me understand the dark matter thing a bit better.
Do you mean - the earth "move", or the earth "rotate" ? Actually it doesn't matter... the earth rotates, or moves, at the same velocity no matter how far away you are.

If you are a billion or a million miles away the earth still rotates at 25,000 miles/day (at the equator) = approx 1,000 km/hour.
20. (Original post by jneill)
Do you mean - the earth "move", or the earth "rotate" ? Actually it doesn't matter... the earth rotates, or moves, at the same velocity no matter how far away you are.

If you are a billion or a million miles away the earth still rotates at 25,000 miles/day (at the equator) = approx 1,000 km/hour.
Okay. And more ground doesn't pass underneath you the further away you are (assuming you're a ghost untouched by velocity)?

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I realise this question might be getting ridiculous now but I really need to know a definitive answer

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