Relative motion of the earth and an aeroplane held above the earth's surface

[shauns87]

Imagine an Aeroplane held above the Earth's surface for 12 hours, having no contact with the surface of the earth. Suppose that the initial location at time t=0 is Asian continent. So after t = 12 hours, can we expect the aeroplane to be in some other continent or will it be in the same location.

 

[Hootenanny]

Imagine an Aeroplane held above the Earth's surface for 12 hours, having no contact with the surface of the earth. Suppose that the initial location at time t=0 is Asian continent. So after t = 12 hours, can we expect the aeroplane to be in some other continent or will it be in the same location.

There is insufficient information to answer your question. We need the velocity of the plane relative to some reference point.

 

[shauns87]

Ok. Let's say the velocity of the plane faster than the rotational speed of the earth. I guess this should be enough.

 

[Hootenanny]

Ok. Let's say the velocity of the plane faster than the rotational speed of the earth. I guess this should be enough.

The velocity of the plane relative to what?

 

[shauns87]

Oh Sorry! The velocity of the plane is relative the Earth's surface.

 

[Lsos]

Well...Velocity = distance / time

Since you already gave the time (12 hrs), according to the above formula as long as the airplane's velocity is at least 1/12 the distance to "some other continent" then the answer is "yes". Assuming it's going in the right direction.

In other words...if "some other continent" is 12 km away, then as long as the airplane is flying that way at 1 km/ hour then yes...it will end up "in some other continent"

Is this really what you're asking?

 

[shauns87]

No, that's not what I meant. Let me pose it again. See, the plane is stationary and it is held above the surface of the earth. However, the Earth is rotating with respect to the stationary plane. So, the Earth will move but the plane will be stationary. So, can we expect an another place after 12 hours under the plane.

 

[Doc Al]

See, the plane is stationary and it is held above the surface of the earth.

The plane isn't stationary with respect to the Earth and atmosphere. It's flying backwards.

 

[russ_watters]

Sounds like he means stationary wrt a hypothetical nonrotating earth, with the actual Earth rotating underneath it.

 

[Lsos]

No, that's not what I meant. Let me pose it again. See, the plane is stationary and it is held above the surface of the earth. However, the Earth is rotating with respect to the stationary plane. So, the Earth will move but the plane will be stationary. So, can we expect an another place after 12 hours under the plane.

That's what I was wondering if you meant.

The short answer is "yes"...if you hold a plane stationary with respect to, say, the center of the earth, while the Earth is rotating beneath, then the plane will end up in another place.

Since the Earth is rotating at ~1000 mph at the equator, then you can actually move 1000 miles in one hour, holding the plane stationary.

BUT...since the natural tendency is for the airplane to be spinning along with the Earth and with the Earth's atmosphere, "holding" that airplane in place while the Earth spins at 1000 mph beneath it requires the exact same power input as flying at 1000 mph.

If we take your train of thought further, we can for instance propose that instead of making huge rockets to send spaceships far away we can simply "hold" them in place. After all, once you take the Earth's rotation (~1000 mph) and the Earth's movement around the sun (~70,000 mph) and the solar system's movement around the galaxy (400,000 mph) and the galaxy's movement (2,000,000 mph?) into account, you should be able to get to places very quickly. The issue is that in order to "hold" something in place, you first have to slow it down that 1000 or 70,000 or millions of mph, and the laws of physics make no distinction between slowing down or speeding up. It's all relative, and it all takes the same exact amount of energy.