would hovering over earth,lead to distance being traveled,since earth would move under your hovering position?

Question

If an airplane were to hover over Greenwich, and continued hovering in space, would it actually have had covered some distance, if it came down after five hours?
Theoretically, it should almost have the same result as an airplane that is covering distance by flying over earth.
how much would inertia affect the outcome?why would it not cover distance if it hovered long enough? would gravity actually pull the hovering plane along with it?

Answer 1

This is actually a tricky question. If you were able to just levitate of the surface of the earth, you would still have angular momentum relative to some fixed coordinates (say distant stars) so you would continue to move with the earth at the same angular speed as the earth. So lets say you counteract that when you leave the surface and no the earth is moving relative to you. The point on the ground you left will move away from you and come back 24 hours later. If you are on the equator, the point on the ground appears to have a linear speed of about 1700 km/hr about 2 to 3 times faster than a jet passenger plane. The linear speeds will decrease as you move either north or south but the angular speed remains constant.

Now since gravity is a radially directed force, and you are really hovering, gravity can only pull you towards the center of the earth. Hence it can't drag you along.

How much inertia you have to overcome is really a question of how much angular momentum you need to lose (see above). This depends on your mass, and how far above the surface you are.

Answer 2

This depends on how you apply the word hover in this problem. traditionally hovering implies maintaining a suspended motion in the air over a fixed location on earth. If this is the case then you would move with the earth and cover a rotational distance, the earth is rotating at 1,000 MPH , of approximately 5,000 miles. Which is exactly what would have occurred if you remained fixed to the earth below the hovering object.

However, if you were to hang above the surface of the Earth in this definition of hovering andlet the earth pass underneath you then you will not have traveled at all, not one bit, but the earth would have spun underneath you and you would come back to earth at a point 5,000 to the east of where you had left earth at the beginning of your hover. You actually covered zero distance in this case but the earth covered a distance of 5,000 miles in executing it's rotational spinning movement.

This is quite different than an airplanes movement. As the airplanes speed of movement and distance traveled is that of relative speed and distance traveled to the earth with the rotational effect of the earth only impacting the position of the earth to the sun and thereofre the timezone/time of the day.

Inertia need not be overcome unless you plan to escape the earths velocity and hover over above the surface of the earth and let it spin underneath you as you watch.

Gravity only comes into play in escaping it, through acceleration to escape velocity or hovering like a helicopter where you need to offset gravity with lift to overcome the gravity of earth.