From the book of Jeffrey Bennett (What is relativity). Airplane flying from Nairobi to Quito at 1670 Km/h.The earth rotates in the opposite direction at the same speed. Seen from the moon, the plane lift from the ground at Nairobi, and then stays stationary while the earth rotation is carrying Nairobi away from the plane and Quito toward it. When Quito reaches the plane position, the plane would drop down to the earth. My problem: is the fuel used by the airplane the same for lifting and then staying put until Quito comes to him? Or it needs much more fuel for lifting, traveling around the earth and then descending?. (perhaps is easier to visualize the question if the craft is an helicopter?). Perhaps it is a question for an aeronautic engineer, or for the YouTube program Myth busters... Remember their experiment with the ball shoot from a vehicle? :)
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$\begingroup$ If you just lift and 'stay put' then you would never leave your initial location above Nairobi. Don't let the perspective confuse you: the need for propelling the aircraft does not depend from where somebody is looking from. So you definitely need to apply throttle to move from A to B. $\endgroup$– user112876Commented Oct 15, 2019 at 7:21
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$\begingroup$ North and south flying will involve the Coriolis effect $\endgroup$– Adrian HowardCommented Oct 15, 2019 at 8:13
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$\begingroup$ Why would you even think this is the case? In terms of fuel costs, it takes a lot less fuel to fly from Nairobi to Kinshasa than it does to fly from Nairobi to Quito. Voting to close as "unclear what you are asking". $\endgroup$– David HammenCommented Oct 15, 2019 at 13:14
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$\begingroup$ The amount of fuel used to take off from Nairobi and descend to either Kinshasa or Quito will be more or less the same. (The cost of descending to Kinshasa vs to Quioto will not be quite the same due to the marked difference in altitude.) But the cost of straight and level flight across most of Africa vs the cost of straight and level flight across most of Africa, the Atlantic Ocean, and most of South America are vastly different. $\endgroup$– David HammenCommented Oct 15, 2019 at 13:18
2 Answers
The thing that's important to remember is that the atmosphere is generally moving along with the Earth. If it weren't, the Equator would be subject to hypersonic winds all the time.
So, if you're on Earth's surface, the plane is moving forward through the stationary air. The plane moves through the air at a certain speed, which generates enough lift to keep it in the air. The plane experiences drag from pushing the air aside, and its engines exert enough thrust to counteract this drag.
If you're in the reference frame where the plane is stationary, the Earth's surface, and the air around the plane, are both moving. The air moves past the plane's wings at a certain speed, which generates enough lift to keep it in the air. The air also experiences drag from the air pushing on it, and its engines exert enough thrust to counteract this drag.
In the end, it doesn't matter whether the plane is moving through the air or the air is moving past the plane. The forces involved only depend on whether one is moving relative to the other. Otherwise, wind tunnels would be useless.
The two cases are simply two perspectives upon the same case. There is no difference between the two other than appearances.
