A Plane Flying West At The Speed Of The Earth Is Actually Stationary

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

09 April 2006

In last week’s discussion of Patrick Ngugis’s question about aeroplanes flying eastwards, it emerged that such an aircraft would NOT appear stationary above the airport even if it was moving at the “speed of Earth’s rotation”. The analysis further revealed that the “speed of Earth’s rotation” can be expressed in two ways: in kilometres per hour or in degrees per hour. The former varies as one moves away from the equator while the latter is the same all over the globe.

From the analysis, the answer to Patrick’s other questions become straightforward, as follows: If a plane flies due east at the “speed of Earth’s rotation” for 24 hours, it will go around the planet once and return to its starting point. If a second aircraft sets off westwards at the same time and moves the same speed, then, after twelve hours, the two aeroplanes will meet at the opposite side of the globe and after another 12 hours, they will both return to the starting point – at the same time.

From the point of view of an observer located on the Earth, the two planes will be seen flying at the same speed but in opposite directions. Thus after 24 hours, both aircrafts will return to the place where they started. However, viewed from “outside” the Earth, the motion of the westbound aeroplane is interesting.

Remember that anything that appears stationary on Earth is actually moving eastwards because of the rotation of the planet. Thus, if an object is moving due east, it “true” speed will be the observed value plus “speed of Earth’s rotation”. Conversely, if the direction is westbound, then the true speed is the measure quantity minus “speed of Earth’s rotation”.

Therefore, the true speed of the westbound plane is “speed of Earth’s rotation” minus “speed of Earth’s rotation”. (Remember, the plane is flying at the “speed of Earth’s rotation”). This is equal to zero, that is, in reality, that aircraft would be stationary! But this situation is only seen if the observer is not standing on the Earth. (Note that “Earth” in this case means the planet plus its atmosphere and satellites, including the moon.)

While you ponder on that, Patrick’s question raises another interesting point: is it possible to put an object in an orbit around the Earth so that it stays above a fixed point on the planet? The answer is yes. This is how geo-stationary communication satellites are positioned in space.

A geo-stationary orbit is only possible directly above the equator. The satellite must be placed at a distance of about 42,000km from the centre of the Earth, that is, about 35,000km above the surface. In order to keep up with the planet, the speed of such a satellite is over 11,000km/h in an eastward direction.

Under these conditions, the satellite cannot fall back to the ground and since there is nothing to slow it down, it does not require any fuel to keep it in motion. But why is such a high speed required to keep up with the Earth’s rotation (compared to the 1,675km/h on the surface)? Well, that is a story for another day.