The Effect Of Throwing Stones In The Air

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

19 June 2005

Mbithi Musyoki has an interesting question: “Why is it that when I throw an object in the air, it doesn't fall behind me even though the earth is moving at a considerably high speed? And stationary things like the birds that hover in the air; why don't they seem to get further behind yet the earth is moving?”

First, we should ask, is this expectation valid?

The Earth rotates once every 24 hours and its diameter is about12,800km. Hence the circumference is about 40,000km. Therefore, the average rotational speed over the equator is about 1,675km/h. The further you go away from the equator, the slower your speed of rotation. And when you are right on top of any of the poles, you will be spinning about a stationary point. The reason for this is that the diameter of rotation reduces as you get closer to the poles. Remember: the line joining poles is the axis of rotation.

Now, when an object is thrown up in the air, it will have two speeds: the upward velocity due the throw, and the horizontal speed in a west-to-east direction due to the movement of the Earth – 1,675km/h. Bear in mind that when the planet rotates, it takes everything bound to it along with it.

The horizontal motion is not in a straight line; it is circular. When two objects are moving around a point at the same speed but with different diameters, the one closer to the centre completes the cycle faster than the second object. The reason for this is that the greater diameter has a bigger circumference. This is also why runners in the outer lanes in athletics are placed ahead in the starting line-up.

Thus the expectation by Mbithi that an object in the air should be left behind is valid. But why don’t we see it happen? The answer is that we don’t throw things far enough for the effect to be observable. Suppose we threw a stone 100 kilometres above the Earth’s surface.

At that altitude, the distance from the axis of rotation is 6,500km, thus the diameter of orbit is 13,000km. Since our stone was launched from Earth, it is already moving due East at 1,675km/h (actually slower than this, but that is another long story…). In one hour it will have moved a distance of 1,675km, which is equivalent to 14.77 degrees for the 13,000km orbit.

In the same duration, the Earth ‘s surface will have advanced by 15 degrees (one hour divided by 24h times 360 degrees). Therefore the stone will lag behind by 0.23 degree every hour. 0.23 degree may sound small but it equal to 25km on the surface of the Earth.

Ordinarily, however, we throw stones only a few metres up – not hundreds of kilometres. Therefore, the effect is too small to be observed.