Question

If the earth orbits the sun at the speed of 29.783 km/sec, what is its velocity in miles per hour? Solve using dimensional analysis.

Answer 1

The earth is about 93,000,000 miles from the sun. It makes an elliptical orbit around the sun in just a shade over a year (365.24 days).

To make our estimation a little easier, let's assume that the earth's orbit is circular rather than elliptical. If we do that, then the earth travels:

pi*2*93,000,000 = 584336233 miles in

365.24 *24 = 8765.76= 8766 hours

584336233 / 8765.76 = 66661 miles per hour.

In reality, the speed is a bit higher than that, not only because the shape of the earth's orbit is elliptical, but also because the entire solar system is moving within the Milky Way galaxy, and the Milky Way galaxy is moving within the universe. So that's a low estimate, but it gives you an idea of how fast we are hurtling through space.