Question

The average distance between the Earth and the Sun is 1.00 x 10^11 meters. Calculate the average speed of the Earth in kilometers per second. Express your answer in scientific notation.

Answer 1

First, remember that the force that attracts our planet at equilibrium is equal to the centripetal force that makes our planet move in something like a circle. Mathematically, this equilibrium looks like this:

$$G\frac{Mm}{R^2}=m\frac{v^2}{R},\\\space\\ v=\sqrt{\frac{GM}{R}}=\sqrt{\frac{6.607\cdot10^{-11}\cdot1.989\cdot10^{30}}{1\cdot10^{11}}}=\\\space\\ =36.4\cdot10^{11}\text{ m/s}.$$

But we know that actually this speed is roughly 30 km/s. Why have we obtained 36 km/s? Because in reality, the distance between the Sun and Earth is around 150 million kilometres.