As December 31st comes to end, when the clock strikes midnight, the Gregorian calendar is reset to January 1st and another year begins. As you may have noticed, we do this every 365 days. Something must be repeating itself annually to represent the start of this new cycle. Obviously, it is a representation of the complete revolution of the Earth about the Sun.

It takes the Earth approximately 365 days to revolve around the sun. But where does this number come from? In math and physics, there is a way to mathematically represent periodic systems, i.e. systems that repeat in a regular pattern. In physics, if you have a system where an object goes around in a circle, that system has a certain period, because there’s a certain amount of time it takes the object to leave one position and return to the same position. The period is represented by T. The orbits of planets are such systems and so they have a period too. It turns out that the period of an orbiting object depends on the speed of its orbit.

To find the period of the Earth, you would have to apply Newton’s law of gravitation and his 2nd law of motion. Newton’s 2nd law simply says that the forces acting on an object are equal to the mass of the object times its acceleration, F = ma. His law of gravitation says that the gravitational force between two bodies depends on their masses (their size) and the distance between them.

According to his 2nd law, we must set the gravitational force equal to the mass of the planet times the centripetal acceleration, a = v^2/R. If we solve for v, we get the orbital speed, and since the period depends on the orbital speed, we can also find the period of the orbit. Plugging all the values in such as the gravitational constant G, the mass of the sun M, and the distance of the earth from the sun R, we can calculate the value of T which comes out to be 365.5 days.

Isn’t that just amazing? Isn’t it just so incredible that with a sheet of paper and a pencil, the laws of physics gives us insight into the motion of heavenly bodies and enable us to predict something as grand as the time it takes this planet to revolve around the sun? This is the power of math. This is the power of science. Happy New Year to you all.