# How to Measure the Mass of the Earth

The idea of measuring the mass of the Earth became a possibility following Sir Isaac Newton’s discovery of the force of gravity. Newton’s law describing the reality’s fundamental features made scientists work from empirical to mathematical logics. In fact, the mass of the Earth can be measured. Through Newton’s discovery, we were able to understand how the earth, the sun, and the moon are bound to each other. In between these objects, there is a force known as the gravitational force. Therefore, it is possible to determine the mass of the earth using Newton’s formulae, knowledge of the radius of the Earth, and the gravitational force. The equation to determine the mass of the earth is:

F= Gm_{1}m_{2 }where; F= m_{2}a a= -2x/t^{2}

R^{2}

F is the force, and while G is the gravitational force (6.67×10-11 m3/kgs2), m1 represents the mass of the Earth, m2 is the mass of the object on the Earth’s surface. While a represents the acceleration of the object, which is negative since it, is accelerating downward. On the other hand, “x” is the distance travelled by the object and “t” is the time taken by the object to fall freely. We can combine the above equations to measure the mass of the Earth using radius, acceleration and the constant gravitation (Avison and John 74). Therefore, the formula will be; m1=aR2/G.

We know that R is around 6378km (6378, 000m) which is measured by observing the angles and lengths of shadows at different positions on the surface of the Earth. On the other hand “G” is the gravitational force, a constant, measured by a physicist, Henry Cavendish (1731-1810) and was found to be 6.673 x 10-11. Therefore, the requirement is to find out an object’s acceleration towards the Earth’s surface. The force is usually negative since the object is falling towards the center of the Earth.

We necessarily do not need to know the mass of the object dropped. Even though any object can be dropped, there is the need to use an object that experiences maximum air resistance. The object should be dropped from a high enough height to minimize the relative time to start and stop the stopwatch. However, it should not be so high that the air resistance affects the results.

In fact, to do the experiment practically, one should find a suitable location to drop marbles or stones. These places should be balconies, stairwells, or rooftops. Therefore, determine the height and, using a stopwatch, determine the time the object will take to reach the Earth’s surface. Using the formula above, one can be able to ascertain the mass of the Earth.

Sir Isaac Newton discovery contributed to the study of physics, therefore, through his efforts, we can determine the mass of the Earth. Notably, the Law of motion and gravitational law are substantially used to determine the mass of our planet (Leeder, Mike and Marta, 25). Isaac’s law of gravity formulates the force of gravitational force that the two masses exert on each other, and it is obtained by;

F=Gm_{1}m_{2}/r_{2=}ma

Gm/r^{2}=g

M=gr^{2}/G

M= (9.8m/s^{2}) (6.37×10^{6}m)^{2}/(6.673×10^{-11}Nm^{2}/kg^{2})

Mass of the Earth (m) = 5.96x 10^{24 }kg.

However, the Earth gains mass daily from the incoming fragments from space. It usually occurs in the form of falling meteors in a night. A certain mass from space accumulates on the Earth’s surface daily. The seemingly large amount is usually insignificant to the earth’s total mass.

**Works Cited**

Avison, John. *The World of Physics*. Cheltenham: Nelson, 1989. Print.

Leeder, Mike, and Marta Pérez-Arlucea. *Physical Processes in Earth and Environmental Sciences*. Chichester: John Wiley & Sons, 2009. Internet resource.