You can measure your mass simply by stepping on a balance. But, have you ever wondered how is the mass of Earth measured? Obviously that balance does not work in space and with such large heavenly bodies as Earth.

So How Is The Mass of Earth Measured?

how can we measure mass of earth

You cannot simply measure them as you measure your mass. First, let’s take an overview of the measurement of mass.

Mass and its measurement

Mass is the quantity of matter contained in a body. So we can measure it by knowing how dense it is (density) and how much space does it occupy (volume)? But this works if the object has a uniform density, not otherwise.

The measurement can also be done by considering some parameter which has a uniform relation with mass. Since the force produces acceleration on an object depending upon its mass, we can know force and acceleration to measure mass.

Every electronic device that measures the mass on a daily basis is based on the principle of balancing force. Let us take beam balance for an instance, it compares the force by which a substance’s weight can be balanced.

An overview of techniques

1. Mass is measured in our daily life by using electromagnetic force restoration method (digital balances). This method produces an electromagnetic force equal to the force produced by the mass and hence calculates the mass of a body.

2. A beam balance can be used to measure the mass of an unknown object by comparing it with a known mass. Simply a known mass is kept at one side and unknown mass at the other and the beam is balanced when the masses at both sides are equal.

3. Space linear acceleration mass measurement can measure the mass of objects in zero gravity using Newton’s second law. It measures the mass by measuring force and acceleration. It uses springs on which fixed force is applied and acceleration is measured by regression analysis to measure the mass (mass = Force/acceleration).

4. Strength and effect of gravitational force can also give an estimation of the mass of massive objects. This is the technique used for astronomical mass measurement, generally mass of huge heavenly bodies.

How astronomers measure mass?

The measurement of mass in space is slightly difficult since there is zero gravity i.e the force that an object experience is zero. It gets even more difficult when the mass is too large like Sun and Earth. To overcome these complications, two different methods (3 and 4) as stated above can be used.

The zero gravity mass measurement of an object smaller in size is not so difficult since we can create a force which can produce a movement on the object. The force and acceleration produced can be used to calculate the mass.

We cannot produce a force that can move Earth and other heavenly bodies so the use of force to produce the acceleration and hence measurement of mass becomes meaningless. So, How can we measure the mass of Earth and other massive bodies?

How can we measure the mass of Earth and other massive bodies?

How astronomers measure mass?

As the earlier mass measurement processes conclude, force and acceleration are the essences of mass measurement. So, in order to measure the mass of Earth as well as the mass of other massive bodies in space we need a force. This force is the gravitational force, which is the property of everybody that exist.

The more massive the objects, greater is the gravitational force they exert. This results in the effect on the other objects which exists in the vicinity of it. For example, Earth’s gravitational force causes the moon to rotate around it and Sun’s gravitational force is responsible for the planets to rotate around it. The distance and speed of the rotating objects directly depend on the gravitational force by which they are pulled. These are the principles on which the mass calculation of larger masses in space is based.

Measurement of the mass of Earth

We know the radius of the Earth as well as the acceleration that is produced by the gravitational force on the surface of Earth. We can use Newton’s formula (acceleration due to gravity = G * Mass of earth/radius of earth squared) to calculate the mass of Earth as we know the gravitational constant ‘G’. The value of ‘G’ was first determined by Henry Cavendish in a laboratory. Cavendish used this experiment to determine the density of the Earth but we can also measure the mass of Earth when we know the density and radius.

Measurement of the mass of any other mass in the Solar system and further

Once the mass of Earth is calculated, the mass Moon or Sun can be determined. The gravitational force between Earth and Sun is equal to the centripetal force required to balance the moon at that distance.

The calculation of gravitational force needs the mass of Earth, the mass of Sun (this is unknown variable) and distance between them whereas the centripetal force needs the mass of Earth, its orbital velocity and orbital radius i.e distance between Sun and Earth. The only unknown variable is mass of Sun since we know other orbital parameters (velocity is the circumference of the distance divided by a years time, radius of the orbit) and mass of Earth. Similarly, other planet’s mass can be calculated once we have the mass of Sun by similar methods.

All these methods of determination of mass have their base in the relation of force with the mass. So once we know how to calculate or compare different forces, we can calculate the mass of anything in our own way.

Ashwin Khadka is a PhD Scholar in Nano Energy and Thermofluid Lab in Korea University, Republic of Korea under Korean Government Scholarship Program. He has a Masters Degree in Physics from Tribhuvan University, Kathmandu, Nepal. He is a science enthusiast, researcher and writer.