How was the mass and the radius of the earth found?

Question

Obviously it was not measured by using a huge metre rule/scale. so how were these values found?

Answer 1

The Indian astronomer Aryabhatta calculated the circumference of the Earth in about 500 AD and got a value less then 50 miles short of the currently accepted one! He used methods similar to Aristarchus, but with much better instruments. India's first satellite was named for him.

The "modern" value for the radius of the Earth comes from the work of Jean-Baptiste-Joseph Delambre and Pierre-François-André Méchain. Towards the end of the 18th century the French needed to rationalise their chaotic system of weights and measures. They decided the unit of length would be the metre and it would be defined as 1 millionth of the distance from the north pole to the equator. Obviously they couldn't measure the distance from the pole, but they were able to measure from Dunkirk to Barcelona. This was done by a process of triangulation, which actually did mean using a huge rule to get the length of at least one of the sides of one of the triangles!

The actual size of the Earth was calculated from their data by the world's first international scientific committee.

Answer 2

The mass of the earth is a classic problem given in physical science and physics classes everywhere.

the force of gravity between an object and the earth is equal to the product of both masses divided by the square of the distance between them, and the whole thing being multiplied by the "Universal Gravitational Constant"

If this is restated, M1 (the mass of the earth) equals the force of gravity (weight of the other object, you perhaps) multiplied by the distance between their centers squared (the radius of the earth in this case), then divided by the product of the "Constant" and M2 (also you perhaps).

Remember not to confuse mass and weight, and use units that are consistant with each other.

Eratosthanes lived in Alexandria Egypt. He knew of a well in the town of Syene where the suns rays went straight to the bottom on a certain day each year. He hired someone to walk between the two cities and record the distance.
On the day of the event he measured the angle of the suns rays to see how far they were from the verticle in Alexandria at the same time.
He assumed that angle in degrees when related to a circle had the same proportions as the distance around the globe would be to the distance from Alexandria to Syene. Plugging in his numbers to the proportion gave the answer.
The problem that we have with his work is that he used the unit of the "stadia". This was related to the size of the ancient race tracks found in those great cities. The problem is, they were not all the same size. As a result we don't really know what his results were in modern terms. Many sources state how 'accurate' his results were, but in truth, we really don't know.

Answer 3

When Newton came up with the his idea of a gravitational constant and the equation:
F=G*(m1*m2)/r^2
there were 2 unknowns:
G - the Gravitational Constant
m1 - the mass of the Earth

If one of those could be found out, then the equation would tell you what the other was if you solved it to
a = (G*m1)/r^2
(Where a is the acceleration due to gravity, 9.8 m/s)

Henry Cavendish, in 1798, performed an experiment using a torsion balance that allowed him to calculate G, and from that it was simple to solve for the mass of the Earth.

Answer 4

The size was measured by Eratosthenes thousands of years ago by using shadows and geometry. You could get a rough idea of the mass by just weighing a cubic meter of rock and then multiplying that weight by the volume of the Earth, but an accurate measure of the mass had to wait for Newton's law of gravity.