Mass of the Earth?

Question

How did the original ancient astronomers and scientists calculate the diameter and mass of the Earth. Please show you calculations.

Sorry " your calculations"

addtionally - how do we know the distances to the other planets?

I asked for calculations not explanations - If I wanted to search goggle I would have.

Answer 1

Erastotenes of ancient Greece empircally calculated the circumference of the Earth and from that its diametre. (Circa 240 B.C.) .He must have read about the Old Testament of the Holy Bible ,which stated that the Earth is round. So on that assumption he deducted that the earth was a a perfect circle.Hence if he could divide it by one hundred parts and measure the distance in per unit of the circle he would obtain the Circumference.Hence the circle would have a complete circumference as 100 per units.

Therefore he measured the angle of the Sun in per units of a shadow that was cast between two city at a angle of 2 per units.
He then had a a professional pace measurer pace the distance between these two points as being the 2 per unit distance of the circumference.

By Simple equation and arithmetic he multiplied the per unit distance by 100 and obtained the circumference of the earth within small percent error. The reason is that the Earth was not really a perfect circle or sphere=its really an oblate
spheroid.
Noting that a per unit angle is equal to a per unit distance on the circumference of a circle.

The person that calculated the Mass of the Earth was Cavendish an English Gospel Preacher. He Used Newton.s Univesal gravitational constant and Newtons law of mass gravity interactions Equation.
He measured the force between two interacting masses using a torsion scale.By knowing the torsion constant and measuring the angle of the twist that the two masses produced during their interaction he obtain the Force between them.
And by simple trig and arithmetic he obtained more acurately Newtons Universal constant, now known as "G".

G = A volume /(4.12 x the mass of the Earth x the period of the interacting mass)

G= R^3/ (M xT^2)=measured ln units m^3/kg sec^2

So the mass of the earth =volume of the earth divide "G" divided by the period square.


The mass of the earth can be closely approximated if you take the mass of a number of material earth samples including water and metals and air.Then add the total mass densities of each samples and divide by the number of sample an average mass density of the earth can be statistically appproximated to about 5 grams per centimeter cube.

Volume of the Earth = 4.12 x (6.378 x10^6 meters)^3

Mass of the earth =volume x density=
Mass =1.06893367910^21m^3 x 5x10^3 kg/m^3=5.3446683 x10^24 Kilograms within a 10%error.

Note; the Earth relative to itself has no weight . Just as two moving masses side by side moving at the same velocity, their relative velocity is zero.

Answer 2

The mass of the earth was not known by "ancient" astronomers (unless you consider 1798 to be "ancient").

The SIZE of the earth was known (with reasonable accuracy) as long ago as around 250 B.C. By that time, it had pretty well been established that the earth was a sphere (on account of the shape of eclipse shadows and other evidence). Eratosthenes of Cyrene did a calculation involving the apparent angle of the sun as seen from two different cities a known distance apart from each other, and deduced the two cities were separated by 1/50 of a full circle. So he just multiplied their distance by 50 to get the circumference of the earth.

The first measurement of the MASS of the earth had to wait another 2000 years. It was done in 1798, by measuring the strength of gravitational attraction between two known masses in a laboratory, and comparing that to the strength exerted on the masses by the earth (i.e., the masses' weight). Then you just multiply.

> how do we know the distances to the other planets?

Knowning that the planets travel in ellipses around the sun, You can use trigonometry to calculate the distances to planets RELATIVE TO the earth-sun distance. For example, by observing Venus you can see that it never gets farther than about 47° away from the sun in the sky. Then you can draw a right triangle with earth, the sun, and Venus at the three corners, and make one of the angles 47°, and with trigonometry you can see that Venus' orbit must be about 73% as big as the earth's. From that, you can then calculate the earth-Venus distance as a fraction of the earth-sun distance.

But to turn that into a number of miles, you also have to know the earth-sun distance. The best early attempt at that was done by observing a transit of Venus (that is, the rare occasion when Venus crosses directly in front of the sun. During the transit, Venus can be seen (when safely filtered!) as a dark circle against the lighter disk of the sun.) When you observe the transit from two widely separated locations on earth, Venus's position against the sun's disk will appear very slightly displaced, due to parallax. (In the same way, if two different (separated) people are looking at a distant telephone pole against a background of mountains, the pole's position against the background will look slightly different from observer "A" to observer "B").

Anyway, by making very careful measurements of Venus' apparent position against the sun as seen from, say, Tahiti and Hudson Bay, you can use trigonometry to calculate the earth-sun distance as a multiple of the Tahiti-Hudson Bay distance. This was first done in the 1760's.

> Please show you calculations.

I've done enough to get you started. Search in Google if you want to know the details of the experiments.

Answer 3

1

Answer 4

I remember a story concerning one of the greek philosophers (Aristarchus?), where they measured the length of a shadow on a stick at different points on the earth at certain times of the day. From this (I believe) they were able to determine the circumference of the earth, and therefore the diameter.

Calculation based information... I am not sure.

Answer 5

Mass(Kg) of Earth is 5.98 x 10 (to the 24th power). The mean radius(m) is 6.37 x 10 (to the 6th power)....the diameter is 2x the radius.

Answer 6

a big set of scales, and a long tape measure.
ITS TRUE!!!
trust me the earth is flat and windows is cool.

Answer 7

Does 'Power' mean anything to you, Dr P...? :)

Answer 8

"goggle"? No wonder you can't finish your homework by yourself.

Answer 9

you can find on
www.enchantedlearning.com