What tools where used to determine the earths mass in the 17th century?

Answer 1

Earth's gravity accelerates objects at a rate of 9.8 m/s/s. G is the gravitational constant. You can figure this out by dropping any object, measuring the speed it was moving when it passes a certain point, and how long it took.

Force = G * mass1 * mass2 /distance^2 is the equation that newton came up with explain how gravity worked.

Since the mass of an object on the earth that you would drop to measure this is so small, we can ignore it, so we end up with the equation of

9.8 = (G * Mass of Earth) / (Earth's radius ^2)

The earth's radius is about 6,360 km. Convert that into meters and you get 6360000 meters.

The gravitational constant is a tricky thing to figure out but some guy named Cavendish figured it out. Read about it http://www.leydenscience.org/physics/gravitation/cavend.htm

Now we know that G = 6.67 x 10^-11 m^3/kg/s^2 so now plug in all the numbers and you get

9.8 = (6.67 x 10^-11 * Earth's Mass) / 6360000^2

6360000^2 = 4.04496 x 10^13

so
9.8 = (6.67 x 10^-11 * Earth's Mass) / 4.04496 x 10^13

We want to get Earth's Mass on it's own side so multiply both sides by 4.04496 x 10^13 and you get:

4.04496 x 10^13 * 9.8 = 6.67 x 10^-11 * Earth's Mass

Divide both sides by the gravitational constant of 6.67 x 10^-11 and you get
Earth's Mass = (4.04496x10^13 * 9.8)/ 6.67 x 10^-11

Plug that all into a scientific calculator and you get for the Earth's mass about
5.94311964 x 10^24 kilograms

And that's how they did it back in the 17th century. Heh neato I figured out the mass of the earth. Never did that before.

Answer 2

Sir Isaac Newton figured out that measuring any body's mass is a simple affair if the body has a satellite. From the satellite's period and distance, calculating the mass of the gravitating body is pretty easy. However, this assumes that the satellite has negligible mass relative to the primary. To get a precise measurement, you either have to know g, the universal gravitation constant, or you have to know the mass of the satellite. I believe this was worked out to a high degree of accuracy during a transit of Venus across the sun.

Answer 3

I dont think of that any of the greater present day techniques of computing mass of the earth (by way of astronomy and charm of alternative lots in area, extreme velocity photographs of gadgets falling in a vacuume) and so on incredibly would desire to be properly utilized in the seventeenth 18th century. to accomplish that could require lots greater precise time retaining and photographs alongside with the theoretical techniques of Newton as to the way gravity works. a coarse approximation would desire to be made by ability of only looking the quantity of the earth (when you consider that they knew it grew to become into kind of a sphere, and that they knew the diameter to interior some %). Then all one has to do is approximate the mass of an regularly occurring piece of the earth by ability of weighing rocks of regularly occurring quantity. i could suspect that they did not comprehend the density of the middle of the earth as properly as we do on the instant yet they might actual be in the main suitable ballpark +/- 50% with this perspective. As for better estimates the formulation in touch a gravitational consistent, and at a similar time as newton would have desperate this kind of continuous existed his wager grew to become into probably somewhat off formulation the accuracy of the "consistent" of gravity that's mandatory to locate the burden of the earth could be lacking I doubt that they might do lots better. Cavendish found out the burden of the earth by ability of measuring the gravitiational consistent in the tip of it slow variety (1798). as quickly as the gravitationl consistent would desire to be desperate properly, and distances regularly occurring then the formulation would desire to be utilized.

Answer 4

tools? none

just a series of equasions based on newtonian thinking and other physics stuff