How did scientists arrive at 9.8 m/s/s as the acceleration for gravity?

Question

Did they use a special tool or equipment? Or did they just made some valid assumption through experiments?

Answer 1

Measurements. The acceleration of gravity is:
g = G*m/R^2
Where G is the gravitational constant 6.67*10^-11 N*m^2/s^2, m is the mass of the planet, and R is the distance between yourself and the planet. For the surface of the Earth, m and R are approximately:
Me = 5.97*10^24 kg
Re = 6.38*10^6 m
Using this, you should get about 9.8 m/s^2.

Answer 2

The swing in a pendulum is dependent on gravity. So if you know the length, mass and period of one swing of the pendulum, you can manipulate a formula to find an accurate value for gravity. The larger the length, mass and period, the more accurate the value of g. I, personally have calculated g to 4 decimal places using a small pendulum.

Of course gravity varies with height above sea level as well as where on Earth you are so calculations change depending on where the experiment is taking place. Hence why 9.8 m/s/s is used as a general rule.

Answer 3

Galileo had determined the acceleration of all objects near the surface of the Earth in the early 1600’s as g = 9.806 m/s^2.
He performed experiements to prove that falling objects accelerate at the same speed regardless of their weight.
He used a ball rolling down an inclined plane to try to find the effects of gravity on objects, and discovered that regardless of the size of the ball, the velocity increased as the ball moved further down the plane. I'm not sure though how he actually figured out the value of 9.806.

Answer 4

The earliest experiments were made by Galileo. He rolled a ball down a very slightly inclined track, and (because the acceleration was so slow) he was able to measure it pretty well, even in his era before clocks. Then, he increased the angle of the track and measured how the acceleration changed. Eventually he had enough data to determine theoretically what the acceleration ought to be with a vertical track.

In later years, of course, with advaced clocks, much better accuracy was achieved.

Answer 5

Galileo got his first estimate by using balls rolling down tracks in a ramp and timing how long it took to get to certain points on the ramp. [ No, he never dropped two of anything off the Tower of Pisa. ] Since then other various experiments have given the precise rate of acceleration for "g". "g" being acceleration due to earth's gravity, not the gravitational constant, or "G" in equations. Newton's equation showing the force of attraction between two bodies is
F=(G*(m1+m2))/d^2
Where F is the force of gravity
G is Newton's gravitational constant or:
G = 6.67*10^-11N m^2 /kg^2
m1 is mass of body 1, m2 mass of body 2
d is distance between the two bodies.

Answer 6

They measured it.

I suppose you could say they used special equipment: an inclined plane. (It's not very special equipment!) By reducing the angle traveled from vertical to some gentle angle, you effectively reduce gravitational attraction in a predictable manner. That allowed measurements with less accurate timepieces.

Answer 7

F=GMem/r^2, F=mg---> g=GMe/r^2
gravity is equal to the gravitational constant times the Mass of the earth and all divided by the square of the radius of the earth. i believe thats correct, though i could have remembered wrong.

Answer 8

I suppose they started with a simple pendulum experiment.