How you can find how is the Earth acceleration?

Answer 1

If you mean the acceleration of gravity, Galileo found it by timing how long balls took to roll down a ramp. He would have timed the fall of objects he dropped, but dropping them straight down causes them to fall too fast to time accurately, so he hit on the idea of rolling balls down a ramp instead.

Answer 2

Not sure what you mean. If you are looking to determine the Earth's acceleration in its orbit around the sun, here you go:

If we can treat Earth's elliptical (and very nearly circular) orbit as a circle, we can determine its approximate acceleration.

Acceleration of a body in a circular orbit is a vector pointing toward the object being orbited (i.e. here, the sun) with a magnitude of (v^2) / R.

where v = velocity
R = radius.

Ok, distance from earth to sun is around 93,000,000 miles.
We know it takes approximately 365.25 days for the earth to orbit the sun. So we can calculate v.
v = distance / time
v = circumference of earth orbit / year
v = 2 * pi * 93,000,000 / 365.25 days
v = 5.84 * 10^8 miles / 365.25 days
v = 1.6 * 10^6 miles/day
v^2 = 2.56 * 10^12 miles^2/day^2
A = V^2/R
A = 2.75 * 10^4 miles / day^2
or, 27,500 miles per day per day

Again, this is an approximate. Johannes Kepler showed that the acceleration increases as a planet travels to the nearest approach in its elliptical orbit.

HOWEVER, if you are just trying to find the acceleration due to gravity at the earth's surface:

Drop an object from a defined height (H).
Measure the time (T) it takes for it to fall.

Its average velocity (V) is = H/T.

Its acceleration can be determined by V = 1/2 * A * T,
solving for A:
A = 2*V/T or
A = 2* (H/T) / T
A = 2 * H / (T^2)

Alternatively: The ramp idea previously mentioned does make it easier to measure the time. You just need to adjust the time to reflect the slowing effect of the ramp.

Adjusted Time = Measured time * Height of Ramp / Length of Ramp

Put another way, if you measure the angle (Theta) that the ramp makes with the ground,
Adjusted Time = Measured time * sin(Theta)
because sin(Theta) = Height of Ramp / Length of Ramp

All this ignores the slowing effect of friction of the object rolling down the ramp. This friction is likely to be a somewhat larger factor than the friction an object free-falling through air encounters.

This is why physics labs often use an inclined plane with small holes perforating it; and through the holes, air is blown. The falling object can then ride on a cushion of air, and the friction effect of solid on solid is normalized to be comparable to that of an object in free-fall.