Sir Isaac Newton was led to ponder the orb of the Moon, and he concluded that the acceleration of the Moon toward the earth was roughly what he would expect it to be if his universal law of gravitation were correct. Convince yourself that this is true through the following calculations.

Objects dropped near the surface of the earth accelerate toward the center of the earth with an acceleration of approximately 9.8(meters)/(second squared). That is, at the end of one second they are moving at 9.8 meters/second, after two seconds at 19.6 meters/second, and so forth. (This value varies a little with your position on the earth.) The distance from the center of the earth for someone performing this experiment is about 6.4 million meters.

According to Newton, this acceleration is caused by the gravitational force of the earth, which is proportional to the inverse of the square of the distance from the center of the earth. That is, the acceleration is proportional to 1/(square of distance from center of earth). At a point along the orbit of the moon, the "experimenter" is roughly 380 million meters from the center of the earth. Convince yourself that the following expression is true, and use it to determine the gravitational acceleration at the orbit of the moon:

(acceleration at surface of earth)(square of radius of earth)=

(acceleration at orbit of Moon)(square of radius of Moon's orbit)

Now you need to calculate the actual acceleration of the Moon to compare with this. Recall that for an object in a circular orbit the acceleration is (square of orbital velocity)/(radius of orbit). The Moon makes a complete circuit of its orbit in 27 days. With this and the orbital radius given above, you can calculate the orbital velocity of the Moon and then it's acceleration, and compare this acceleration with the result of your calculation in the previous paragraph. Do you share Newton's satisfaction?

p.s. It might be useful to recall that a day is 86,400 seconds.