By 1687, there had been a great number of works done on the motion of the planets, but no mathematical explanation was derived for such work.  Following his first Law of Motion, Newton was able to derive that same year mathematical calculations that will govern the physics of Universal Gravitation up to date.  He reasoned that there had to be a force acting on the moon in other for it to orbit the earth, otherwise the moon would travel in a straight line.  Newton reasoned that the force that attracted the apple to fall on his head was the same force that attracts the moon to orbit around earth.  Thus he said: “I deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve; and thereby compared the force requisite to keep the Moon in her orbit with the force of gravity at the surface of the Earth; and found them answer pretty nearly.” (Jewett, Pg 390)  To keep this in simple terms observe the following diagram:

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

    Here, G has a measured experimental value of 6.673 x 10-11 Nm2/kg2.  To come up with such formula, Newton knew from Galileo’s experiments that an object fell to the Earth’s surface at a rate of about 9.8m/s2, this is a constant value since if a feather without air resistance and a cannonball are both dropped from the same height, both will reach the ground at the same time. 
    But why doesn’t the moon collapse with the earth as the apple did?
Newton reasoned that the moon travels at a constant acceleration around the earth and is projected at the right velocity, thus creating its own orbit since the constant velocity and attraction by both bodies set a path for the moon to follow. 

Check out this cool thought experiment!

http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

Here, the same concept applies, if the velocity of the cannon ball is adjusted to the right speed, there will be a point where the cannon ball will create a uniform path and create its own orbit!!!!!!!

 

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