Newton's reasoning for the orbit of the Moon
Newton reasoned that the same laws of motion and gravity that determine
the fall of an apple also determine the motion of the Moon around the
Here is his picture, adapted from the Principia
Here is what Newton did.
- He didn't know the value of G.
- But by measuring the acceleration of an apple when he dropped
it, he could measure M G
- Supposing that the mass of the Moon is much less than the
mass of the Earth, that is enough to get the relation between
the period P of the Moon's orbit and its distance a
- He knew the distance a to the Moon.
- So he could calculate its period P.
- "I deduced that the forces whch 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 orb with the force of gravity at
the surface of the earth, and found them to answer pretty nearly."
Note that the same laws that govern matter on Earth are those that
govern the heavens. This was a complete change in thinking from
ASTR 121 Home
Davison E. Soper, Institute of Theoretical Science,
University of Oregon, Eugene OR 97403 USA