Orbits and Law of Gravity
Reasoning that an attractive force of gravity could explain both motions (i.e. falling and orbiting), Newton devised his universal Law of Gravity
- force of m on M: FM<m = (GMm)/r2 -- attractive and radial
- force of M on m will be equal and opposite to this
- Newton’s gravitational constant G important
- gravitational acceleration a = GM/r2 at earth’s surface
- hence the mass of earth M = ar2/G
- a = 9.8 m/s/s and r = 6400 km are well known
- measurement of G (Cavendish) “weighs the Earth”
- also weighs planets, the Sun, and the Universe
Newton’s thought experiment for achieving Earth orbit
- Place a cannon on a high mt. and fire horizontally f.5-8
- If velocity just right, circular acceleration (v2/r) exactly equals gravitational acceleration GM/r2