Newton: "Unify The Heavens And Earth" Flashcards
Newton
1642-1726 1/r^2 law of universal gravitation Physics behind kepler's laws (derived from his laws) Tidal effects of gravity F = ma
Newton’s inspiration for Gravity
No matter how high one climbs, earth pulls down
Would the earth pull down from the moon?
Wouldn’t the moon just fal down?
Realized moon is FALLING, but never falls DOWN
Why doesn’t the moon just fall down?
If you throw a rock in deep space, moves in a straight line at constant speed forever
Push forward = speed up
Pull back = slow down
Pull sideways = change direction/bend path (speed DOESNT change)
Moon is also a rock in perpetual motion - earth’s gravity pull sideways in it?
This sideways motion is key! If we stopped the moon, it would fall just like a dropped Apple
A treatise of the system of the world
A book (?) published by Newton in 1728
How did Newton modify Kepler’s 3rd law?
P^2 = 4π^2/G(M+m)•a^3
a = (rmax + rmin)/2 = a1 + a2
Consequences of Newton’s 3rd law
Two bodies orbit common centre of mass
Each orbit is congruent ellipse with focus at one COM point
Ratio of semi major axes a1/a2 = m2/m1
Tides
They both stretch and compress Also can have tidal heating (ex Io to Europa) Also Roche limit Also hill radius and Lagrange points (?) Also precession of equinoxes
Now that we have Newtonian gravity, what can we do?
Can find mass of an object by seeing how stuff rotates around it
Mass of supermassive black hole
Perihelion/aphelion speeds
Transfer orbits, how long they take, how to get to Mars
Newton’s main concern with gravity
How do we really know it’s gravity holding solar system together and not some other 1/r^2 force?
Force of gravity has unique mysterious property that all objects experience same acceleration in Fg field (needed Einstein to resolve)
Newton did a bunch of experiments to verify it
So he looked at the solar system to see if it had that property too - earth and moon fall at same rate if stopped! (Except tides but that’s expected)
Hill sphere
Similar to Roche limit
Sun’s tidal force disrupts moons orbit around earth if close enough
Moon orbit tidally stretched as sun moves closer
At hill radius moon can be in permanent full or new position, orbiting sun
Precession of equinoxes
Caused by tides Moon and sun exert different tidal forces on earth bulge Bulge caused by earth rotation Torque on earth not constant North Star changes as result (wobbles) Equinoxes change 20 mins each year
How did Newton check all his math?
The moon!
