Transcript Newton`s Law of Universal Gravitation

Newton’s Law of Universal Gravitation
Nicolaus Copernicus- Polish astronomer
who said that the Earth revolves around
the sun, not the other way around!
Johannes Kepler- German astronomer
who discovered 3 basic laws of planetary
motion. Kepler said there was a “holy
spirit” force that kept the planets revolving
around the sun.
Isaac Newton- The force of attraction
between two objects of mass depends on
the two masses, the inverse-square of the
distance between them, and a universal
constant.
FG = G m M/ R2
G = 6.67 E -11 Nm2/kg2
Mass of the Earth = 5.98 E 24 kg
Radius of the Earth = 6.38 E 6 m
Newton realized that all objects fall in curved
paths.
Objects in orbit travel in curved paths
around another object. Ex: Earth around
the sun, or moon around the earth. We
say these objects are “falling around” the
bigger object.
The same gravity that pulls an apple off of a
tree is pulling the moon around the earth!
Inverse-square law F ~ 1/R2
If you double the distance, force is reduced
to ¼, If you cut the distance in half, force
increases 4 times!
Gravity affects the ocean tides. When the
moon is in line with an ocean, that ocean
will have a high tide. When the moon is at
a 900 angle to the ocean, it experiences
low tide.
The tidal pattern is every 6 hours. Example:
Florida’s coast may experience high tide at
midnight, low tide at 6 am, high tide at
noon, low tide at 6 pm.
Gravitational field strength – g
g = G M/ R2.
M= mass of planet,
R = radius of planet
g is the free fall acceleration for that planet.
Kepler- Three laws of planetary
motion.
1. Each planet travels in an elliptical orbit
around the sun, and the sun is at one of
the focal points.
2. An imaginary line drawn from the sun to
any planet sweeps out equal areas in
equal time intervals.
3. The square of the orbital period is
proportional to the cube of the average
distance between planet and sun. T2~R3
Period of a satellite in circular orbit
T = 2p(r3/GM)1/2 r = distance between
centers of mass, M= mass of planet
Speed of a satellite in circular orbit
vt = (GM/r)1/2
M= mass of planet,
r = distance between centers of mass