Chapter 12 Gravitation and Newton’s Synthesis
12-8 Principle of Equivalence; Curvature of Space;Black Holes
12-6 Gravitational Field
12-2 Vector Form of Newton’s Law of UniversalGravitation
12-3 Gravity Near the Earth’s Surface; GeophysicalApplications
12-1 Newton’s Law of Universal Gravitation
12-7 Types of Forces in Nature
12-5 Kepler’s Laws and Newton’s Synthesis
12-4 Satellites and “Weightlessness”
G = 6.67 X 10^-11 NM^2 kg^-2
Cavendish
experiment :
Now, knowing g and the radius of the Earth, the
mass of the Earth can be calculated :
mE = grE^2 / G = 5.98 X 10^24 kg
- The satellite is kept in orbit by its speed—it is continually falling, but
the Earth curves from underneath it.
- Objects in orbit are said to experience weightlessness. But they still have a gravitational force acting on them.
- No normal force because the satellite and all its contents are in free fall.
This is what leads to the experience of weightlessness.
- The orbit of each planet is an ellipse, with the Sun at one
focus.
- An imaginary line drawn from each
planet to the Sun sweeps out equal areas in equal times.
- The square of a
planet’s orbital period is proportional to the
cube of its mean distance from the Sun.
Keepler's law can be derived from Newton's laws : (T1/T2)^2 = (s1/s2)^3
The gravitational field : g = F/m
The gravitational field due to a single mass
M : g = (-GM . r / r)^2
- Strong nuclear force (binds protons and
neutrons together in the nucleus)
- Weak nuclear force (responsible for some
types of radioactive decay)
- Electromagnetism
- Gravity
Except for gravity, the forces we experience
every day are due to electromagnetic forces acting at the atomic level.
Inertial mass: the mass that appears in
Newton’s second law
Gravitational mass: the mass that appears
in the universal law of gravitation
Principle of equivalence: inertial mass and
gravitational mass are the same
If the gravitational field is strong enough,
even light cannot escape, and we have a
black hole.