2 types of Mass:
1. Inertial mass (F=ma)
2. Gravitational Mass (F= mM/d^2) -usually
thought of as weight
Einstein's general theory of relativity describes gravity as a curvature of
spacetime caused by the presence of matter. If the curvature is fairly weak,
Newton's laws of gravity can explain most of what is observed. For example, the
regular motions of the planets. Very massive or dense objects generate much
stronger gravity. The most compact objects imaginable are predicted by General
Relativity to have such strong gravity that nothing, not even light, can escape
their grip.
Three main tests of general relativity:
1. Deflection of starlight by the sun
2. Advancement of the Perihelion of
Mercury
3.
Gravitational Redshift
The Schwartzschild radius (developed in 1916) of an object is related to its
mass by the (really large) equation:
Radius required
for a specific mass to escape gravity and create a black hole where :
- M is the mass of the object
- G is the gravitational constant and
- c is the speed of light
LaPlace's Theorem (1798):
A luminous body with earth's density could be
so large that light cannot escape. (Newton's Law->escape
velocity/energy->equation of Schwartzschild radius) how?
Gravitational Orbits
Conic sections are used for celestial mechanics
(discovered Mena by 325 BC) deriving equations for the conical sections of
orbits using LaGrange's calculus of variations on L=T-V (T is kinetic energy, V
is potential energy and total enegy is T + V) to get to p = h^2/GM
Newton's 3 Laws of Motion:
1. Law of Inertia- body/mass will move in a straight line @ a constant
speed unless acted upon by another force
2. F=ma
3. For every action
there is an equal and opposite reaction
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