Newton, Einstein, and Gravity. Chapter 5. Guidepost.
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Astronomers are gravity experts. All of the heavenly motions described in the preceding chapters are dominated by gravitation. Isaac Newton gets the credit for discovering gravity, but even Newton couldn’t explain what gravity was. Einstein proposed that gravity is a curvature of space, but that only pushes the mystery further away. “What is curvature?” we might ask.
This chapter shows how scientists build theories to explain and unify observations. Theories can give us entirely new ways to understand nature, but no theory is an end in itself. Astronomers continue to study Einstein’s theory, and they wonder if there is an even better way to understand the motions of the heavens.
The principles we discuss in this chapter will be companions through the remaining chapters. Gravity is universal.
I. Galileo and Newton
A. Galileo and Motion
B. Newton and the Laws of Motion
C. Mutual Gravitation
II. Orbital Motion
B. Orbital Velocity
C. Calculating Escape Velocity
D. Kepler's Laws Re-examined
E. Newton's Version of Kepler's Third Law
F. Astronomy After Newton
III. Einstein and Relativity
A. Special Relativity
B. The General Theory of Relativity
C. Confirmation of the Curvature of Space-Time
Mathematics as a tool for understanding physics
Forefather of modern science: conducts experiments using scientific method.
Used inclined planes and tried to eliminate friction to study motion.
Determined that objects (without friction) naturally maintain motion-they have inertia
Acceleration of gravity is independent of the mass (weight) of the falling object.
Friction interferes with falling bodies so they fall differently.
Without friction, all bodies fall at same rate near Earth’s surface.
• “If I have seen farther than others, it has been by standing on the shoulders of giants.”
1st Law: A body continues at rest or in uniform motion in a straight line unless acted upon by some net force.
Example: A spacecraft moving in space will continue to travel forever in a straight line unless some external force acts on it.
2nd Law: The accelerationa of a body is inversely proportional to its mass m, directly proportional to the net forceF, and in the same direction as the net force.
a = F/m F = m a
Acceleration is the rate at which velocity changes: a race car goes from 0 to 200 mph in a few seconds!
Aristotle’s “natural” and “violent” motion are rejected. Newton says that constant speed in a straight line is natural, and any accelerated motion is forced.
3rd Law: To every action, there is an equal and opposite reaction.
A rifle pushes on a bullet and the bullet pushes on the rifle
The same force that is accelerating the boy forward, is accelerating the skateboard backward.
A rocket is pushed up by forcing exhaust out of engine.
For astronomy, a body of mass m orbits another body of mass M.
Gravity & Inverse Square Law
The universal law of gravity allows us to understand orbital motion of planets and moons:
(SLIDESHOW MODE ONLY)
In order to stay on a closed orbit, an object has to be within a certain range of velocities:
Too slow object falls back down to Earth
Too fast object escapes Earth’s gravity
Satellite projection animation
(SLIDESHOW MODE ONLY)
(SLIDESHOW MODE ONLY)
1st Law: The orbits of the planets are ellipses with the sun at one focus.
2nd Law: A line from a planet to the sun sweeps over equal areas in equal intervals of time.
3rd Law: A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed.
Py2 = aAU3
All laws of planetary motion are proved using law of gravitation!
Planet Platonic Solid
Mercury Inside the Octahedron
Albert Einstein (1879 – 1955) showed that Newton’s laws of motion are approximate. For low velocities they work well, but not for high velocities (near the speed of light.)
This is equivalent to:
The laws of physics are the same for all observers, no matter what their motion, as long as they are not accelerated.
Light clock animation
Length contraction animation
A new description of gravity
“Observers can not tell the difference between acceleration and gravitational forces.”
Which also means:
“Mass tells space-time how to curve, and the curvature of space-time (gravity) tells mass how to accelerate.”
Imagine a light source on board a rapidly accelerated space ship:
As seen by a “stationary” observer
As seen by an observer on board the space ship
For the accelerated observer, the light ray appears to bend downward!
Now, we can’t distinguish between this inertial effect and the effect of gravitational forces
Thus, a gravitational force equivalent to the inertial force must also be able to bend light!
This bending of light by the gravitation of massive bodies has indeed been observed:
During total solar eclipses:
The positions of stars apparently close to the sun are shifted away from the position of the sun.
New description of gravity as curvature of space-time!
A massive galaxy cluster is bending and focusing the light from a background object.
acceleration of gravity
inverse square law
center of mass
general theory of relativity
1. How did Galileo idealize his inclines to conclude that an object in motion stays in motion until it is acted on by some force?
2. Give an example from everyday life to illustrate each of Newton’s laws.