Lecture 7: Down to Earth

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Lecture 7 Down to Earth
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Aristotles Law of Free Fall
Heavier objects fall faster than lighter ones
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Galileos Law of Free Fall
All objects fall at the same speed
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Galileos Expt. Performed on the Moon(in a
vacuum)
The hammer and the feather both fall at the same
rate!
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Newtons Law of Universal Gravity
The force which makes an apple fall to the ground
is the same force which makes the moon go round
the Earth
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Gravitational Mass
The force on an object is proportional to its
mass. This is called the gravitational mass of
the object F ? mG
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Inertial Mass
Recall from Lecture 5 that mass measures an
objects resistance to motion. This is called
the inertial mass of the object F mIa
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Newtons Equivalence Principle

• Gravitational mass is equivalent to inertial
  mass mG mI
• This is remarkable because there is absolutely no
  reason why this should be so!

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Experimentally verified by

• Newton, using pendulums made from different
  materials (wood and gold)
• Eötvös (1889), using a torsion balance
• Modern-day experiments show that mG mI to 1
  part in 1011

A torsion balance is a device which measuresvery
weak gravitational forces betweenmasses. Very
slight deflections are amplifiedby reflecting a
light ray from a mirror.
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This Explains Galileos Law

• Consider two objects A and B, with massesm and
  2m, respectively
• The gravitational force on B is twice that on A
• But twice as much force is needed to get B
  moving the same rate as A
• So A and B fall at the same rate!

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Einsteins Happiest Thought
I was sitting in a chair in the patent office at
Bern when all of a sudden a thought occurred
to me If a person falls freely he will not feel
his own weight... I was startled. This simple
thought made a deep impression on me. It
impelled me towards a theory of gravitation.
This means that gravity can be cancelled out by
acceleration
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Einsteins Equivalence Principle

• In any given location, it is impossible to
  distinguish between the effects of accelerated
  motion and those of a gravitational field
• In short, gravity is equivalent to acceleration
• Explains Newtons equivalence principle

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Consequence of Equivalence Principle
Artificial gravity can be created by acceleration
If there were no windows in the elevator,
Einstein would not be able to tell whether he is
at rest on Earth or accelerating at a constant
rate through space
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Consider shining light in a freely falling
elevator

• A person in freely falling elevator will not
  experience gravity
• to him light would move in a straight
  line(c.f. dotted line)
• But to a stationary person outside, light will
  move in a curved path (c.f. solid line)

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Consider shining light in a uniformly
accelerating spaceship

• A person outside the spaceship would see light to
  move in a straight line (c.f. solid line)
• But a person in the spaceship would see light to
  bend towards the floor (c.f. dotted line)
• The curved path is the same as in the previous
  case!

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Bending of light by gravity

• The previous two experiments both show that light
  would be bent by gravity
• Predicted by Einstein in 1911 (and corrected in
  1915)
• Experimentally verified during a solar eclipse
  in 1919 by Eddington

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Effect Observed During a Solar Eclipse
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Bending of light by gravity (contd)
Expected... because light is energy, and by E
mc2, energy is equivalent to mass
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Gravitational Lenses
Light from a distant object (star or galaxy) is
bent by the gravity of another object in between
it and Earth
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Types of Gravitational Lenses
Multiple images
Arcs or rings
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Einstein Crosses
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Galaxy Cluster 00241654
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Cosmic Magnifying Glass
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Galaxy Cluster Abell 2218
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Gravitationally Lensed Image of Highest Redshift
Galaxy
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Gravitational Red-shift

• Light is red-shifted in a gravitational field
• This is related to the slowing down of time in a
  gravitational field
• since atoms vibrate slower and emit light with
  longer wavelength (smaller frequency)

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Thought Experiment (from Einsteins Mirror)

• Excited atoms have more energy than the
  unexcited ones, and this makes the belt rotate
• Have we created a perpetual motion machine?
• No, because light has lost energy at the bottom
  and therefore appears red-shifted

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Experiment to detect gravitational red-shift on
Earth

• Performed by Pound and Rebka at Harvard in 1960
  
• Light travelled from the bottom to the top of a
  23 m high tower against Earths gravitational
  field
• In this experiment, light was found to have been
  red-shifted by a tiny amount

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Gravitational Blue-shift

• Similarly, light is blue-shifted when falling
  down a gravitational field
• because it gains energy in doing so

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Summary

• Newton found that the gravitational mass of an
  object is equivalent to its inertial mass
• Einstein postulated that gravity is equivalent to
  acceleration
• Immediate consequences
• bending of light by gravity
• gravitational red-shift
• The full theory built upon this postulate is
  general relativity (next lecture!)