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Measuring Distances in Astronomy with Geometry
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Slide 9

Astronomical Distance Ladder

Astronomical Distance Ladder

Slide 10

Special Theory of Relativity (STR)

Special Theory of Relativity (STR)

Speed of light (in vacuum): c = 300,000 km/s

Constancy of the speed

of light: Michelson &

Morley experiment

No signal or object can travel faster than c

[The ultimate speed limit!]

Slide 11

Basic Principles

Basic Principles

The speed of light is the same to all observers

The laws of physics are the same to all observers

Observable Consequences

Simultaneity is a relative concept

Length contraction: moving rulers appear to be short

Time dilation: moving clocks appear to run slow

The apparent mass (inertia) of an object increases as its speed increases (impossible to accelerate it up to c)

Equivalence of mass and energy: E = mc2

Special Theory of Relativity (STR)

Slide 12

Special relativistic effects are important when the SPEED of an object is CLOSE TO THE SPEED OF LIGHT: v ≈ c

Special relativistic effects are important when the SPEED of an object is CLOSE TO THE SPEED OF LIGHT: v ≈ c

Slide 13

Simultaneity and time are relative, not absolute

Simultaneity and time are relative, not absolute

Marion Jones sees A flash before B

Marion Jones sees A and B flash simultaneously

Slide 14

Measuring the length of a moving object: Length Contraction

Measuring the length of a moving object: Length Contraction

The apparent (i.e., measured) length of a moving object is shorter than the true length (measured when the object is at rest)

Slide 15

Measuring time on a moving clock: Time Dilation

Measuring time on a moving clock: Time Dilation

A moving clock runs slower than its counterpart at rest

Stationary Clock

Moving Clock

Slide 16

A Thought Experiment: Length Contraction and an Apparent Paradox The Garage Attendants Perspective

A Thought Experiment: Length Contraction and an Apparent Paradox The Garage Attendants Perspective

Slide 17

Solution: The driver and garage attendant do not agree on the question of whether the two doors were closed simultaneously

Solution: The driver and garage attendant do not agree on the question of whether the two doors were closed simultaneously

A Thought Experiment: Length Contraction and an Apparent Paradox The Drivers Perspective

Slide 18

The scientist in the laboratory witnesses time dilation,

The scientist in the laboratory witnesses time dilation,

while the Uranium atoms witness length contraction

A Real Laboratory Experiment: Direct Verification of Time Dilation and Length Contraction as Predicted by the Special Theory of Relativity

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