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Fermi's Piano Tuner Problem

How Old is Old?

If the Terrestrial Poles were to Melt...

Sunlight Exerts Pressure

Falling Eastward

What if an Asteroid Hit the Earth

Using a Jeep to Estimate the Energy in Gasoline

How do Police Radars really work?

How "Fast" is the Speed of Light?

How Long is a Light Year?

How Big is a Trillion?

"Seeing" the Earth, Moon, and Sun to Scale

Of Stars and Drops of Water

If I Were to Build a Model of the Cosmos...

A Number Trick

Designing a High Altitude Balloon

Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Calendar Calculations

Telling Time by the Stars - Sidereal Time

Fields, an Heuristic Approach

The Irrationality of

The Irrationality of

The Number (i)i

Estimating the Temperature of a Flat Plate in Low Earth Orbit

Proving that (p)1/n is Irrational when p is a Prime and n>1

The Transcendentality of

Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions

Maxwell's Equations: The Vector and Scalar Potentials

A Possible Scalar Term Describing Energy Density in the Gravitational Field

A Proposed Relativistic, Thermodynamic Four-Vector

Motivational Argument for the Expression-eix=cosx+isinx

Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Additional Notes on Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics
A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File
On Expansion of the Universe - PDF File

How Do Police Radars Really Work?

A car, traveling at speed, V, approaches a police radar, scanning for speeders with a frequency, frequency. Calculate the approximate frequency shift of the reflected signal.

Consider a single photon from the police radar. The photon must interact with the approaching car for a finite time while it is being reflected. Call this time, deltat. Let an interaction force, ± f, exist between the photon and the car for the time, deltat. The force exerted by the photon on the car, +f, acts to remove energy from the car. The force exerted by the car on the photon, -f, acts to add energy to the photon. Therefore, we expect the photon frequency to increase. During the time deltat, the car travels a distance deltas = V deltat. We may now write two equations, one for a change in momentum, deltap, and one for a change in energy, deltaE:

deltap = f deltat
deltaE = f deltas = fV deltat

Since the photon energy, E, is equal to hn, where h = Planck's constant = 6.63 X 10-34 j sec, then

deltaE = h deltafrequency

Also, since photon momentum equals h/c, where c is the speed of light, then

deltap = 2hfrequency/c + h deltafrequency/c

where the first term on the RHS represents deltap for an elastic reflection (i.e., one for which deltaE = 0), and the second term takes into account the change in frequency due to the change in energy.

Dividing eq. 1 by eq. 2, and substituting for deltaE and deltap from eqs. 3 and 4, we find

(2hfrequency/c + h deltafrequency/c)/(h deltafrequency) = 1/V

This equation may be simplified to read

deltafrequency/frequency = 2V/(c-V) approximately 2V/c

where the final step results from V << c. Now, let V = 60 mph = 27 m/sec, and let frequency = 5 X 108 Hz. Then,

deltafrequency= 90 Hz

The police radar detector easily detects this frequency shift.

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Responsible NASA Official: Theresa.M.Scott (Acting)