### Re: Is there a difference between gravitational redshift and doppler redshift?

Date: Wed Oct 4 23:04:24 2000
Posted By: Bryan Mendez, Grad student, Astronomy and Astrophysics, University of California at Berkeley
Area of science: Astronomy
ID: 969797941.As
Message:

Hello,

Yes, there is a difference in gravitational and Doppler redshift (or blueshifts). The difference is in the physical mechanism that produces the effect. The effect is however the same: the color (wavelength) of a light wave is altered from its original color.

Doppler shifts affect all kinds of wave phenomena. They are a result of detecting a wave that was emitted by an object moving relative to the observer. The effect is commonly noticed in sound. If you are standing on a street corner and a car drives by while blaring its horn you will hear the pitch of the horn rise as it approaches you and fall as it moves away. The reason for this is that sound is a wave traveling through the air, and the pitch is a result of the wave's wavelength (the distance between two crests of the wave). Short wavelengths are high pitches and long wavelengths are low pitches. As the car approaches you the sound waves emitted by the horn are intercepting you at shorter and shorter intervals, compressing the sound wave that you hear and thus making the pitch rise. As the car moves away the waves intercept you at greater and great intervals stretching the wavelengths out to lower pitches. Another way to think of this effect is to imagine being in a boat on a lake. Some other boat has created a large wake and your boat is passing through the waves on the surface of the water. If you were to just hold your boat stationary as the waves passed they would do so with some regular frequency and hence wavelength. If instead you turned your boat and drove toward the oncoming waves they would pass by your boat with a higher frequency and shorter wavelength. If you turned your boat away from the waves and drove away from them they would hit you at a lower frequency and longer wavelength.

Light is also a wave phenomenon and thus has a Doppler effect. Just as wavelength corresponds to pitch for sound, color corresponds to wavelength for light. So, if a flashlight emitting green light was moving toward you, the wavelengths would get compressed and the color would change. How much it changes depends on how fast the flashlight is moving toward you. If it is moving sufficiently fast (many millions of miles per hour) the light would change to blue, and hence the term blueshift. Likewise if the green light is moving away from you then the wavelengths stretch to redder colors. Hence the term redshift.

Gravitational redshifts (or blueshifts) occur to light also but for a completely different reason. A projectile fired away from Earth's surface looses kinetic energy (the energy of motion) in order to gain potential energy (energy of position). Thus, said projectile looses speed as it tries to escape a gravitational field. Light must also loose energy to escape a gravitational field. But light cannot loose speed. It must always travel at the same speed, the speed of light (186,000 miles per second). The energy of light corresponds to its color. Blue light has more energy than does red light. So, if a green beam of light is sent away from Earth's surface it must loose energy and become more red, hence the term redshift.

For the Doppler shift the amount of change in color depends on the relative speed of the observer of the light and the emitter of the light. For gravitational redshift the amount of color change depends upon the strength of the gravitational field and the distance between the emitter of the light and the observer of the light. A green light sent from the surface of Earth would appear redder as observed at the distance of the Moon than it would from low Earth orbit. It takes more energy to get out to the Moon than it does to get to low Earth orbit. Also it takes more energy to escape a stronger gravitational field than it does a weaker one. The strength of a gravitational field is proportional to the ratio of the mass to the size of an object. An object with the same mass as Earth but smaller would have a stronger pull at its surface. Black holes have such a strong gravitational pull that it costs light an infinite amount of energy to escape their surface. Thus light cannot escape the surface of a black hole. It can escape from just above the surface. A green light emitted from just above the surface of a black hole might be observed from far away with very long wavelengths corresponding to invisible radio light.

So to sum up, yes the two causes have the same effect but are very different physically.

I hope that helps. If you have any further questions, please feel free to email me.

-Bryan Mendez
bmendez@astro.berkeley.edu

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