Is there a drag on Earth caused by its motion relative to the CMB rest frame?

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Motion relative to the CMB rest frame creates a dipole moment in the wavelength of CMB photons in the direction of motion. Observations suggest that the Earth has a motion relative to CMB rest frame of 600 km/s.

As indicated in this study, for a spacecraft at a speed we shall dub 'ludicrous speed', the drag from the CMB photons would become very significant, as they would be blueshifted to the point where pair production occurs. This effect also theoretically limits the energy of observed cosmic rays, or at least the distance that such cosmic rays can travel. Even before this point though, momentum will be transferred to the spacecraft , producing drag.

My question is this: Does this drag exist even at the low peculiar velocity of Earth? I imagine it is a vanishingly small force, but it does have an awful long time to act. How would one calculate the force imparted at our peculiar velocity?

 

[mfb]

Technically: Sure. The energy density is 0.25 eV/cm³. For a rough approximation, assume Earth flies through space and picks up all photons "in front of it", re-emitting the energy isotropically. That is not true as the CMB photons move around, but that will just give some prefactor not far away from 1. Then Earth feels a radiation pressure of $0.25 \frac{eV}{cm^3} \cdot 600 \frac{km}{s} \frac{1}{c} = 8\cdot 10^{-17} Pa$ or a force of 32 mN. This leads to an acceleration of 5*10^-27 m/s². If Earth would freely float through the CMB, over 10 billion years this would change the speed of it by 1.7 nanometers per second. Yeah... forget it. To make it worse, Earth is not floating freely, it orbits the Sun. The column density of Sun is larger by a factor of about 100, so the effect on Sun is even smaller by a factor 100.

 

[Chronos]

The momentum of Earth is quite large compared to CMB photons and CMB photons strike Earth from all directions, not just in the direction of movement. The term 'vanishingly small' is an exaggeration when it comes to characterizing the drag on Earth due to the CMB. Rest assured solar photons would have a greater affect than CMB photons. You can play around with this calculator; http://www.georgedishman.f2s.com/solar/Calculator.html, for an idea of how much they hinder the motion of earth. Needless to say we can safely ignore that effect on Earth's orbit. It would be safe to say collisions with space debris dwarf the contributions of photons to impeding the Earth's motion.

 

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Technically: Sure. The energy density is 0.25 eV/cm³. For a rough approximation, assume Earth flies through space and picks up all photons "in front of it", re-emitting the energy isotropically. That is not true as the CMB photons move around, but that will just give some prefactor not far away from 1. Then Earth feels a radiation pressure of $0.25 \frac{eV}{cm^3} \cdot 600 \frac{km}{s} \frac{1}{c} = 8\cdot 10^{-17} Pa$ or a force of 32 mN. This leads to an acceleration of 5*10^-27 m/s². If Earth would freely float through the CMB, over 10 billion years this would change the speed of it by 1.7 nanometers per second. Yeah... forget it. To make it worse, Earth is not floating freely, it orbits the Sun. The column density of Sun is larger by a factor of about 100, so the effect on Sun is even smaller by a factor 100.

Ok, that is a very small effect indeed. Is there any scenario other than UHE cosmic rays where this drag would be worth considering? Interstellar or intergalactic dust or gas?

 

[mfb]

For the cosmic rays, it is not really a drag, it is just a conversion probability.

Repeating the same approach from above with 10^-20 m² atoms of 1 u, we get 5*10^-10 m/s² or a cooling time of 40 million years (as the force is proportional to speed). I don't trust the numbers enough to say if this is lower than a billion years, but a fast gas cloud far away from galaxies might actually experience some drag over time.

 

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Thanks mfb and Chronos. I'm enjoying this lightsail calculator as well.