# Shouldn't cosmic rays slow down Earth's movement around the Sun?

Maybe a dumb question. Are cosmic rays slowing down earth's (or any planets) movement around the sun? To me it sounds like an analogy of moving a mass through air and being slowed down by the impact of air-molecules with the mass (here cosmic ray particles)

• They should arrive more or less from all directions. – Alchimista Aug 9 '19 at 8:12
• @Alchimista But they are blueshifted when they arive from ahead, and redshifted when they arive from behind. Should be neglible though - especially compared to solar wind. – Taemyr Aug 9 '19 at 10:49
• Compare the energies of both. Cosmic rays are in GeV-PeV ranges; what's the energy of earth's motion? – Kyle Kanos Aug 9 '19 at 12:29
• @KyleKanos so they do in fact slow down the movement? – rst Aug 9 '19 at 13:31
• @Alchimista but so do air-particles when moving through air, you have to account for the relative movement (as the earth moves around the sun) – rst Aug 9 '19 at 13:32

• Wikipedia puts the flux of GeV particles at around $$j=10^{4}\:\rm m^{-2}\:s^{-1}$$.
• Assume for simplicity that the bulk of the cosmic rays at this energy are protons, for which an energy of $$E=1\:\rm GeV$$ corresponds to a momentum of $$p=\frac1c\sqrt{E^2-m_p^2c^2}\sim 10^{-19}\:\rm kg\:m/s$$.
• At the flow rate indicated that gives a momentum flow rate (a.k.a. pressure) of about $$P=jp=10^{-15}\:\rm kg\:m^{-1}\:s^{-2}.$$
• Multiplying by the cross-sectional area of the Earth, that produces a force of $$F = P\, \pi R_\oplus^2 \sim 1 \:\rm kg\:m\:s^{-2}.$$
• Dividing that by the mass of the earth gives an acceleration of $$a =F/M_\oplus \sim 10^{-26} \:\rm m/s^2.$$
• The orbital velocity of the Earth is $$v\approx 30\:\rm km/s$$, so at that rate it would take about $$T = v/a \sim 10^{22}\:\rm y$$ to slow the Earth down to a halt.
For comparison, the age of the Earth is on the ballpark of $$10^{9}\:\rm y$$, which puts a comfortable factor of eleven orders of magnitude between the unrealistic overestimate in the bullet points above (why is it an overestimate? because it doesn't factor in the momentum coming in from the back!) and reality.