Solar Flares hitting Earth

Question

When the earth is hit by solar flares, will it make the earth move faster through space when the magnetic field bends?

Answer 1

A solar flare of coronal mass ejection (CME) moves at about $1000km/s$, which is fast. The mass of material that interacts with the Earth is on the order of $10^6$ tons. This means it has a momentum of $10^{15}kg~m/s$. I will assume this is the momentum absorbed by the Earth, and that this momentum is in the radial direction. Now let us consider the momentum of the Earth. The Earth has a mass of about $6.0\times 10^{24}kg$. The angular velocity of the Earth is then about $30km/s$ so it momentum tangential to its orbit is about $1.8\times 10^{29}kg~m/s$. The solar flare is then $14$ orders of magnitude smaller. I will leave it to readers to compute resultant velocity and so forth. However, it is clear the velocity change is negligible. Even if Earth gets impacts by several a year over a billion years the delta-vee $\Delta v$ will be $4$ or $6$ orders of magnitude smaller than the orbital velocity of the Earth.