USAAAO — 2025 First Round

Suppose a rocket around a star of mass M wishes to execute an orbital transfer from a circular orbit with radius R to a larger one with that of radius 8R. One common way to do this is known as a Hohmann transfer, which has an intermediate elliptical orbit. This process requires two burns, with total delta-v Δv = k√(GM/R) for some k. Assuming instantaneous burns, compute k.