Eero wrote:

Consider an astronaut who orbits circularly with a spacecraft at distance L
from a planet's center. The planet's radius, mass and acceleration of
gravity at its surface are R, M and g.
Now, the astronaut wants to fire a bullet and hit the planet. What minimum
initial speed of the bullet is necessary to do this?(Supposing no air
resistence)

What have you done so far to approach this problem?