Dynamical friction due to gravity

[sapz]

Homework Statement

Hi there. Can anyone help me with this question, or maybe give me some approach to this question? I really don't know how to start solving it.

In this question we will show that gravity can act as an effective friction
force. Massive objects moving in a uniform medium will be slowed down due
to gravity. When the massive object moves it will create a wake behind it
of over dense gas that will slow down the object due to gravity interaction
between the object and the over dense region behind it. We will assume that
we have a massive object with mass M moving at a velocity vM in an infinite
gas cloud with a density ρ.

1. Assume each small gas particle feels only the gravity of the big object
and moves at a constant acceleration that is given by its initial position
relative to the object. In a short time span Δt, gas particles up to which
radius will reach the center object (neglect the center objects motion)?
How much mass do they have?

2. During the time the excess gas mass has fallen the massive object has
moved by what distance (assume constant velocity)? Assume that all
of the fallen mass has reached the original position of the object, what
force will the object feel from the extra mass behind it?

3. If two massive objects are going through a uniform medium, who would
be slowed down more, the heavier one or the lighter one? How does
this compare to aerodynamical drag whose force is proportional to the
area?

Homework Equations

The Attempt at a Solution

 

[haruspex]

Not even an attempt at the first part? It's very easy. Just use the usual s/t/u/v/a equations for constant acceleration. (Radius here refers to the distance to the massive object, not the radius of the particle.)