# Dynamical friction due to gravity

• sapz
In summary, the conversation discusses the concept of gravity acting as an effective friction force on massive objects moving in a uniform medium. It explores the idea of a wake of over dense gas being created behind the object, which interacts with the object and slows it down. The conversation then goes on to discuss how this concept can be applied to calculate the distance and force experienced by the object, as well as how it compares to aerodynamical drag.
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?

## The Attempt at a Solution

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.)

## 1. What is dynamical friction due to gravity?

Dynamical friction due to gravity is a phenomenon in astrophysics where a massive object moving through a medium, such as a galaxy or a cluster of galaxies, experiences a deceleration due to the gravitational interactions with the surrounding medium. This results in a decrease in the object's velocity over time.

## 2. How does dynamical friction due to gravity affect the motion of objects?

Dynamical friction due to gravity causes objects to slow down as they move through a medium. This is because the object's gravitational pull creates a wake in the medium, causing a drag force that opposes the object's motion.

## 3. What factors affect the strength of dynamical friction due to gravity?

The strength of dynamical friction due to gravity depends on the mass and velocity of the moving object, as well as the density and distribution of the surrounding medium. The more massive and faster the object is, and the denser and more concentrated the surrounding medium is, the stronger the dynamical friction will be.

## 4. Can dynamical friction due to gravity be beneficial?

Yes, dynamical friction due to gravity can be beneficial in certain situations. For example, it can help to slow down and stabilize the orbits of objects in a galaxy or a cluster of galaxies, preventing them from flying off into intergalactic space.

## 5. How is dynamical friction due to gravity related to dark matter?

Dynamical friction due to gravity is one of the pieces of evidence for the existence of dark matter. The observed amount of dynamical friction in galaxies and galaxy clusters is much greater than what can be accounted for by the visible matter alone. This suggests the presence of a large amount of invisible, gravitationally interacting matter, which we call dark matter.

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