Thursday, November 3, 2011

Here Comes the Sun

Second Author:  Eric

Anonymous argues that the Sun is undergoing, and is powered by, free-fall collapse, claiming that a contracting body heats up.  They claim that this accounts for the Sun's heat, and that the timescale for collapse is long enough for us to not notice.  Let's prove this argument wrong with some basic physics.

Let's first calculate the total potential energy contained in the Sun, given its mass and radius.
We begin with our formula for gravitational potential energy:


Now let us examine how this potential energy is related to the velocity of a free-falling element of mass near the surface of the Sun.  Setting our potential energy equal to kinetic energy, we get the following relation:

As an order of magnitude calculation, let's replace our velocity with the solar radius divided by the free-fall time.  Anonymous objects to this substitution on the grounds that friction and interactions between the particles will slow this velocity down.  However, it likely won't be slower by more than an order of magnitude, and the answer we will get will still be way too small.  Making the substitution and solving for the free-fall time, we get:

Given that we calculated the free-fall time to be on the order of 24 minutes, our "questionable" substitution would have to be off by many orders of magnitude to make the collapse slow enough.


1 comment:

  1. What are you assuming about the density of the Sun in order to get the 3/5 on the front? (This assumption is fine for OOM calculations, but it's good to know what you're assuming.)

    When you solve for the velocity of a free-falling element of mass, where are you assuming it has freely fallen from?

    I enjoyed Anonymous's interjections :) I think by the definition of free fall, if friction and interactions between the particles slow it down, it's no longer free fall. Pressure is just interactions between particles, after all.

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