What is the Jeans length of our Sun?

[Maximum7]

The Jeans instability is the collapse of a cloud of gas or dust. Recently, a vSauce short claimed that if you wanted to destroy the Sun, you would need to spread its material far enough that it wouldn't recollapse into a star again. vSauce gives the number at 10 AU (Astronomical units)

 

I usually trust vSauce but I have no clue how he got this number and I can't find any additional sources supporting it. Is 10 AU correct?

 

Jeans instability - Wikipedia

 

How To Destroy The Sun

 

[Genady]

25 minutes ago, Maximum7 said:

I have no clue how he got this number and I can't find any additional sources supporting it.

A short Internet search returns many sites explaining how to calculate Jeans length. Just plug in the numbers.

[swansont]

49 minutes ago, Maximum7 said:

if you wanted to destroy the Sun, you would need to spread its material far enough that it wouldn't recollapse into a star again

Oh, is that all you’d have to do? </sarcasm>

[TheVat]

Since it's about balancing thermal energy and gravitational work, I would think V Sauce (Mike Stevens) would need a way to obtain the thermal energy after the sun has been spread around - seems tricky, given we don't know what energy inputs would be (and losses) to achieve this drastic effect.  

(more a Veritasium fan, myself, and Derek Muller has a stronger CV for talking about physics imo)

 

The approximation (simplified) formula for Jeans' length is 

r being the cloud radius.  And the T, as I said, is the tricky one.

I get 30 inches.  Wait.... that's my jeans length.  Sorry.  

[Maximum7]

2 hours ago, Genady said:

A short Internet search returns many sites explaining how to calculate Jeans length. Just plug in the numbers.

I’m looking at the equation right now. I don’t know if the temperature of the gas would be the same as the sun itself. 

[Genady]

7 minutes ago, Maximum7 said:

I’m looking at the equation right now. I don’t know if the temperature of the gas would be the same as the sun itself. 

What do you mean, temperature of the Sun?

[swansont]

2 hours ago, Maximum7 said:

I’m looking at the equation right now. I don’t know if the temperature of the gas would be the same as the sun itself. 

Fusion would stop and you’re causing an expansion of the gas. So lower, but the sun doesn't have a uniform temperature.

As TheVat implied, it’s not a trivial exercise to determine that.

[Ammaniya]

Yes, 10 AU is correct!

[Genady]

40 minutes ago, Ammaniya said:

Yes, 10 AU is correct!

Knowing this, one can calculate the gas temperature.

[Maximum7]

3 hours ago, Ammaniya said:

Yes, 10 AU is correct!

You did it? The math checks out?!

[swansont]

17 hours ago, Maximum7 said:

The Jeans instability is the collapse of a cloud of gas or dust. Recently, a vSauce short claimed that if you wanted to destroy the Sun, you would need to spread its material far enough that it wouldn't recollapse into a star again

It’s not clear here if you think 10 AU is how far you need to disperse the material. The wikipedia article says “All scales larger than the Jeans length are unstable to gravitational collapse, whereas smaller scales are stable” which implies spreading the material far apart would be an unstable situation. What’s happening is that by spreading the material out the density drops, increasing the Jeans length, but the size of the cloud is smaller than 10AU, so the thermal energy exceeds the magnitude of the gravitational energy. The Jeans length is where they are equal.

(It also seems that the analysis ignores the role of inelastic scattering in the process, which I’m sure astrophysicists have noticed, so it’s a more subtle situation, that is, the Jeans length would not be constant in time for a given mass and size)

[Ammaniya]

20 hours ago, Maximum7 said:

You did it? The math checks out?!

No... Pff, I did not. But everywhere I googled and tried finding, I was told that it CAN be correct, and at some places it did say that it is correct, so idk... Sorry if I overthrow.