# Solar System destroyed vs Supernova

1. Jul 8, 2014

### Easternwind

I wanted to find out the difference between a supernova, and the energy it would take to blow up the Solar System.

This guy:

Says it would take the equiv of 5.09x 10^37 Tons of TNT to blow up the Solar System

Wikipedia says a Super Nova is 1x10^28 Tons of tnt.

So the Super Nova would be much smaller.

Then I did my own calcs ( all numbers are J )

I took the gravitational binding energy of the Sun 6.9 x 10^41

Then of the planets, For the planets I took earth's:
binding energy of earth = 2 x 10^32

Multiplied it by 9 for each planet , and then doubled that number for a decent estimate:
So : 36 x 10 ^32

so Binding energy of sun + 36 x 10^32

and I got
6.900000036 x 10^41

As the energy needed to destroy the SS by over coming the binding energy

( for this whole thing I am ignoring distance from the cause and such, assume they are all right near each other )

And the energy of a Supernova is 10^44

So with my way of doing things, and the others guys both contridict, Mine shows that a SN would be about 200x a Solar systems destruction.
And the tnt Guy's seems to show a Supernova is MUCH less than a Solar System level explosion

Thank you for the help!

2. Jul 8, 2014

### Bandersnatch

Hi, Easternwind.

First of all, you've got contradicting numbers. At one point you say a supernova releases 10^28 t(tons of TNT), which is about 4*10^37 Joules. Then you say it's 10^44 J.

Next, you're reading the page wrong. The colums with ~5*10^37 t(=~2*10^46 J) are for an explosion that is allowed to spread out in mostly empty space of the Solar System. You've done calculations equivalent to the "Raw energy" colums on the page, which is shown as ~5*10^31 t(~2*10^41 J, ~2*10^48 ergs).

Once that's out of the way, the results converge. Your value for Sun's binding energy differs by a factor of 3, for whatever reason, but it's a minor thing - the orders of magnitude match.

3. Jul 8, 2014

### Easternwind

As for your first point.
That is because one I got from the
"Equivalent of TNT" Wiki Page, and One I got from the definition of a FOE, which is one supernova.
Does that mean that page was incorrect? Because 10^44 has to be the correct number for Supernovae from what I have seen.

On your second point, I actually got it from the bottom of the page.
I wasn't seeing the energy needed and those 2 columns, now I do though.

You say I am doing a spread out one, so you are saying that
5 x 10^37 tons of tnt is the spread out one and 5x 10^31 would be if they were stacked. I see that now

And that the 5 x 10^ 31 = 2 x 10^ 41 J, which is similar to my equations 6.9 x 10^41
I see that now

==

However, a Supernova is said to be 10^28 Tons of TNT.

so if a Supernova = 10^28 tons of TNT
and
The Solar System requires 10^31 to blow up.

That would put destroying the SS at 3 exponents above a supernova.

However my equation gives = 6 x 10^41 to destroy a SS
and a SN in Jules is 10^44

So THAT would put a super nova at 3 exponents above destroying a SS

So, I am assuming that my number of 10^28 tons, is wrong for a supernova, and it is actually more, Since you say 10^28 tons = 10^37 J , so 10^47 J should be 2.4 x 10^34
so that would be 3 exponents more for the solar system again. Which is pretty close to the way I did it with the binding energy and the SN jules.

Except I think this one comes out to like 1000x stronger
and mine came out to be 140x stronger, due to the numbers in front of the exponents.
I will try to do that math when I get back.

Am I right in all this?

Thanks for all the help .

Last edited: Jul 8, 2014
4. Jul 9, 2014

### Bandersnatch

You really need to read carefully what your sources say. Look at the units in the list on the TNT eq. wiki page. It doesn't say what you think it says.

The only difference I can see between your calculations and those you link to, is in the binding energy for the Sun. Yours is roughtly three times higher. His is correct.
Show us your work, so we may spot the error.

5. Jul 9, 2014

### willem2

He does have the mass for neptune ten times too big, so the needed energy is a 100 times too big.

6. Jul 9, 2014

### Easternwind

Would that be significant? My calc gave the energy for the planet destruction as being like .00001% of the total.

7. Jul 10, 2014

### Bandersnatch

It's not significant in the sort of calculations you're comparing. I.e. the sum of binding energies for each body("raw energy" in the table). It is significant if you take spreading out of the explosion into account(the rightmost column on the webpage). It's all discussed in there.

By the way, your estimate for the combined binding energy of the planets is way off. You took Earth's binding energy as the baseline, when you should've taken Jupiter's to net you about three orders of magnitude higher a value.
It's all still dwarfed by the Sun's, of course.

8. Jul 10, 2014

### Easternwind

Yeah I mostly estimated on the planet side due to it not really mattering.

So would you say I am right that a Supernova is hundreds of times more powerful than a raw mass SS destruction?

9. Jul 10, 2014

### Bandersnatch

Sure.

There's still that factor of 3 error in your calculations, but roughly speaking yeah.

10. Jul 10, 2014

### Easternwind

Which part is the factor of 3 error in?

11. Jul 11, 2014

### Bandersnatch

Yours:
His:
2.30E+48[ergs]=2.3*10^41 Joules

6.9/2.3=3