Could a 50-kilogram antimatter bomb destroy a 720 km diameter asteroid?

That would be more than twice 40 times the energy of the largest nuclear bomb ever tested, 50 megatons: https://en.wikipedia.org/wiki/Tsar_Bomba

That is a lot of explosion

Whether that destroys the asteroid depends on what it is made of and exactly where the explosion occurs.

Edited May 29, 20196 yr by Strange
orders of magnitude

 

3 hours ago, Strange said:

That would be more than twice the energy of the largest nuclear bomb ever tested, 50 megatons: https://en.wikipedia.org/wiki/Tsar_Bomba

Edited (fixed factor):

50 kg of antimatter would release 100 kg * (299792458 m/s)^2 = 9*10^18 J (assuming the all protons annihilated with antiprotons, and no neutrinos nor antineutrinos carried some energy with them)

1 megaton of TNT is 4.184*10^9 J

9*10^18 J / 4.184*10^9 J  > 2 gigaton of TNT.

Edited May 29, 20196 yr by Sensei

I got the 50 megatons figure from here:

Quote

2.1×1017 J

Yield of the Tsar Bomba, the largest nuclear weapon ever tested (50 megatons)

https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1018_to_1023_J

Confirmed by:

Quote

teragram of TNT

Tg

megaton of TNT

Mt

4.184×1015 J or 4.184 petajoules

1.162 TWh

46.55 g

https://en.wikipedia.org/wiki/TNT_equivalent

 

But I think I missed an order of magnitude, it should be at least 20 times the size of that bomb.

11 minutes ago, Sensei said:

50 kg of antimatter would release 50 kg * (299792458 m/s)^2 = 4.494*10^18 J (assuming the all protons annihilated with antiprotons, and no neutrinos nor antineutrinos carried some energy with them)

Do you need a factor of 2 in there for the mass of the antimatter plus the mass of the matter? (I think I made the same mistake with my calculations - so I think it should be 40 times).

14 minutes ago, Strange said:

Do you need a factor of 2 in there for the mass of the antimatter plus the mass of the matter?

You're right. We would need to have clarification from OP whether "50 kg" is mass of antiprotons alone, or mass of ready-to-be-used anywhere fuel i.e. together with enough regular matter to be able to ignite it all in the space at once, or "50 kg" is mass of ready bomb, together with the all electronics etc. needed to sustain it working.

Edited May 29, 20196 yr by Sensei