# What is the speed that we can reach using tsar bomba as a propellant?

The idea of using an atomic bomb as a propellant was introduced in project orion, but it did not work out because of the interdiction of using the atomic bombs. So I decided to calculate the speed that can reach a bomb using tsar bomb, and what one of you to correct me if I have any errors.

Using $E=mc^2$, $m = 27 ton$, $c=300000000\frac{m}{s}$, $E = 27000 \cdot 300000000^2 = 2430000000000000 = 2.43 \cdot 10^{21} J$.

But now I am stuck in, how to calculate the speed?

• There is nowhere near enough information to solve the problem -- how big an object are you accelerating with the bomb? -- but you're already on the wrong track. You're using the mass-energy equivalence formula, but hydrogen bombs don't have anything close to total conversion of mass to energy. (You also have the units wrong -- you need to use meters instead of km, so the e=mc^2 figure would be 2.43x10^21 joules). The actual yield of Tsar Bomba was about 210 petajoules, or 2.1x10^17J. en.wikipedia.org/wiki/Tsar_Bomba – Russell Borogove Jun 2 '18 at 22:57
• It depends on the mass of the spaceship what you want to accelerate with it, and on the effectivity of its drive. – peterh Jun 2 '18 at 23:50
• I also imagine, if you manage to fill in all the variables, you'd get a lot less delta-v than you would expect. Orion used magazines full of bombs, and fired bomb after bomb to build up speed. A single bomb won't get you far. Making the bomb bigger means it'd be harder to not blow yourself up. – Saiboogu Jun 2 '18 at 23:55
• @RussellBorogove yes it's 210 petajoules because not all the bomb will be transformed to energy thank you ;) – Taher Jun 4 '18 at 1:56
• @Saiboogu yes and there is a big problem and danger for the spaceship because of the heat emitted by the bomb and may be other radiation problem .. – Taher Jun 4 '18 at 1:57

First, your calculation has the serious mistake: Not the whole tsar bomb became energy, only a very small part of its core. Its energy yield is known: $2.1 \cdot 10^{17} J$. On the mass-energy equivalence, it means a conversion of 22g of total mass converted to energy, from the 27tons of the bomb.

There is no technology to use Tsar Bomb as spaceship propulsion. There are plans for nuclear propulsion using fissile micro pellets.

There is a missing input data in the question: the mass of this imaginary spaceship. Another missing input is the effectivity of the drive.

However, because only a very small part of the total fissile material converts to energy in any nuclear reaction, we can use the Newtonian mechanics to calculate it.

If we imagine a typical, around 30% effectivity of the termodynamical energy conversion, in the case of an 1000ton spaceship, the resulting speed is

$E=\frac{1}{2}mv^2 \Rightarrow v=\sqrt{\frac{2E}{m}} = \sqrt{\frac{2 \cdot 0.3 \cdot 2.1\cdot 10^{17} J}{10^6 kg}} \underline{\underline{\approx 355 \frac{km}{s}}}$.

• thank you for your response but if you can see here en.wikipedia.org/wiki/… it says that we can reach 12% speed of light can you explain this to me ? – Taher Jun 3 '18 at 1:06
• @Taher The project Orion is theoretically possible, from the engineering it is on the border of impossibility: Investing some billions, something might come out. From the point of that antimatter is in the picture, the project becomes fairy tale. There is no effecient way to produce antimatter. The billions of \\$s invested into antimatter production until now created lesser antimatter what could light a bulb for a minute. – peterh Jun 3 '18 at 1:10
• @Taher The same "hahahahah", from the mouth of professional astronomers and physicists, had made your question closed and deleted, if I don't save it with my votes and answer. Now the world wants your votes. Never forget what I said here! Never forget it in your entire life! Become a physicist or an engineer! – peterh Jun 3 '18 at 1:37
• Project Orion didn't use micropellets. It used bombs in the 0.1-0.3 kt range. – Hobbes Jun 3 '18 at 10:34
• Bussard ramjets probably won't work space.stackexchange.com/questions/22107/… – Organic Marble Jun 4 '18 at 2:02