I was reading about how powerful supernova were and found out there are even bigger supernovae also called hyper nova. A large explosion was discovered in 2016 I believe (or was it 2017). I would like to know on a human scale how much power that is. Suppose an inventor produced an engine technology that has the output of the largest superluminous super nova to project a space shuttle. How fast would the space ship be projected forward? That is the output pushes air to project the space ship forward. What speed would it reach. Part of me wants to say faster than light. I imagine the ship will travel so fast it would disintegrate since matter cannot exceed the speed of light.
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$\begingroup$ What did you find on Wikipedia, for example the energy output of a supernova compared to the Sun (billions?)? What’s the Sun’s energy output compared to a nuclear power station (billions?)? What’s the possibility your spaceship could harness such energy (zero?)? $\endgroup$– Chappo Hasn't ForgottenCommented May 9, 2018 at 23:54
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$\begingroup$ A massive object can travel as close to the speed of light as it likes without reaching it if it can gain enough energy. No amount of energy will push it as fast as light. And from the point of view of anyone on that ship, regardless of what speed they are traveling at relative to some other object, light will still be traveling at the same speed of light (surprise) from their point of view as everyone else measures. $\endgroup$– StephenG - Help UkraineCommented May 10, 2018 at 6:47
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2 Answers
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This puts us in the realm of silly numbers.
A supernova has enough energy to rip a massive star apart. Putting all that energy into one small rigid body isn't going to end well.
A hypernova gives off about $10^{46}$ Joules. We will need the formula for relatavistic kinetic energy $E=mc^2(\gamma-1)$ where $\gamma$ depends on velocity. The mass of the shuttle is about $2\times 10^6$ kg, and $c^2=9\times 10^{16}$
So $10^{46} = (2\times 10^6) \times (9\times 10^{16}) (\gamma - 1)$. Rearranging, $\gamma = 5.5\times10^{22}$.
In relativity $\gamma = 1/\sqrt{1-v^2/c^2}$ So even this massive amount of energy won't make the shuttle go faster than light. It will make it go at
99.99999999999999999999999999999999999999999998%
of the speed of light.
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1$\begingroup$ If we use a more massive spacecraft, such as the entire planet Earth, we get get gamma approximately 20000, so velocity is only 99.995% of c. If we take the entire solar system so as to be sure of all our familiar home comforts, it's something like 30% of lightspeed. $\endgroup$ Commented May 10, 2018 at 11:45
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1$\begingroup$ +1 for "silly numbers". Next question is find a substance that can withstand that kind of energy input. Sounds like a job for xkcd what-if. $\endgroup$ Commented May 10, 2018 at 15:03
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1$\begingroup$ @JonathanLandrum he did already, indirectly. In #73 he posed the question of what is brighter in terms of delivering energy to your retina: a supernova viewed from 1AU, or an H-Bomb pressed against your eye. Spoiler, its the supernova by a factor of about one billion. The only materials strong enough to survive that much energy are ones that are far enough to be unaffected by it. $\endgroup$– CodyCommented May 10, 2018 at 19:51
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This comment will not answer about the speed of a rocket, because I don't know other factors involving. But this comment will give you energy scales, which you can work on later for the speed of a rocket. I cannot put this comment in the "comment" because it will be too long.
Hypernovae (a.k.a. supernovae Ic broad line (SNe Ic-BL) and superluminous supernovae (SLSNe) are core-collapse supernovae (CCSNe).
Typical CCSNe are believed to be delayed neutrino-driven explosions, where total explosion energy is $10^{53}$ erg. For typical SNe (i.e., not SNe Ic-BL nor SLSNe), only $\sim 1$% of the total explosion energy is converted into radiation, i.e., $\sim 10^{51}$ erg.
SNe Ic-BL and SLSNe radiate $\gtrsim 10^{51} - 10^{52}$ erg, more than those of the typical SNe. Because they are more energetic than $\sim 10^{51}$ erg predicted from typical CCSNe, their explosion mechanisms or energy sources are under debate. Currently, the power from a spinning down magnetar is the most favored candidate. The magnetar spin-down can supply $\sim 10^{52}$ erg, with peak $\lesssim 10^{45}$ erg/s.
Talking in term of power, i.e., luminosity, typical SNe has peaks UV/optical/NIR outputs $\lesssim 10^{43}$ erg/s. SNe Ic-BL are about the same scale, but they are more energetic because spectral evidence implies fast moving ejecta. SLSNe are $\gtrsim 10^{44}$ erg/s.
To illustrate how powerful these SNe are, we normally compare them to solar radiation $\sim 10^{33}$ erg/s.
Note that there are even more powerful explosions predicted such as pair-instability supernovae (PISNe). PISNe can supply $\sim 10^{53}$ erg. But because of very massive ejecta, the peak luminosity is predicted to be comparable to those of SLSNe, but with very long timescale. Some slow-evolving SLSNe are candidates for PISNe.
Hope this is helpful for you to use in calculating the speed of a rocket.
answered May 10, 2018 at 14:53