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I calculated the amount of energy needed to send ISS to orbit. It seems crazy expensive. I'm approximating my calculation with the following equation:

$$\begin{align} E_\text{tot} &= E_\text{kin} + E_{\text{pot}}\\ &= \frac{1}{2} m v_\text{orb}^2 + mgh \end{align}$$

where $m$ is the mass of the ISS (450 tons) $v_\text{orb}$ is the orbital speed of ISS (7.66 km/s), $g$ is the gravitational acceleration constant and $h$ is the orbital height of ISS (400 km).

I know it's a rough estimate but it should give numbers in the ballpark. I plug in the numbers and get $$ 1.49\cdot 10^{13} \text{ joules}$$

It's 3577 tons of TNT or 41 Hiroshima bombs.

Am I doing something wrong? It seems impossible to release that much energy with chemical thrusters. I know ISS was sent up by a lot of rockets, it's still too crazy for me.

edit:

Calculations were wrong; it's not 3577 tons of TNT, but instead it should be 3.577 tons of TNT.

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Your calculation of $E_{tot}$ is correct.

However, acc. Wikipedia:

The Little Boy atomic bomb dropped on Hiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 TJ)

So that was $63 \times 10^{12}\text{ J}$.

We get:

$$\frac{1.49 \times 10^{13}}{63 \times 10^{12}}=0.24$$

which appears a more reasonable result.

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  • $\begingroup$ Thank you! Makes way more sense. Before posting I tripple checked my calcuations - My numbers were off because i misread 4.184 giga Joules as 4,184 giga Joules. $\endgroup$ – nammerkage Mar 18 at 9:21
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Your estimate of the energy to put the ISS into orbit seems quite reasonable, about 15 TJ. When it is on the Earth's surface it already has some rotational energy (it is moving at about 465 m/s) which will reduce the needed increase in kinetic energy a little, but the effect is not large.

Your estimate of the energy yield of the Hiroshima bomb is a little low though. Wikipedia (nuclear bomb yields), for example, gives estimates from 54 - 75 TJ. So the energy of the Hiroshima bomb would be sufficient to put about 5 space stations in orbit, which seems more reasonable.

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