In Chapter 1 of 2010: Odyssey Two, Arthur C. Clarke wrote that an astronaut achieved a tenth of the speed of light in less than two minutes, and this meant an acceleration of about a quarter of million gravities.
Let's check. Here, I feel that the term "gravity" is not technical enough: Does it mean \( 1~\mathrm{ms}^{-2} \), the unit acceleration in SI units? Or g-force, an acceleration of about \( 9.8~\mathrm{ms}^{-2} \)?
Given that:
$$ u = 0~\mathrm{ms}^{-1} \\ v = \frac{c}{10} \approx 3.0 \times 10^7~\mathrm{ms}^{-1} \\ t=120~s $$
We have:
$$ a = \frac{v-u}{t} = \frac{3.0 \times 10^7}{120}~\mathrm{ms}^{-2} \\ \approx 250,000~\mathrm{ms}^{-2} $$
Indeed! The term "gravity" here should mean \( 1~\mathrm{ms}^{-2} \), which is the unit acceleration in SI units.
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