exupero's blog

Nuances of a shorter walk in the sun

In the previous post I proposed a shorter route for the astronaut walking around the Moon in the story "A Walk in the Sun". While the intuition that the route will keep her in the sun and allow an easier pace is correct, there are some caveats.

Here's a plot of longitude over time, with the Moon's night longitudes shaded and the astronaut's longitude shown in blue as she walks ten miles per hour away from the solar terminator:

I've defined the site of the crash as 0° longitude, and the story states that from the time of the crash sunset is three days away. Walking ten miles per hour gives the astronaut a comfortable margin. In fact, her average speed can dip almost as low as eight and a half miles per hour before she's in danger of sunset catching up to her:

Unfortunately, while sunset may not catch her, she won't catch her ride. Rescue is due at day 30, but at such a leisurely pace she won't return to the site of the crash by then. To get back in time, she'll need to walk more like nine and a half miles per hour:

If the astronaut had crashed at 80°N and walked only that latitude back to her crash site (as illustrated above), a pace of ten miles per hour would quickly have her chasing sunrise rather than sunset chasing her, and she would have spent most of her time sitting as she waited for rescue to arrive:

She'd even be safe walking as slowly as two miles per hour.

Now let's see how she covers longitudes looping from the equator up to the pole and back:

The curve looks very different. While she does manage to stay in sunlight, she loses buffer between her and sunset on the outbound journey, then rapidly gains longitude near the pole, after which she's quite safe for her walk back to the equator.

Though the route is only 70% as long as the great circle around the equator, she can't walk 70% of the speed. If she does, night will catch her around day 8:

She has to walk at least eight and a half miles per hour to keep in the sun.

The good news is if she can maintain that pace until day 10, she can slow down after, dropping as low as about five and a quarter miles per hour without missing her ride off the Moon:

In this scenario, that's not such a terrible dynamic. The route demands the fastest pace when the astronaut is freshest and equipment is in the best shape, then, when her stamina will be waning and equipment may need fixing, she has lots of margin to slow down for rest and repairs.