In Geoffrey Landis's short science fiction story "A Walk in the Sun", an astronaut is stranded on the moon and has to circumnavigate it on foot to keep her spacesuit's solar panels in daylight. Given the Moon's circumference of about 6,800 miles, circumnavigating it in 29½ days requires an average pace of around ten miles per hour, which seems more or less feasible in the Moon's weaker gravity, even in a bulky spacesuit. However, as I reread the story not long ago, I realized that walking the Moon's full circumference isn't necessary. The astronaut could have used a shorter route, given some careful navigation.
We're not told explicitly where on the Moon the astronaut crashed, but since the sun is due west, presumably she's near the lunar equator. Following the sun means she walks a 6,800-mile great circle:
While a great circle is the shortest distance between two points on a sphere, the stranded astronaut doesn't need to get from Point A to Point B, she just needs to traverse every longitude and return to her point of origin quickly enough. If she'd crashed closer to a pole, she could have stayed in the sun just by walking her current latitude:
In the extreme case, if she'd crashed on the pole, she could have found some high ground and faced the sun, then turned in a circle to follow the sun going around the horizon. (We'll ignore the Moon's axial tilt relative to sun; a simplified model is still good enough for this largely qualitative discussion.) Standing exactly on the pole is not quite ideal, since only half the sun would be visible, but since the sun's apparent size is only half of a degree, as long as the astronaut is further than a quarter of a degree from the Moon's pole, she should be able to receive full sun, especially since the Moon has no atmosphere and the sun's brightness isn't diminished at low angles.
It seems, then, that from an equatorial crash site the shortest route the astronaut needs to walk is a circle that loops around the nearest pole:
The diameter of such a circle is the straight-line distance between the equator and the pole, which we can find with the Pythagorean theorem and the Moon's radius, R:
From the diameter we calculate the circumference of the circle:
That's 70% the distance of a 6,800-mile great circle walk, requiring an average pace of less than seven miles per hour for the 29½-day trek. If the astronaut maintains a moving average of ten miles per hour, as in the story, she can complete the route in 20 days, leaving the remaining nine and a half days available for rest, repairs, and detours around obstacles.
This approach does assume her solar panels can be angled in whatever direction the sun is, which on this route may be directly ahead, to one side, or behind, depending on where the astronaut is and her walking speed.
The major disadvantage of such a route, however, is that it's much more complicated to navigate than simply following the sun westward for a month. The astronaut needs to deviate progressively more northward on the outbound part of the journey, and track the sun's altitude to try and time it so the sun grazes the southern horizon after 14¾ days, then while heading south she needs to deviate progressively westward until the sun is again high in the sky. In the absence of outside help, the odds of ending up somewhere other than her starting point are much greater.
If you have alternative routes to suggest, feel free to email me, and if you're interested in additional hard science fiction reading, I recommend Andrew Fraknoi's compilation of novels, short stories, plays, and anthologies, several of which are available online for free.