Sub-orbital “hops” (ballistic flights from point-to-point) are possible, but come at fairly high cost—it takes nearly as much energy to fly hundreds of kilometers on the Moon in a ballistic hop as it does to go into orbit and then descend elsewhere.This is incorrect. Here I look at suborbital hops on airless worlds. A minimum energy ellipse going from point A to B would have a focus on the midpoint of the chord connecting A & B:
The other focus would be at the moon's center, of course.
The vis viva equation tells us
v=sqrt(GM(2/r - 1/a)
In this case GM is the moon's gravitational parameter, r is the moon's radius and a is the semi major axis of the ellipse.
Let's say A is 300 km from B. That'd be about 9.9 degrees separation. Here's a pic:
.67 km/s to hop and another .67 km/s for a soft landing. For low lunar orbit that would be 1.68 km/s to take off and another 1.68 km/s to soft land. Energy goes with square of speed. (.67/1.68)2=.16. The energies differ by more than a factor of 6! How on earth did Spudis conclude these are nearly the same?
Here is my Lunar Hopper spreadsheet. There's a tinted cell user can input distance between point A and B. This is the first document I've uploaded to Google docs, hope it works.
Spudis suggests spherical pit bots for lunar drones. These bots use micro thrusters to hop and hover. Whether the hop is 5 meters or 500 kilometers, the most efficient hop is the minimum energy ellipse described above. On the moon a ten minute hover costs about one km/s delta V. Spudis justifiably grouses about the tyranny of the rocket equation. But these pit bots rely on reaction mass to move. They don't circumvent said tyranny.
Various folks talk about lunar drones at Spudis' forum. Someone who goes by the name finkh mentioned pogo sticks. An interesting notion, in my opinion.
When I was a kid, my pogo stick used a spring. Solar cells might provide energy over time to compress a spring, thus avoiding the use of reaction mass. No more nasty rocket equation! On landing the spring absorbs the impact. The compression on impact might be a way to recover some energy.
I moved over a variety of terrains with my pogo stick. I could move forward, backward, left or right. It seems feasible to develop a robot with similar abilities.
But as I recall, getting from point A to B on a pogo stick was more strenuous that walking. So I'm not sure compressing a spring on impact is a great way to regain energy. Looking at existing robots like Big Dog, it looks like powerful engines are needed to power the device. Once again, the need for a better Alpha rears its ugly head. Elon Musk seems to be working on improved solar panels and energy storage. Hopefully Tesla Motor's R&D will have applications in space exploration.
How much impact can a pogo stick take? The 300 km hop pictured above hits the ground at .67 km/s or about 1500 miles per hour. No, I wouldn't want to be on that pogo stick.
This list of pogo stick records says Biff Hutchison jumped nearly 3 meters high. By my arithmetic he hit the ground at about 7.5 meters/sec or about 17 miles per hour.
Assuming 17 miles per hour is maximum jumping and landing velocity, a lunar pogo could jump about 36 meters (assuming the hop was a minimum energy ellipse from point A to B). This hop would be about 9 meters high.
A jump 36 meters long and 9 meters high isn't spectacular but such a device might have uses. And I like the image of a pogo stick on the moon.