Mars Lander, Take II: Crashing onto the Surface

In my last article, I spent almost the entire piece exploring gravitational physics, of all unlikely topics. The focus was on writing a version of the classic arcade game Lunar Lander, but this time, it would be landing a craft on the red planet Mars rather than that pockmarked lump of rock orbiting the Earth.

Being a shell script, however, it was all about the physics, not about the UI, because vector graphics are a bit tricky to accomplish within Bourne Shell—to say the least!

To make the solution a few dozen lines instead of a few thousand, I simplify the problem to two dimensions and assume safe, flat landing spaces. Then it's a question of forward velocity, which is easy to calculate, and downward velocity, which is tricky because it has the constant pull of gravity as you fire your retro rockets to compensate and thereby avoid crashing onto the planet's surface.

If one were working with Space X or NASA, there would be lots of factors to take into account with a real Martian lander, notably the mass of the spacecraft: as it burns fuel, the mass decreases, a nuance that the gravitational calculations can't ignore.

That's beyond the scope of this project, however, so I'm going to use some highly simplified mathematics instead, starting with the one-dimensional problem of descent:


speed = speed + gravity

altitude = altitude - speed

Surprisingly, this works pretty well, particularly when there's negligible atmosphere. Landing on the Earth's surface has lots more complexity with atmospheric drag and weather effects, but looking at Mars, and not during its glory days as Barsoom, it's atmosphere-free.

In my last article, I presented figures using feet as a unit of measure, but it's time to switch to metric, so for the simulation game, I'm using Martian gravity = 3.722 meters/sec/sec. The spaceship will enter the atmosphere at an altitude of 500 meters (about 1/3 mile), and players have just more than 15 seconds to avoid crashing onto the Martian surface, with a terminal velocity of 59m/s.

Since I'm making game out of it, the calculations are performed in one-second increments, meaning that you actually can use the retro rockets at any point to compensate for the tug of gravity and hopefully land, rather than crash into Mars!

The equation changes only a tiny bit:


speed = speed + gravity + thrust

Again, there are complex astro-mechanical formulas to figure out force produced in a retro rocket burn versus fuel expended, but to simplify, I'm assuming that fuel is measured in output force: meters of counter thrust per second.

That is, if you are descending at 25 meters/second, application of 25 units of thrust will fully compensate and get you to zero descent, essentially hovering above the surface—until the inexorable pull of gravity begins to drag you back to the planet's surface, at least!

Gravity diminishes over distance, so too much thrust could break you completely free of the planet's gravitational pull. No bueno. To include that possibility, I'm going to set a ceiling altitude. Fly above that height, and you've broken free and are doomed to float off into space.

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Dave Taylor has been hacking shell scripts for over thirty years. Really. He's the author of the popular "Wicked Cool Shell Scripts" and can be found on Twitter as @DaveTaylor and more generally at www.DaveTaylorOnline.com.