This time around we look at one of the more advanced topics in space, that of navigation. Unlike the movies, where spacecraft go zipping around, behaving more like aircraft in an atmosphere than boxes of thrusters in a vacuum, space navigation is a bit more complicated and typically involves hurtling through space at high velocity on a trajectory that is difficult to change in any significant way. A good grasp of mathematics is required to explore this field, and for advanced studies calculus is an absolute requirement, especially in things like matrices (which I never got my brain wrapped around). I rely a good deal on my ability to visualize the geometry of objects moving in three-dimensional space (which is where the need for matrices comes in when you’re dealing with different frames of reference) as a crutch when the math gets too hard.
Pretty much the first reference that everyone notes is from JPL, entitled “The Basics of Spaceflight”. This was part of the background reading recommended to participants in the Space Generation Forum back in 1999, where I first learned of it. Somewhere in the depths of the Lunar Library I have my original copy. In 2001 it was updated and web-ified, taking advantage of the power of hyperlinks to flesh out many of the concepts by linking to more thorough explanations of particular topics. Mini-quizzes check comprehension as the student works through the text, helping to make sure they don’t get in too far over their heads. This reference should be comprehensible to brighter middle-school students.
Once you’ve got the ‘Basics of Spaceflight’ down, it’s time to move on to a more advanced text, and the best one around is “Understanding Space: An Introduction to Astronautics”, edited by Jerry Jon Sellers. Developed by the folks at the U.S. Air Force Academy, this textbook is the best one around for easing people into the complexities of orbital mechanics and space navigation. It’s written at the undergraduate textbook level, but should be easily comprehensible to bright high-schoolers on a strong math track. I read through the 2000 edition as part of my extra studies for International Space University (ISU), but it has been updated with a hardcover 2004 edition. Better graphics and more of them for the explanations help make the concepts a bit more understandable. This one remains one of my favorites.
From here the reference books start getting tougher as the topics move from the circular restricted 3-body problem to things like perturbation theory and rotating frames of reference. Some tools to help with this are a pair of very different software programs available over the internet. The first is the open-source freeware program Orbiter. It has been around at least since my days at ISU, and is continually updated and added to by its growing community of fans. It takes great pride in the accuracy of its physics engine, and Bruce Irving of the Music of the Spheres blog has prepared an introductory tutorial which has an accompanying teacher’s guide. As Bruce describes it:
“Orbiter (written by Dr.Martin Schweiger of University College London) is great for demonstrating concepts such as planetary rotation, orbits, relative motion, forces, Newton’s Laws, and more. Advanced students can use it as a lab for experiments in physics, including orbital mechanics and atmospheric flight. Using some of the hundreds of avaialble free add-ons, students can explore the history of rocketry and Space flight, from Robert Goddard’s early rockets to Apollo, the space shuttle, and beyond. Orbiter is also expandable – users can even use free 3D modeling software to build and fly their own spacecraft.”
Bruce (who goes by the name Flying Singer at the Orbiter forums) was also kind enough to give a presentation on using Orbiter at the ISDC I helped put together, so a special shout-out to him for that.
Moving into the realm of what the professionals use, we have Satellite Tool Kit (STK) from AGI. We had a seminar on how to use the software as part of our studies at ISU, and I think that might have been where I first started getting really keen on space navigation as an area of interest. So much so that when the Team Project rolled around I wanted to work on the Trans-Mars Injection and arrival calculations, which I did. AGI has recognized the value that this program holds in the classroom, and so have created a Educational Alliance Program to provide educators with support resources. I wanted to use the Astrogator module for the Team Project, but we were too poor to buy the license.
Once you’ve got some hands-on experience with how orbital mechanics is used in space navigation, it’s time to whip out the definitive reference for this category, and that would have to be David Vallado’s “Fundamentals of Astrodynamics and Applications”, a meaty tome that weighs in at 958 pages all-in (the 3rd edition from 2007 has 1055 pages). It’s the most comprehensive treatment out there, and even includes a section on continuous thrust trajectories like the one used to take ESA’s SMART-1 mission to the Moon. It has an online support page for software and errata relating to the book.
One thing it doesn’t really touch on is a newer type of spacecraft trajectory that takes advantage of the warps in gravity caused by the planets, and the linkages between these warps. Researcher Ed Belbruno, author of “Fly Me to the Moon”, was one of the early ones to actually figure out how to make these work to our advantage, and used it to rescue a Japanese mission that had been inserted into a bad orbit. Using the warp in the Earth’s gravity well created by our Moon, he was able, over time, to put the spacecraft into a relatively usable orbit. These were termed ‘weak stability boundary trajectories’ which is a mouthful, but a very simple idea in practice. A good way to think of it is in terms of a surfer who has ridden his board to the top of a wave. Small adjustments in where he points the tip of the board will have a significant result in where he ends up at the end of the ride. The SMART-1 probe took advantage of this phenomenon when it rode up Earth’s gravity well and then slipped over the gravity ‘hill’ at the Earth-Moon L-1 point and rode down into the Moon’s gravity well.
The different gravity wells of the planets are linked by ‘ripples’ that are constantly moving as the planets move. These can be imagined as long waves in the Sun’s gravity well, and spacecraft can be sent sliding along the crests of these ripples, riding them (very, very slowly) to different points of the Solar system along what is, in effect, an interplanetary highway system. The significance of this is that we can create Hubble-ized space instruments (i.e. people can repair and upgrade them) that we can send out to Jupiter or Saturn to, for example, keep an eye on incoming objects from the Oort Cloud and Kuiper Belt. When it’s time for servicing, the space probe is nudged back onto the interplanetary highway system and returns back to near-Earth space where it can be retrieved and serviced. In this way, we can get more value out of our space probes by reusing them and making them better instead of just throwing very expensive instruments into the void one after another.
These are the kinds of exciting new developments that are going on in the field of space navigation. Moonwalker Buzz Aldrin earned his doctorate for his work on the kinds of free-return trajectories that allowed us to conceive of a rescue for Apollo 13. We’ve come a long way since then as our mathematics, and computing heft, have advanced significantly, and so this is not a stale, dry field where we know everything, but rather one where there is significant work yet to be done. We can use these new understandings of space flight to change the way we approach how we design our space architecture.
And hopefully, there will soon be jobs for astrogators to take us to the Moon, the asteroids, Mars, the moons of Jupiter, and beyond…