Asteroid missions: be patient, or bring lotsa gas
by Tom Hill
|Unfortunately, asteroids that have the potential for short, low-fuel missions are extremely rare.|
An asteroid mission is an exciting prospect. Its allure includes the possibility of using less propellants than a lunar landing mission and not requiring the development a separate landing vehicle. The idea of exploring new territory is always enticing and cannot be overlooked, while mission timelines are possible that are on the order of an extended lunar stay, serving as stepping-stones to much longer Mars missions.
It turns out that two of the criteria used to argue for an asteroid mission—low propellant use and short timelines—are linked to each other through the mathematical dance of orbit mechanics and the rocket equation. Unfortunately, asteroids that have the potential for short, low-fuel missions are extremely rare. In an ironic twist, the same attributes that make them good candidates for such a mission contribute to the rarity of such an opportunity.
Recent articles have focused on asteroid missions where the explorers don’t have to travel any farther than a few times father from the Earth than the Moon, so those missions are the focus of this study. Other mission scenarios are possible, such as the Gaiashield mission proposed by Zubrin in Entering Space, but that mission in particular does not claim to hold journey durations or distances low.
Missions to near Earth asteroids working to take advantage of a pass close to Earth essentially meet an asteroid at the fringe of Earth’s gravitational influence. The craft travels out to the rendezvous point, taking between days and weeks depending on the propellant budget and trajectory chosen, and then adjusts its path to drift with the space rock within Earth’s gravitational well. This period of time is called the proximity operations period. When the asteroid reaches the opposite side of Earth’s sphere of influence, the craft fires its engines again to return to Earth.
The mission sounds easy, right? Theoretically, as far as space missions go, it is easy. Finding a candidate asteroid that supports such a mission is not. Asteroids, like the planets or any other object traveling through space, follow the laws of orbital mechanics in their paths, and those laws complicate mission planning.
Six terms are necessary to define an orbit and an object’s place within it. When describing an orbit using classic Keplerian elements, there are three major terms that affect the shape of the orbit: inclination, eccentricity, and semi-major axis. Another consideration is the phasing of the Earth in its orbit with the asteroid in question.
Inclination describes the angle that the target orbital plane makes in comparison to another plane and is typically measured in degrees. For planetary bodies, inclination is defined as the angle between the orbit in question and Earth’s orbital plane. Earth’s orbital plane is also called the ecliptic. Asteroids that pass near Earth are inclined to its orbital plane by some amount, and that amount varies greatly. Objects in the initial data gathered for this survey had inclination values between 0.1 and 63 degrees. While an orbit’s inclination is not related to the size of that orbit, inclination plays a large role in suitability for a mission profile described here. An asteroid in an orbit with any measurable inclination compared to the ecliptic will only be capable of a truly close approach to Earth when it crosses the ecliptic plane, a point also known as the nodal crossing. Even on these close approaches, the differential speed of the asteroid compared to Earth is approximately 500 meters per second for each degree of inclination of the asteroid’s orbit.
|Near Earth asteroids can go years between close approaches that would allow the kind of missions discussed here.|
Eccentricity describes the shape of an orbit, and it is a dimensionless quantity. At the theoretical yet never achieved eccentricity of zero, an object is in a perfectly circular orbit around its parent body. Increasing eccentricity describes a more elliptical orbit, with the near point of the orbit growing closer to the parent body and the far point growing more distant, up through an eccentricity value of 1. An eccentricity of 1, another theoretical value, describes an infinite ellipse also called a parabola. The infinite varieties of ellipses available create some interesting situations, although very few produce orbits that are compatible with a low delta-v mission to an asteroid. All but the lowest eccentricities can create a situation where the orbit of the target asteroid crosses Earth’s orbit at an angle that drives delta-vs to an unacceptably large value. The missions that are the focus of this paper require the right balance of eccentricity and the next term, semi-major axis.
While eccentricity specifies the shape of an orbit, its semi-major axis, expressed in units of length, relates to the amount of time it takes for an object to orbit its parent. The orbits of two objects with the same semi-major axis but different eccentricities can look very different, but take the same amount of time to make one circuit around a parent body. Objects with a semi-major axis much smaller or larger than that of Earth can cross Earth’s orbit, but doing so requires a relatively high eccentricity and these objects rapidly fall out of consideration for low delta-v missions.
Phasing is not an orbital parameter per se, but it requires mention here. Any asteroid that makes a close approach to Earth will, in all likelihood, make another pass at some time in the future. The closer the orbital period is to Earth’s, the more time between close approaches there will be. The same effect can be seen in the launch windows that allow missions to other planets. The outer planets, having orbital periods much greater than Earth’s, regularly align for a minimum-energy launch window approximately once each Earth year. Mars, with an orbital period much closer to that of Earth, aligns for a mission only once every 26 months. Near Earth asteroids, many with periods even closer to Earth’s than Mars, can go years between close approaches that would allow the kind of missions discussed here.
The research for this article is easy to duplicate for anyone interested. The list of near earth asteroids and their orbital elements (a potentially large web page) was downloaded in January of 2007 and saved as a text file. The list was converted into spreadsheet format, and only those asteroids with semi-major axes between the arbitrarily-chosen values of .9 and 1.1 astronomical units (AU) were used for further study. This smaller list (still containing over 300 objects) was then sorted by inclination followed by eccentricity, based on an initial assumption that inclination would be a larger delta-v cost than inclination for a mission to that asteroid.
The top candidates from the list were then examined using the orbital viewer from the JPL NEO office. The viewer contains a disclaimer that it is for visualization only, and experience shows that this warning should be taken seriously. Due to the basic nature of this research, however, the viewer was deemed acceptable.
Each candidate asteroid was observed in the viewer to find the closest approach that was less than 0.02 AU between now and 2100. The date and distance were recorded, and this information could be used as a starting point for further analysis.
Three asteroids jumped out as candidates to show the complexities of a crewed mission to each. The first one, 1991 VG, requires a relatively low delta-v to enter and exit proximity operations (833 m/s each) and comes fairly close to Earth at five lunar radii. The one problem with this asteroid is that its close approach doesn’t take place until the year 2068. If doubling the proximity delta-v is an option, then there’s another mission opportunity with the asteroid 2000 SG344, which comes within three lunar radii in 2028. The tradeoff is a required delta-v of 1686 m/s to both enter and exit proximity operations. Nearly doubling delta-v needs again opens an opportunity with the asteroid 2001 GP2 in the year 2020.
|The fact remains that it requires a lot of propellant to get anywhere interesting in the solar system, and perhaps an asteroid mission will help kick-start architectures that will take us to other destinations.|
Hopefully, new discoveries will provide a larger selection of asteroids and mission dates that require less energy to visit using the mission profile described here. The particular class of asteroids best suited for this type of exploration is underrepresented in the NEO list, because of their difficulty to discover. Some of the detection methods described in NASA’s recent NEO report to Congress would increase the number of such asteroids in the database. It is also possible that other candidates will make themselves obvious using more exact orbital determination methods on the list we currently have. This will remain unknown until someone doing research within the area using better tools makes their study public.
Asteroid missions are exciting for their daring, their potential for scientific return, their ability to help protect the planet, and their meaning in humankind’s growth into a spacefaring species. Opportunities to carry them out while keeping people within Earth’s “neighborhood” are not common, however, and many of those instances require a lot of propellant in order to make the mission happen. This is not necessarily a bad thing. The fact remains that it requires a lot of propellant to get anywhere interesting in the solar system, and perhaps an asteroid mission will help kick-start architectures that will take us to those other destinations.