There's been an upsurge in interest
in crewed missions to visit a near Earth asteroid. The prospects of new spacecraft,
along with the more distant, yet still possible, larger rockets to push the new craft to the moon, Mars and beyond have fired
the imaginations of scientists and laymen alike. Many say that a near-Earth asteroid
is the next logical step after The United States' return to the moon sometime before 2020.
Others say that an asteroid mission could be taken on before the return to the moon.
They say such a mission could alleviate the "been there, done that" feeling which some detractors love to bring up
any time the Vision for Space Exploration is mentioned.
The interest has led to a number
of articles in space trade news (such as this Space.com article) and even in mainstream newspapers such as USA Today, where the classic but overstated "huge asteroid impact" graphic was placed above
the fold on page 1, and missions to asteroids were part of the discussion within. Crewed asteroid missions also received a short mention in NASA's report (Acrobat required) to Congress on the NEO threat. (A new article discussing possible missions including a candidate asteroid came out after submitting
final text to The Space Review)
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. In a related issue, the asteroids that have the potential for short, low fuel missions are extremely rare.
A sample of the difficulty can be seen on this chart from the NEO office at JPL. Most close approaches listed on the chart are high speed (>5km/sec relative velocity) and very
distant (>10 lunar distances) and none listed on 24 March 2007 are close with low relative velocity. 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 Earth-lunar radii away from Earth, 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. A sample mission is pictured in figure 1. The craft
travels out to the rendezvous point, then adjusts its orbit to drift with the space rock within Earth's gravitational well
before leaving the asteroid when it reaches a certain point in its journey. Therefore,
these missions can naturally be divided into three parts: journey out, proximity operations,
and return to Earth.
|Figure 1: Mission scenario considered for this analysis
Starting from low Earth orbit (LEO),
the journey out phase of the mission starts when a crew fires their engines to climb to the very fringe of Earth's gravity
well. The maneuver is timed so that the spacecraft's position intersects the asteroid's
position at some point in the future. Like trans-lunar injection burns of past and
future missions, this maneuver places the spacecraft on a trajectory taking it away from Earth on a path that will follow
one of the classical conic sections: an ellipse, a parabola, or a hyperbola. The path chosen will impact the amount of time spent in transit as well as the amount of
propellants required for the entire mission.
The journey out orbit that requires
the least amount of propellant is elliptical in shape. This orbit is labeled 'C' in figure 1.
To minimize propellant usage on the first burn, the ellipse is aligned so that the highest point of the ellipse is
the place where the spacecraft and asteroid meet, allowing some distance for safety. The
problem with such an orbital choice is that ellipses with maximum altitudes of multiple lunar radii have extremely long periods,
that is, the time to complete a full trip around the Earth. This relationship is not
linear, either. An ellipse that reaches twice the distance from the Earth to the moon
has a journey-out time of 14 days, roughly equivalent to one-half of the moon's journey around the Earth. Doubling the distance to four times the Earth-moon radius creates a one-way journey of 38 days.
Burning more propellants during the
departure burn in LEO can change the shape of the departure orbit and decrease the duration of the outward journey. Adding energy to the transfer orbit in this way will make it take the shape of a larger ellipse, a theoretical
parabola ('B' in figure 1), and eventually a hyperbola ('A' in figure 1), and any of these orbits can be phased to allow intercepting
an asteroid. Enlarging the transfer orbit will decrease the travel time to the target,
which will have the benefits of requiring less supplies for the crew and decreasing the loss of high-energy propellants due
to boiloff, but there is a cost. By increasing the Earth departure speed, mission
planners also have to increase the propellants required to maneuver the craft into phase 2 of the mission, proximity operations.
After drifting for the necessary
period of time, the spacecraft will have to fire its engines again to align its velocity with the inbound asteroid. As mentioned before, the size of this maneuver will vary depending on the velocity of the craft relative to
the asteroid at rendezvous time. The smallest delta-v required would take place if
an elliptical orbit were chosen for the departure trajectory. Then, at maneuver time,
the craft would be practically motionless relative to Earth and the burn would only have to approximate the velocity difference
between the Earth and the target asteroid. If a faster route to the rendezvous were
chosen, the burn would have to combine nulling the spacecraft's motion relative to Earth and accelerating the craft's motion
in the direction of the asteroid.
After firing the engines to enter
proximity operations, the explorers will be ready for the first footfall on new real estate since 1969. Many methods of carrying out the exploration of an asteroid have been suggested, and those methods are not the
subject of this paper. As the astronauts explore potentially some of the oldest material
in the solar system, they, their craft and the asteroid will drift through the fringes of Earth's gravitational influence. The amount of time spent there will depend largely on the asteroid target and its orbit
relative to Earth. Asteroids that move slower relative to Earth will stay in its vicinity
longer and allow more time in the proximity phase. At the end of the exploration period,
it will be time to fire up the engines and return home.
Return to Earth
When the engines shut down, the craft
starts its fall to Earth. The amount of time spent in this mode will likely be similar
to the amount of time spent traveling to the asteroid, but some adjustments to the flight path could take place and speed
up the trip. The mission ends with a high-speed reentry, testing a useful piece of
hardware for future missions to Mars.
The mission sounds easy, right? Theoretically, it is easy. Finding a candidate
asteroid that allows an easy 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
and the asteroid in question.
Inclination describes the angle that
the orbital plane makes in comparison to another plane and is typically measured in degrees.
The Earth's equator serves as the reference plane for objects orbiting our home world, and as a satellite crosses the
equator, the angle between the spacecraft's velocity vector and the equator defines the orbital inclination. Samples of inclinations for Earth-orbiting satellites include 97 degrees for weather satellites, 52 degrees
for the International Space Station (ISS), 28 degrees for the Hubble Space Telescope, and very near 0 degrees for communications
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 .1 and 63 degrees. Figure
2 shows the inclination of a sun-orbiting object and how it is measured.
|Figure 2: Solar system inclination illustrated
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 for the asteroid's orbit. In an extreme case of traveling to an asteroid of 7 degrees inclination, the spacecraft would have to add velocity
equal to half the low Earth orbit speed of 3.5 kilometers per second!
There may be some very special cases
where an asteroid with a very low inclination makes a close approach to Earth at a time other than the nodal crossing. In such a case, the asteroid would actually be above or below the Earth relative to the
ecliptic plane, but would not require a large delta-v in order to begin or end proximity operations.
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. Eccentricities greater than 1 are reserved for objects following a hyperbolic course. They are either leaving the parent body for the first time or simply passing through the gravitational influence
of the parent body.
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 take the right balance
of eccentricity and semi-major axis. Figure 3 shows how delta-vs increase greatly
when a target orbit differs through eccentricity or inclination, including examples of a good case and a bad case. Figure
4 shows what the orbit shapes in a good case and bad case of eccentricy may look like from above the ecliptic.
|Figure 3: Differing inclinations or eccentricities lead to high delta-v requirements quickly
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 a year. Mars, however, with an orbital period much closer
to that of Earth, aligns for a mission only once every 26 months.
Near Earth asteroids, with periods even
closer to Earth, can go years between close approaches that would allow the kind of missions discussed here.
|Figure 4: Two orbits have nearly the same semi-major axis as Earth, but different eccentricities
Criteria for a Candidate Asteroid
A candidate asteroid must have orbital
elements that when considered together allow a mission with relatively low delta-v. For
this study, initial numbers used for candidate NEOs were an inclination of less than 1 degree, eccentricity of less than .1,
and a semi-major axis greater than .9 that of Earth but less than 1.1. Further investigation
showed that while this criteria helped narrow the list of potential candidates, it was not sufficient to produce a good list
of targets, although it did narrow down the list of 1000+ to less than 300 candidates.
Taking the interplay between orbital
mechanics into account, such as seeing the dependency of eccentricity and semi-major axis, cut the number of candidates appreciably.
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 .9 and 1.1 AU were used for further study. This smaller list (still containing
300+ pieces of space rock!) 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 viewed 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. One asteroid(2007
CA19), rated 1 on the Torino Scale on February 17th for an impact in 2012 was nowhere near
Earth throughout the year according to the visualizer. Since this study is related
to how often such opportunities arise, and not dedicated to finding a mission date with any precision, the orbit visualizer
was considered adequate.
Each candidate asteroid was observed
in the viewer to find the closest approach that was less than 0.02 AU date between now and 2100 generating views such as those
shown in figure 5. The date and distance were recorded, and this information could
be used as a starting point for further analysis. As research using the tool progressed, the time that the asteroid was near
Earth was recorded, and used to provide an extremely rough estimate of the delta-v maneuver required for a spacecraft on a
mission to explore the space rock using the profile described here. Again, due to
the limitations of the tool, the estimates must be taken as being very preliminary, but they do point out the wild differences
in delta-vs required for some asteroids compared to others. In one comparison, the
delta-vs required to rendezvous with two different asteroids differed by a factor of nearly 5x.
[Update on 11 Apr
07: There is a web page which will do most of this work for anyone interested. It is also located on the JPL NEO site.
It can be found here.]
[Update on 26 Jan 08: According to this site (scroll to the bottom of the list), 1991 VG may be human-made: a returning piece of space junk. That would impact the target's
interested as an asteroid to visit. There is similar speculation over SG344.]
|Figure 5: A graphic representation of a good asteroid mission opportunity
Based on this analysis, the following
asteroids represent some of the best candidates for a survey mission until the year 2100.
They are listed in order of increasing delta-v required to rendezvous with them. Again,
a reminder that these are representative, because the visualizer used to carry out the analysis is not meant for precise orbit
determination. In fact, the best candidate based on a combination of encounter date
and delta-v, 2000 SG344, is listed here as having a close encounter in 2028, while the JPL NEO website doesn't place SG344 as having a potential impact Earth (the criteria for describing a potential impact are not explained
on the web page) until 2068.
5/10/2028 (57, 85)
10/6/2020 (38, 57)
A note on the repeats described in
this table: Future encounters with the asteroid do take place, as the periodicity
between the Earth and the asteroid align. In all cases examined in this study, the
future encounters are not as close as the ones featured in this table.
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. It is also possible that other candidates make themselves obvious using more exact orbital
determination methods. This will remain unknown until someone doing research within
the area using better tools makes their study public.
The New Scientist article, published after submitting the final version of the TSR summary of this
article, mentions an asteroid named 1998 KY26. According to the New Scientist article, this asteroid makes close approaches
with Earth in 2013 and 2024. 1998 KY26 was not considered in this work, due to its semi-major axis being 1.22, eccentricity
of 0.2, and inclination of 1.4. A quick check of the orbit using the visualizer does not show approaches close enough for
consideration under the criteria used here. The 2013 close approach distance is 0.124AU (60 times lunar distance) and the
2024 encounter comes as close as .079AU (40 times lunar distance). These distances would not correspond to the 90-day mission
length described in the article without propellant expenditures to accelerate the outward bound and return leg of the mission,
though the delta-v (estimated using the same procedure used for other delta-vs cited in this article) required for proximity
operations appear favorable, on the order of 300 m/sec. The New Scientist article states that 1998 KY26 may not be
a good candidate for exploration due to its high rotation rate, a factor not considered for this research.
It is unclear whether
the article's mention of KY26 as a candidate is due to better propogation methods on the researcher's part (KY26 is not listed
on the NEO risk page, but neither are most of the asteroids considered in this paper) or through setting different criteria
describing a close approach and not considering the delta-v cost of such a mission.
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 propellants 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.