Space debris: why the US cannot go it alone
by Kirk Woellert
|The US cannot afford to, nor should it attempt to, deal with space debris on its own.|
First, there are thousands of space debris objects actively tracked and many thousands more that are not tracked. Although on a large scale there are clusters and gaps in the debris field, each of these objects are in unique orbits. Various types of orbital maneuvers would need to be continuously executed. These maneuvers will include changes in the vehicle altitude, period, right ascension, and inclination. A first order analysis of the mission profile would consider the most costly maneuver in terms of energy, a change in orbital inclination. Typically such analysis calculates the change in velocity or “deltaV” required to perform a maneuver. Although there are relative concentrations at select inclinations between roughly 60° and 100°, space debris takes on many inclination values spanning 0°–100°. Atmospheric drag dominates for circular orbits below about 200 kilometers. Hence any space debris orbiting at or below these altitudes will decay in a reasonable period of time.
For purposes of this discussion, consider a space debris collection satellite performing an inclination change at an altitude of 500 kilometers. The orbital velocity for a satellite at any altitude is given by:
(1) V = GMe/r where;
G = universal gravitational constant
Me = mass of the earth
r = Radius of the earth plus the altitude of the satellite
Using these values, the orbital velocity V = 7613 m/s. This would be the initial velocity of the spacecraft prior to any maneuver.
Next let’s calculate the velocity change required for an inclination plane change. The formula for deltaV for an inclination change is:
(2) deltaV = 2 x (Vi) x Sin (theta/2), where:
Vi = initial velocity of the spacecraft prior to the maneuver
Theta = angle between the planes of the initial and final orbits
As a minimal case, what is the deltaV required for a 1° inclination change? From equation (2); Vi = 7613 m/s, theta = 1, resulting in a deltaV = about 66 m/s.
Ion propulsion is very efficient and while propellant requirements are important, in this context they are less of a mission driver than the time required for maneuvers. How long must a typical ion thruster fire to achieve a deltaV of 66 m/s? A review of the literature shows calculating this involves tradeoffs and intermediate calculations that are probably beyond the scope of this forum. Instead we can draw upon real world experience and observations of aerospace professionals. The NASA Dawn spacecraft, which utilizes a contemporary ion thruster, can be a reference case. The Dawn web site quotes its ion engines at full thrust can achieve a velocity change of “0-60mph in 4 days”. That is equivalent to a deltaV of 27 m/s in 4 days. For this discussion the acceleration in this case should be computed:
v = 27 m/s
t = 4 days = 345,600 sec
(1) a = v/t = (27 m/s) / (345600 sec) = 7.8 x 10e-5 m/sec2 or .00078 m/sec2
How long would the Dawn spacecraft need to achieve a 66 m/sec deltaV? Solving for t in equation (1):
t = v/a = (66 m/sec) / (.00078 m/sec2) = 844,800 sec = 9.7 days
Per the aforementioned analysis, a 1° change in inclination would require 9.7 days. This time does not include fine orbit maneuvers required to close to within a reasonable distance to the target debris. Another limiting factor to this concept is the mission profile does not allow for the advantage of continuous acceleration often cited for ion propulsion.
Continuing on with the analysis, NORAD tracks about 19,000 objects in orbit. Assume half of these objects, or 9,500, require an inclination plane change maneuver of at least 1° for the vehicle to achieve co-orbit with the target. This implies the time to capture these objects would be (9,500 x 9.7 days) = 254 years. Admittedly this analysis is simplistic but it gives some sense of the time scale involved.
|Space debris concerns all spacefaring nations and should be addressed as an international issue utilizing a multilateral approach.|
Ion engine operation is limited by erosion of thruster elements caused by exposure to charged particles of the exhaust stream. Current ion thruster technology has demonstrated continuous firing for 3.5 years. The ion thrusters on the Dawn spacecraft launched in 2007 have a design mission life of 5.5 years. In either case, it’s well short of the two and half centuries for a single spacecraft to address a significant portion of all debris on orbit. An ongoing program to replace aged vehicles would be needed. To achieve practical results in a reasonable time frame, a constellation of such vehicles would be needed. A program of such scope is obviously a multi-billion dollar initiative.
It should be noted that many of the logistical and technical challenges of removing space debris are similar to those involved with ballistic missile defense. A space debris collector capturing a space debris object is subject to the same orbital mechanics as a kinetic ASAT. A space- or ground-based laser used to vaporize small pieces of debris is subject to the same physics as a laser used for destroying ballistic missile or adversary satellites. The US has not elected unilaterally field a global ballistic missile defense system in part due to the huge costs and technical challenges. Why would a space debris removal system be any different?
It seems reasonable to assume, based on this “back of the envelope” analysis, that the technical and resource challenges involved with eliminating the space debris hazard would be daunting for the US to achieve on its own.
From a policy perspective a unilateral approach by the US is counter to historical precedent and trends in US space policy. The ISS the most audacious example to date of international cooperation cost an estimated $100 billion to design and deploy. Would the ISS exist today if the U.S. were the only country willing to pony up the money? Space science program managers appear to want more international cooperation. Indeed, as noted in this publication, NASA and ESA are actively working to promote international cooperation in space science programs as a way to address limited budgets (see “Doing more for less (or the same) in space science”, The Space Review, May 4, 2009). The U.S. civil space budget is already under considerable stress with the competing requirements of safely retiring the Space Shuttle, operating the ISS, and pursuing the Constellation program. It seems improbable Congress would appropriate the additional funding for NASA to effectively clean up space debris.
The assertion that space debris is a problem best left to the DOD seems misguided. The US military budget is already committed to fighting wars in Iraq, Afghanistan, and, as evident in recent news, may need to commit resources to stabilize Pakistan. The DOD space acquisition track record is not exactly a paragon of success with several major programs experiencing major cost and schedule overruns (e.g. NPOESS, FIA). More fundamentally, assigning the responsibility of cleaning up space debris to the DOD has implications for the US as a signatory to the Outer Space Treaty. As space assets are dual-use by nature, what prevents a space debris removal vehicle from also performing in the role as a space adversary ASAT?
Space debris concerns all spacefaring nations and should be addressed as an international issue utilizing a multilateral approach. International cooperation takes significant time to build consensus and on occasion has led to ineffectual results. Nevertheless, the US can best protect its interests in space not by unilateral action but by using its influence and leadership to establish an effective international response to mitigating—and perhaps one day eliminating—the hazard of space debris.