# Can Hubble be Moved to the International Space Station? 1

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2 Basic Orbital Mechanics Orbital inclination changes are costly. They are also common. Most satellites launched into geosynchronous orbit transfer from a 8 inclination orbit when launched to a 0 inclination orbit that keeps them over the equator when they are operating. To move to the ISS orbit, Hubble would have to accomplish a similar inclination change, from 8, to 51. However, typical communications satellites are much lighter than Hubble, and the inclination-change maneuver requires much less propellant at geosynchronous altitude (35,800 km) than at Hubble s altitude (590 km). The energy requirements for changing orbits are usually discussed in terms of the quantity v, the change in velocity required to move from one orbit to another. For the classic Hohmann two-kick transfer, the change in inclination requires a velocity change v = vsin β /, where v is the orbital velocity and β is the angle between the two orbital planes. This works out to 3.1 km/s for the HST-to-ISS inclination change. Less efficient orbital transfer maneuvers would require a larger v. In contrast, changing from the HST orbital altitude of 590 km to the lower ISS altitude of 390 km would require much less energy, with a v of only 0.13 km/s. The mass of propellant required to perform the inclination changed can be calculated from the rocket equation: m fuel v / v exhaust = ( m + m )( e Hubble booster 1). The mass of Hubble m Hubble is 11,100 kg. The mass of a chemically propelled booster suitable for this operation would be in the range 5000 kg (e.g. the Centaur IIA upper stage with associated control and interface hardware). With typical exhaust velocities of 5 km/s for chemical propulsion, the required fuel mass is approximately 14,000 kg, which is within the capacity of large upper stages currently used to launch geosynchronous satellites or interplanetary missions. Unfortunately, the thrust from most large upper stages would exceed the structural limits of Hubble, which is roughly Newtons (N). For example, the Centaur IIA thrust is about N. A gentler solution is required. Gentler chemical propulsion modules exist, but their fuel capacity is currently below that required. One interesting possibility is to modify the Interim Control Module, designed and built by the Naval Research Laboratory, and now in storage (shown at right). This was a backup unit intended for the ISS that was built at the time when there was uncertainty in the Russians ability to deliver their propulsion module. Another possibility is to use electric propulsion, as envisioned for SLES. Various kinds of electric propulsion modules exist, including the ion engine that was used for the Deep Space-1 mission, Hall-effect engines that have been used in over 100 satellites, or arcjet v = v 0 v 0 π cos i

3 thrusters. A summary of electric propulsion options can be found at Electric propulsion generally has a much higher v exhaust, and hence requires much lower fuel mass than chemical propulsion. However the low thrust is both a benefit and a problem. Changing the orbital inclination takes much longer with low thrust. Furthermore, the thrust can only be applied on the bright side of the orbit if the electric power is provided exclusively by solar panels. The low-thrust transfer maneuvers require a larger v to accomplish the same change in inclination. Computing optimal orbit transfers is complicated, but we can get a ballpark estimate from Edelbaum s equation (1961, Propulsion Requirements for Controllable Satellites, ARS Journal, 1079). This equation assumes a constant thrust that switches signs at the antinodes. In the case of a simple change of inclination for a circular orbit, the equation reduces to: This formula implies v = 4.7 km/s for the HST-to-ISS inclination change. For this ballpark estimate, let us assume a thrust of 1N and an exhaust velocity of 0 km/s. This plausibly within the range of state-of-the-art Hall-effect thrusters such as the Pratt & Whitney T-0. Assuming the same mass for the booster, the fuel mass is now approximately 4300 kg instead of the 14000kg required for chemical propulsion. The time it would take to achieve the orbit transfer is roughly v/a where a is the acceleration from the thruster. With our putative 1N thruster, this acceleration is very small: m/s. It would take approximately 3.0 years to get to the ISS. To make the transfer times reasonable would require several of these thrusters (one year is perhaps a reasonable upper limit to the acceptable amount of time.) Alternatively, a higher-thrust unit, such as the NASA 457M (shown at right), which has tested at 3N, could be used if it could be space-qualified for the required total impulse (lifetime limitations are a serious technical issue for this kind of thruster). As a very rough guide, it takes approximately 0 kw of electric power to produce one Newton of thrust. Each solar array wing on the ISS delivers 64 kw of power, so this requirement is high, but is not unheard of. A serious technical issue is the fact that HST is in shadow nearly half the time. Thus the constant-thrust assumption used above would only be valid if there is another source of power during dark time. Perhaps simpler would be to use a hybrid of chemical propulsion and electric propulsion, e.g. making use of the existing ICM chemical propulsion capability. Clearly, the amount of power or propellant required to move HST to the ISS orbit is very large. The engineering challenge is no doubt significant. Nevertheless, transfer to the ISS orbit is a budgetary and engineering problem, not a physics question. The most significant challenge may be the autonomous rendezvous with HST, which is a challenge that must be tackled even to bring HST back to earth.

4 Would Hubble and the ISS make good neighbors? While changing the orbital inclination appears technically possible, it is not entirely clear that Hubble can operate at the ISS altitude, or, if it could, whether that would be desirable. Among the technical issues that would have to be addressed are the following. The density of the atmosphere near solar maximum is sufficiently high at 390 km that Hubble may have difficulty pointing. Any rendezvous with the ISS would have to be done exceedingly carefully, perhaps assisted by the shuttle. There are enough contamination concerns about the ISS environment that it is unlikely that it will be desirable to operate Hubble near the ISS. Instead the ISS would serve as a base for servicing. If Hubble were left at a higher altitude, there are several options for servicing: (1) shuttle could visit the ISS, have the tiles inspected, and then proceed to Hubble; () Hubble, equipped with a propulsion module, could transfer to the ISS orbit for servicing. A major complication is the fact the orbits will precess at different rates, imposing timing constraints for low-energy orbit transfers. At their current altitudes, the orbits would precess such that the nodes would line up about once every two years. It is unlikely that a propulsion module with enough power to change the orbital inclination could be left attached to Hubble for science operations. It probably would be too massive and would affect the center of gravity. Instead, if Hubble were to be serviced and then moved to a higher orbit, the propulsion module would have to be stripped down. Parts such as solar panels could be re-used on the ISS itself. Benefits of moving to the ISS orbital inclination While the cost is likely to be considerable (although perhaps not compared with the \$400M estimated for a shuttle mission), and there are clearly technical issues concerning servicing once the orbital inclination has been changed, there are nevertheless a host of attractive features of this solution that make it worthy of continued technical study. This solution satisfies all of the CAIB requirements, to the extent that any mission to the ISS satisfies those requirements. Servicing Hubble in this manner will realize the enormous scientific return on the \$50M invested in equipment that was to be installed on the next servicing mission. With Hubble in the ISS orbit it is possible to consider additional upgrades. With current technology it is possible to realize yet another factor of 10 improvement in capability. Concepts exist for an optimised coronagraph to detect planets in orbit around nearby stars, or a wide-field imager to explore the mysterious dark-energy that is responsible for accelerating the cosmic expansion. dω 3nJ RE cosi The precession of the line of nodes is given by =, where J = is a dt a (1 e ) coefficient describing Earth s oblateness, R E is Earth s equatorial radius, a,e, and i are the orbit semi-major axis, eccentricity, and inclination (respectively), and n is the orbital mean motion (GM E /a 3 ) 1/.

5 De-orbiting Hubble when a suitable replacement is finally in orbit would simply be a matter of docking it to the ISS and de-orbiting them together (the ISS has propulsion already). NASA is already planning for an autonomous propulsion module. That part of the engineering challenge must be met whether or not the scientific mission is extended. Servicing Hubble is noble work for the International Space Station.

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