Minimize Drag-free Cubesat

Drag-free CubeSat

The Drag-free CubeSat project of NASA is a cooperative international venture by a team from the following institutions: Stanford Hansen Experimental Physics Laboratory at Stanford University, Stanford, CA, USA, KACST (King Abdulaziz City for Science and Technology), Riyadh, Saudi Arabia, SRI International, Menlo Park, CA, USA, and the University of Trento, Italy. As of 2012, the project is funded for research and development, but not yet for flight. The funding primarily comes from KACST in Saudi Arabia, but there is also some additional support from NASA/ARC (Ames Research Center).

The goal for a future Drag-free CubeSat mission is to: 1)

• Demonstrate inexpensive drag-free technology in a nanosatellite mission

• The performance goal is derived from the NASA Earth Science Goals for future geodesy: namely a drag-free target performance of 10-12 m s-2 Hz-1/2 in the frequency range of 10 mHz to 1 Hz.

• To demonstrate integration of the new technology and to provide an in-orbit performance test.

The performance is limited primarily by the minimum impulse bit and thrust noise of available CubeSat scale thrusters. A propulsion system specifically tuned for a drag-free nanosatellite, would improve the performance by a factor of 10. After propulsion, the next largest disturbance forces are a function of the stability of the thermal and magnetic environment achievable on a CubeSat. All of the dominant error sources will be calibrated to 10-12 m s-2 Hz-1/2 through a series of on-orbit experiments. 2)

The MGRS (Modular Gravitational Reference Sensor) utilizing a spherical TM (Test Mass) has been under development at Stanford for a wide range of applications since 2004. MGRS represents the next generation of technology for space gravitational wave detection and other spaceborne gravitational precision experiments.

Background:

The design of drag cancellation missions of the future will take advantage of the technology experience of the past. The importance of data for modeling of the atmosphere led to at least six types of measurement: (a) balloon flights, (b) missile-launched falling spheres, (c) the 'cannonball' satellites of Ken Champion with accelerometers for low-altitude drag measurement (late 1960s and early 1970s), (d) the Agena flight of LOGACS (1967), a Bell MESA accelerometer mounted on a rotating platform to spectrally shift low-frequency errors in the accelerometer, (e) a series of French low-level accelerometers (e.g. CACTUS, 1975), and (f) correction of differential accelerations for drag errors in measuring gravity gradient on a pair of satellites (GRACE 3), 2002) . 4)

The independent invention of the drag-free satellite concept by Pugh and Lange (1964) to cancel external disturbance added implementation opportunities. Its first flight application was for ephemeris prediction improvement with the DISCOS flight (1972)—still the only extended free test mass flight. Then successful flights for reduced disturbance environment for science measurement with gyros on GP-B (2004) and for improved accuracy in geodesy and ocean studies (GOCE, 2009) each using accelerometer measurements to control the drag-canceling thrust. LISA (Laser Interferometer Space Antenna), DECIGO (DECI-hertz interferometer Gravitational wave Observatory), BBO (Big-Bang Observatiory) and other gravity wave-measuring satellite systems will push the cancellation of drag to new levels (Ref. 4).

The range of applications for drag-free technology is broad. A summary is provided in Table 1. The listed applications are separated into four distinct categories: navigation, Earth science, fundamental physics, and astrophysics. Two key performance metrics for each application are also shown. The first metric, called drag-free performance, is the residual acceleration of the test mass in units of m/(s2Hz1/2). For an ideal drag-free satellite, the residual acceleration is zero, but in practice small, residual forces act on the test mass, perturbing its trajectory with respect to a pure geodesic. The primary goal of drag-free satellite design is to minimize these residual forces. The second metric, called metrology in Table 1, is either the measurement of the absolute position of a drag-free test mass (e.g. via GPS) or the differential measurement of the distance between two drag-free test masses (Ref. 2).

Category

Application

Drag-free performance
(m/s2Hz1/2), frequency (Hz)

Metrology (m)

Navigation

Autonomous, fuel efficient orbit maintenance

≤ 10–10, near zero frequency a, b

≤ 10 absolute

Precision real-time onboard navigation

≤ 10–10, near zero frequency a

≤ 10 absolute a

Earth science

Aeronomy

≤ 10–10, 10–2 to 1 Hz a

1 absolute a

Geodesy, GRACE

10-10, 10–2 to 1 Hz a, b, c

10-6 differential a

Future Earth geodesy

≤ 10-12, 10–2 to 1 Hz a, b

10-9 differential a

Fundamental
physics

Equivalence Principle tests

≤ 10-10, 10–2 to 1 Hz a

≤ 10-10 differential a

Tests of general relativity

≤ 10-10, near zero frequency a

≤ 1 absolute a

Astrophysics

Gravitational waves

3 x 10-15, 10-4 to 1 Hz

10-11 differential

Table 1: Applications of drag-free technology (Ref. 2)

Legend to Table 1: a performance to be demonstrated by a 3U CubeSat, b demonstrated, c non drag-free.

The first drag-free satellite, Triad I with the DISCOS (DISturbance COmpensation System), launched in 1972, achieved a drag-free performance of better than 10–10 m/s2 over 10-day periods and extended the time required for ephemeris updates to several weeks. Since then, two other drag-free satellites have flown: NASA’s GP-B (Gravity Probe-B), which tested two predictions of general relativity with ultra-precise drag-free gyroscopes in LEO, and ESA’s geodesy mission, GOCE ( Gravity field and steady-state Ocean Circulation Explorer).

The measurement of Earth’s gravity field is among the main goals of the GRACE mission. At the core of this mission are precision accelerometers that measure all non-gravitational forces, which are removed from the gravitational measurements in the data postprocessing. A drag-free system simplifies the data analysis by canceling the non-gravitational forces on-orbit and also allows for improved performance by reducing the dynamic range of the measurement.

In addition to geodesy, drag-free technology enables precision distributed Earth-observing sensors, gravitational science and astrophysics missions, and precise orbit determination and maintenance. In a NASA Earth Science Technology Office Study on drag-free technology, drag-free systems were found to have the following benefits:

1) a 50% reduction in fuel consumption for a continuously drag-compensated system compared with one corrected once after 4 weeks for a 350 km altitude satellite

2) a 30%-50% reduction in navigation error if drag were directly compensated, and

3) a potential for substantial cost savings for drag-free satellite constellations in an orbit with substantial drag.

The target performance of the Drag-free CubeSat is 10–11 m/(s2Hz1/2) between 10 mHz and 1 Hz, which is roughly 10 times better than the GRACE accelerometers and comparable to the drag-free performance of GOCE. The performance is limited primarily by the minimum impulse bit and thrust noise of available CubeSat scale thrusters. A propulsion system specifically tuned for a drag-free nano-satellite, would improve the performance by a factor of 10. After propulsion, the next largest disturbance forces are a function of the stability of the thermal and magnetic environment achievable on a CubeSat. All of the dominant error sources will be calibrated to 10–12 m/(s2Hz1/2) through a series of plan on-orbit experiments (Ref. 2).

 


 

Spacecraft:

The spacecraft is a commercial 3U CubeSat bus (i.e. a nanosatellite) such as the Pumpkin CubeSat Kit with commercial EPS, ADACS, and GPS unit: the payload volume is 10 cm x 10 cm x 26 cm. The nanosatellite measures 34 cm x 10 cm x 10 cm with a mass of ~ 4 kg at launch.

EPS (Electric Power Subsystem): Use of three solar panels, with 8 cells on each (±z, orbit normal sides and +x, radial, see Figure 1). When in sunlight, the power produced is 6.5-9.3 W, depending on the attitude. The batteries provide 30 Wh of power. This is sufficient to power all subsystems during drag-free operations with margin. If a sun-synchronous orbit is not available, then drag-free operations must be intermittent or deployable solar arrays must be used.

The daily downlink is about 17 MB during drag-free operations, less when the satellite is not operated drag-free. The duration of drag-free operations is ~70 days, assuming a 400 km average altitude. A commercial modem, transmitting and receiving over amateur radio frequencies is used to send telemetry and receive commands. Flash memory on board the satellite will be sufficient to store all payload and spacecraft data for the entire mission. One GB of storage provides sufficient space to store about 1 year of operations data.

The primary payload is a scaled down version of the MGRS (Modular Gravitational Reference Sensor), developed at Stanford, which drives a cold gas thruster to compensate for drag and maintain the position of the satellite with respect to the test mass. The nominal propulsion system is MiPS (Micro-Propulsion System) produced by VACCO Space Products.

The MGRS consists of a cubical housing that contains and shields a free-floating spherical test mass. A DOSS (Differential Optical Shadow Sensor), mounted to four sides of the housing, measures the position of the spacecraft with respect to the test mass in all 3 directions. The test mass, housing and associated electronics fill a volume equivalent to 1U of a CubeSat. Hence, the payload is also referred to as the 1U GRS. In addition, a caging mechanism is used to mechanically secure the test mass during launch - and release it once the satellite reaches its designated orbit.

DragfreeCubeSat_AutoA

Figure 1: Illustration of the Drag-free CubeSat (image credit: Stanford University)

The drag-free control system uses the satellite position measurement provided by the shadow sensor and a small cold gas thruster in the aft of the satellite to compensate for atmospheric drag and keep the spacecraft centered with respect to the test mass. A commercially available ADACS (Attitude Determination and Control System) will maintain the satellite’s attitude pointed in the direction of the drag force, as well as control the satellite’s roll angle.

The general layout of the Drag-free CubeSat is shown in Figure 1. The main components are:

• a VACCO MiPS cold gas thruster in the aft end (–y)

• the 1U GRS in the center unit with the a test mass at the satellite center of mass

• a test mass caging system to the aft of the 1U GRS

• the spacecraft bus forward of the 1U GRS (+y) consisting of a motherboard, CPU, radio, and EPS (Electric Power System)

• the ADACS at the front of the satellite. The satellite structure is a custom designed aluminum frame.

 

Launch: A launch of the Drag-free CubeSat is assumed to be as a secondary payload in compliance with the P-POD (Poly Picosatellite Orbital Deployer) launcher, accommodating the nanosatellite into LEO (Low Earth Orbit). A launch of the mission could be planned for the timeframe 2015; however, an arrangement has yet to be made.

Orbit: A sun-synchronous orbit is preferred (due to its constant solar illumination), the preferred altitude is 400 km.

Mission profile:

The technology demonstration mission produces some science data, including very precise nanosatellite drag measurements. The mission profile is divided up into three phases:

1) launch and initial orbit checkout

2) drag-free operations

3) post-drag-free operations.

The total mission lifetime is limited by the amount of fuel contained in the MiPS thruster. Assuming an average altitude of 400 km, the total drag-free duration is ~70 days depending on the on-orbit efficiency of the drag-free and attitude control system. Higher altitudes result in longer lifetimes, as shown in Figure 8.

During the initial orbit checkout, the test mass is caged and the thruster is kept off. The communications, EPS, UV LED charge control, DOSS, GPS, and DFACS (horizon sensor, rate gyros, magnetometers, reaction wheels) subsystems are all checked for proper functionality. Then, the ADACS is used to establish nadir-fixed orientation control (y-axis is ram, z-axis is orbit normal, x-axis is radial pointing). Finally, the caging system releases the TM (Test Mass) and the DOSS is used to determine transient test mass dynamics and the final location of test mass inside housing.

At the start of the drag-free operations phase, the DFACS is activated and the test mass is “captured” by the satellite. The satellite is operated in a nominal drag-free mode for roughly 5 days. After this period of time,orbit estimation software on the ground is used to estimate the low frequency acceleration bias (3-axis) of the satellite. Then the “center” position of the spacecraft with respect to the test mass is adjusted in order to compensate for the estimated acceleration bias. Drag-free operations are continued for another five days and a new acceleration bias estimate is produced and compensated for by re-centering the test mass sensor null. This process is repeated several times until a minimum zero-frequency acceleration bias is achieved.

Once the optimal drag-free performance is achieved, three test mass disturbance evaluation tests are performed. The first test involves modulating test mass center position at 1 mHz and using the DOSS and thrust profile to estimate the test mass-to-spacecraft stiffness. The second and third tests cycle heaters and electromagnets on board the spacecraft, respectively, with a 1000 second periodicity in order to estimate the dependence of drag-free performance on temperature and magnetic field. After these three tests are completed nominal drag-free operations are resumed until all of the fuel is consumed.

During post-drag-free operations, the test mass is re-caged and un-caged several times and the DOSS is used to estimate test mass release dynamics. At the end of the mission, the test mass is re-caged and the satellite is shut down.

 


 

Payload/experiment complement:

The payload consists of the test mass and housing, the DOSS position sensor, the UV LED (Light-Emitting Diode) charge control system, the caging mechanism, the cold gas thruster, the ADACS, and the drag-free control laws. The attitude and translation control system (thruster, ADACS and control laws) are considered part of the payload, since they are an integral part of the primary function of the satellite.

Figure 2 shows a cross section of the 1U GRS and caging mechanism. Both are mounted to a central titanium bulkhead which provides the only attachment point to the CubeSat structure. The bulkhead geometry and material are chosen to minimize the conductive heat path to the GRS housing. Thermal stability of the housing is important for the overall drag-free performance of the system.

DragfreeCubeSat_Auto9

Figure 2: Schematic view of the 1U GRS (right), with caging mechanism (left). The large central plate is the titanium bulkhead (image credit: Stanford University)

Test mass and housing: The nominal test mass is a 25.4 mm diameter, 171 g sphere of 70%/30% Au/Pt. This material is chosen because it is dense, it can be machined, and it has a low magnetic susceptibility. The TM (Test Mass) will be grade 10, i.e. round to 250 nm, which is a factor of 20 times less round than the GP-B (Gravity Probe B) flight rotors, and have a mass unbalance of < 1 µm, 100 times that of the GPB rotors. The TM and housing inner surface are coated in SiC, which has a quantum efficiency supporting UV charge control. In addition, SiC has a high elastic modulus and is extremely hard. Consequently, it is difficult to obtain large areas of contact, and therefore significant bonding with the spacecraft, even when constrained by a high preload, for example during launch. The coatings of the TM and housing, which has no exposed sensitive components, are designed such that the TM can repeatedly touch the housing wall in a µg environment without damaging the TM or housing or sticking.

The housing is a 7 cm aluminum (6061-T6) cube with a 5 cm cubic internal cavity to accommodate the test mass. The housing is fabricated in two halves in order to allow its inner surface to be coated with SiC. Four faces (+x, –x, +z, –z) of the housing each have four holes to accommodate the emitters and detectors of the DOSS. The –y face of the housing has a 26 mm hole to accommodate the plunger of the caging mechanism, which, when actuated, holds the test mass against the +y inner face of the housing during launch. Recessed into the +y inner face of the housing is a UV LED used to control the electric charge on the test mass via UV photoemission. A sheet of mu-metal covers all external surfaces of the aluminum housing in order to magnetically shield the test mass. The magnetic shield is designed to reduce the magnetic field inside the house by a factor of 100 relative to the outside.

The 1U GRS (Figure 2) is designed to attenuate thermal loads from the outside of the satellite. A COMSOL finite element model of the Drag-free CubeSat with the 1U GRS, ADACS, MiPS thruster, and additional mass to account for unmodeled components was created for both thermal and structural evaluation. A ±1 K sinusoidal temperature variation on the exterior surface of the satellite was applied as a boundary condition on the top (axial) and side (transverse) faces in separate analyses.
Table 2 shows the axial and transverse thermal attenuation factors as a function of frequency. The attenuation factor represents the temperature difference on the interior surface of the housing at the specified frequency when a 1 K exterior temperature variation is applied at that same frequency.

Frequency

1 mHz

10 mHz

100 mHz

Axial attenuation factor

10-3

10-5

10-7

Transverse attenuation factor

2 x 10-3

2 x 10-5

2 x 10-7

Table 2: Axial (z-axis) and transverse (x and y axes) thermal attenuation factor

The same FEA model was also used to perform a structural analysis of the Drag-free CubeSat. Based on the NASA (General Environmental Verification Specification), a bounding static load of 14.1 g was applied in the axial and transverse directions in separate analyses. The CubeSat and 1U GRS structure yield strengths which are more than four time greater than the bounding launch stresses.

DOSS (Differential Optical Shadow Sensor): The DOSS is the sensing system that measures the position of the test mass relative to the housing. This data is used as input to the drag-free and attitude control of the satellite. The DOSS is based on measuring light intensity thus allowing the use of non-coherent light sources. Its dynamic range is large and limited only by the size of the detector and the beam waist. Two light beams of equal intensity are tangent to and partially blocked by the TM. The two intensities and their difference are measured, thus canceling common mode noise in the signals. The measurement principle is illustrated in Figure 3 for a one dimensional measurement with one pair of detectors.

The DOSS requires two pairs of parallel beams for a three-dimensional position measurement. Four pairs are planned for redundancy. The LEDs, with a wavelength of 1550 nm, are used for the light source. A low-power FET input amplifier (such as the OPA129 or OPA140) is at the core of the amplifier. Data acquisition will use a DSP (Digital Signal Processor) for lock-in detection and amplification.

DragfreeCubeSat_Auto8

Figure 3: Top: circular TM, two detectors and the partially blocked light beams. Bottom: simulation of the left and right signals and their difference (image credit: Stanford University)

A complete DOSS system has been developed and tested at Stanford, using flight like components and circuits (Figure 4). Without using its differential capability the system has achieved a measured sensitivity of 20 nm/Hz1/2 above 10 mHz, with a 1/f trend below 10 mHz. The noise amplitude spectral density is shown in Figure 5.

DragfreeCubeSat_Auto7

Figure 4: Photo of the flight-like DOSS system (image credit: Stanford University)

Legend to Figure 4: Photodetector (top): 3 mm FCI InGaAs quadrant photodiode with amplifier board containing power supply filter, first amplifier stage and 2nd stage differential amplifier. Bottom: complete system for a 50.8 mm sphere.

DragfreeCubeSat_Auto6

Figure 5: Measured amplitude spectral density vs. frequency of the flight-like DOSS system at Stanford (image credit: Stanford University)

Test mass caging mechanism: The fundamental requirements of the caging system are to prevent damage to the sphere during launch and to release the sphere after arrival of the satellite on orbit. The caging system and entire Drag-free CubeSat are designed to handle the prescribed NASA GEVS (General Environmental Verification Specification), which is 14.1 g-rms for the lightest satellites.

The caging system design (Figure 6) is based on the flight-proven DISCOS system and consists of a vacuum-compatible dc motor with gearbox, a moving “motor cart” to which said motor is mounted, a set of spur gears to transmit the output torque of the motor to a lead screw, a bronze nut into which the lead screw is threaded, a titanium bulkhead to which the nut is affixed, and which also acts as the attach point of the caging system to the spacecraft structure, a plunger on the end of the lead screw (the aforementioned actuated surface), and a set of precision-machined steel shafts and dry shaft bearings that guide the motion of the plunger. As designed, the total travel of the plunger is 25 mm, and the mass is 0.354 kg, including 0.120 kg for the motor.

DragfreeCubeSat_Auto5

Figure 6: Model of the test mass caging system (image credit: Stanford University)

To hedge against the possibility of binding after the plunger is engaged to the proof mass, the motor will be operated at two different voltages, so that the stall torque of the motor is higher when retracting the plunger than when engaging it. Although the ACME screw should prevent back-driving under most conditions, random vibration testing is planned to verify the pre-load remains at or above the required load of 200 N while the caging system is unpowered.

The measured magnetic flux density of the motor is 0.4 mT. Assuming a dipole approximation for the far field, the magnetic field strength at the nominal position of the proof mass (120 mm away, perpendicular to the dipole) would be 0.12 µT, or less than 1/100th the strength of the Earth’s magnetic field at sea level.

Test mass charge control: Charge management by UV photoemission using the 254 nm line of an rf mercury source was successfully demonstrated by the GP-B mission in 2004-2005. Newer technology allows the use of commercially available LEDs operating in the 240-255 nm range as the UV source. Passive charge management will be used, relying on a virtual “wire” generated by photoemission and without bias is utilized for the proposed low capacitance 1U GRS. The power and mass are estimated at 0.1 W and 3 g, respectively. A number of UV-LED models have successfully completed environmental testing, and a complete test mass charge control system using UV LEDs will be demonstrated on a microsatellite in 2013.

MiPS (Micro Propulsion System): The baseline propulsion system for the Drag-free CubeSat is MiPS produced by VACCO Space Products (Figure 7). The Drag-free CubeSat requires one thruster at the aft end in order to compensate for atmospheric drag. Each unit is 509 g, has a maximum thrust of 55 mN, a specific impulse of 65 s, and total impulse of 34 Ns.

The thruster lifetime during drag-free operations as a function of the average orbit altitude is shown in Figure 8. The drag-free and attitude control system design assumes an average altitude of 400 km, resulting in a thruster lifetime of about 70 days. For comparison, the twin GRACE satellites fly at an altitude of ~450-460 km.

DragfreeCubeSat_Auto4

Figure 7: VACCO Micro Propulsion System (image credit: VACCO Space Products)

DragfreeCubeSat_Auto3

Figure 8: Estimated lifetime of drag-free operation (image credit: Stanford University)

DFACS (Drag-free and Attitude Control System): The DFACS is a 6 degree-of-freedom (DOF) sensing and 4 DOF actuation system. The DFACS block diagram is shown in Figure 9. Drag-free (translation) actuation is performed with a single port of the MiPS thruster oriented in the –y direction, which opposes the main drag force. Attitude actuation is done with the ADACS (Attitude Determination and Control Subsystem), the baseline unit is the Maryland Aerospace MAI-400) at the front end (+y) of the satellite. The primary 3 DOF translation sensor is the DOSS, with the IMU accelerometers (baseline unit is the Analog Devices ADIS16405) providing back-up information. Attitude sensing is a fusion of the horizon sensor that is part of the ADACS and the rate gyros included in the IMU (Inertial Measurement Unit). Both drag-free and attitude control inputs, as well as the output of both attitude and translation sensors are optimally combined by an EKF (Extended Kalman Filter), providing realtime attitude and translation estimates and covariances. The transverse ports of the MiPS periodically desaturate the reaction wheels.

DragfreeCubeSat_Auto2

Figure 9: Drag-free and attitude control system block diagram (image credit: Stanford University)

The control law design consists of relatively fast inner attitude control loop with a bandwidth of roughly 0.5 Hz and a slower drag-free outer control loop, operating at ~0.1 Hz. Attitude and rate estimates (3 DOF), denoted Φ (dot) and ω (dot)respectively, provided by the EKF are fed into the inner loop attitude controller, which sends a command, w, to the reaction wheels of the ADACS. The reaction wheels provide the commanded torque, T, to the spacecraft, which is also disturbed by atmospheric drag torques, D.

A nonlinear numerical simulation of the DFACS has been implemented. It incorporates the satellite mass properties, the MiPS thruster performance, the DOSS and ADACS sensing noise, an ADACS torque limit of 10 mNm, and simulated drag forces and torques for a 400 km circular polar orbit. The atmospheric drag model bounds the model used to design the GOCE drag-free control system.

The resulting stable position and attitude (pitch and yaw only) of the Drag-free CubeSat are shown in Figure 10. The position origin is the center of mass of the test mass. The parabolic arcs, ~400 µm in amplitude, associated with the along-track satellite position are evident (blue curve). The transverse position of the satellite is maintained to within ±200 µm, and the pitch and yaw angles are < 10º.

DragfreeCubeSat_Auto1

Figure 10: Simulated performance of the Drag-free and attitude control system (image credit: Stanford University)

Legend to Figure 10: x, y, z position in units of µm and pitch angle, θ, and yaw angle, φ, in units of 10º.

Expected performance:

A detailed acceleration noise budget (drag-free performance) has been compiled for the Drag-free CubeSat. The budget contains 30 terms: 6 S/C-to-TM stiffness, 8 magnetic, 6 thermal, 4 electric, 4 Brownian, 1 cosmic ray, and 1 sensing noise term. Calculation of each term in the acceleration noise budget follows the methodology used for the LISA (Laser Interferometer Space Antenna) gravity wave mission.

The resulting composite acceleration noise and the 10 largest individual noise terms are shown as amplitude spectral densities in Figure 11. The dominant acceleration noise contribution is due to stiffness, which is the residual coupling (weak spring) between the satellite and test mass. The stiffness (~10–6 m/s2m) is a composite of both gravitational and electromagnetic terms. The spectrum of the simulated motion of the satellite, shown in Figure 10, is multiplied by the stiffness to produce the associated acceleration noise. This noise term alone is ~10–11 m/(s2Hz1/2). In order to estimate the acceleration noise to better than 10–12 m/(s2Hz1/2), the stiffness contribution must be calibrated to at least 10%. The dashed curve in Figure 11 shows the uncalibrated performance and the solid black curve is the 10% calibrated performance.

The other two dominant error sources are magnetic interactions with the test mass (magenta curves in Figure 11), primarily above 100 mHz, and self-gravitation (red curve in Figure 11). Self-gravitation is the gravitational attraction of the TM to the satellite, which can be compensated for at low frequencies by carefully choosing the “zero” position of the satellite with respect to the test mass. At higher frequencies (Figure 11), self-gravitation disturbances are driven by temperature changes, which change the geometry of the satellite via its coefficient of thermal expansion. The peaks in the self-gravitation and thermal terms are caused by temperature variations at harmonics of the orbit frequency. The three largest acceleration noise terms (stiffness, magnetic, and thermally driven self-gravitation) will be individually estimated by dedicated on-orbit tests.

DragfreeCubeSat_Auto0

Figure 11: Acceleration noise performance at an altitude of 400 km (image credit: Stanford University, Ref. 2)

Legend to Figure 11: The dashed and heavy black curves are the un-calibrated and calibrated composite acceleration noises, respectively. The leading noise terms are: calibrated TM-to-satellite stiffness coupling to satellite motion (grey), self gravitation to the satellite (red), magnetic (magenta), electric disturbances (brown), thermal effects (blue), and optical sensing (green).


1) Andreas Zoellner, John W. Conklin, Sasha Buchman, Karthik Balakrishnan, Robert L. Byer, Grant D. Cutler, Dan B. DeBra, Eric Hultgren, John A. Lipa, Shailendhar Saraf, Seiya Shimizu, Jun Zhou, Abdul Alfauwaz, Ahmad Aljadaan, Hamoud Aljibreen, Mohammed Almajed, Muflih Alrufaydah, Salman Althubiti, Haithem Altwaijry, Turki Al-Saud, Victor Aguero, Scott D. Williams, “The Drag-free CubeSat,” 9th Annual Spring CubeSat Developer's Workshop, Cal Poly State University, San Luis Obispo, CA, USA, April 18-20, 2012, URL: http://mstl.atl.calpoly.edu/~bklofas/Presentations/DevelopersWorkshop2012/Zoellner_Drag-Free_CubeSat.pdf

2) John W. Conklin, Karthik Balakrishnan, Sasha Buchman, Robert L. Byer, Grant D. Cutler, Dan B. DeBra, Eric Hultgren, John A. Lipa, Shailendhar Saraf, Seiya Shimizu, Andreas Zoellner, Abdul Alfauwaz, Ahmad Aljadaan, Hamoud Aljibreen, Mohammed Almajed, Turki Al-Saud, Badr Alsuwaidan, Salman Althubiti, Haithem Altwaijry, Paolo Bosetti, “The Drag-free CubeSat,” Proceedings of the 26th Annual AIAA/USU Conference on Small Satellites, Logan, Utah, USA, August 13-16, 2012, paper: SSC12-VI-8

3) B. D. Tapley, S. Bettadpur, M. Watkins, Ch. Reigber, “The Gravity Recovery and Climate Experiment: Mission Overview and Early Results,” Geophysical Research Letters, Vol. 31, 2004, URL: http://www.csr.utexas.edu/grace/publications/papers/2004GL019920.pdf

4) D. B. DeBra, J. W. Conklin, “Measurement of drag and its cancellation ,” Classical and Quantum Gravity, Vol. 28, Issue 9, May 7, 2011


The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: ”Observation of the Earth and Its Environment: Survey of Missions and Sensors” (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates.