Probing General Relativity with Photometric Monitoring of Gas Giant Moons Katie Breivik, Department of Physics Shane L. Larson, Faculty Advisor, Department of Physics

Abstract General relativity is the modern description of gravity needed to correctly understand modern technical applications like the global positioning system (GPS) and precision satellite orbits. Tests of general relativity effects are important for understanding the underlying structure of the theory and its applications to modern science and engineering. In the solar system, precision tests can be carried out by monitoring astrophysical effects, in particular planetary orbits, as Einstein originally proposed with Mercury. The work in this proposal will use observations of the moons of Jupiter and Saturn as high precision probes of general relativity. Observations will be made using the new twenty-inch telescope located on the top of the SER building at USU in Logan.

Introduction When he first published general relativity, Einstein proposed three classic tests to demonstrate the validity of the theory as a description of gravity [1]. The first classic test of general relativity was the successful prediction of the anomalous perihelion precession of Mercury, observationally determined to be 43”/century [see e.g., 2]. Because orbits are elliptical, not circular, certain parts of the orbit are closer to the gravitating body. The point of closest approach is called the periapsis, or in the case where the Sun is the gravitating body, perihelion. Over time the location of Mercuryʼs perihelion is slowly shifting, rotating around the Sun. A heuristic picture illustrating periapsis precession for Jupiter and one of its moons is shown in Figure 1 below. The rate of this perihelion shift can be calculated with general relativity, and shown to agree with the astronomical observations. This relativistic effect is measurable but small because Mercury is far from its gravitational source, the Sun. A higher precision measurement could be made if the perihelion shift were larger, providing a stronger test of the predictions of general relativity. As the source of gravity becomes closer, the perihelion Figure 1: Example of periapsis precession. Table 1: Orbital data for gas giant moons.

Moon Orbital Period Precession Rate Brightness (magnitude) Amalthea 0.498 d 22”/year 13.0 Io 1.769 d 2.7”/year 4.80 Europa 3.551 d 0.84”/year 5.17 Mimas 0.942 d 3.4”/year 12.1 Enceladus 1.370 d 1.8”/year 11.8 Tethys 1.888 d 1.1”/year 10.3 precession of an orbit is much more pronounced. This has been predicted to be the case for gas giant planets, such as Jupiter and Saturn, and their moons [3]. This has not been previously attempted, and the capability to measure the effect is only now made possible with the use of modern large aperture telescopes and CCD imaging technology. Table 1 shows that the predicted precession effects are fifty times greater, in some cases, than Mercury. In this work, I propose an extended observation campaign, using the USU 20” telescope located on the Logan campus, to observe the moons of Jupiter and Saturn, and fit their orbits to measure the periapsis precession rate. The funds from this proposal will provide for the acquisition of the CCD camera needed to make this project possible. In the rest of this proposal I describe the required observations and procedures for this project.

Observations and Analysis As shown in Table 1 above, the individual moons of the gas giants have orbital periods on the order of days, and will move appreciably over the course of a single night. Multiple imaging acquisition runs, separated by a couple of hours, will provide the fundamental data sets needed for orbital fitting. During the course of a year, the combination of the orbital motion of the Earth and the orbital motion of the gas giants themselves will bring the planets and Sun in close proximity on the sky, making imaging impossible. Using desktop sky simulation software (such as Starry Night [4] or XEphem [5]), we estimate we will not be able to image if Jupiter or Saturn are within 15 degrees of the Sun in the sky. Over the next year, Jupiter will be proximate to the Sun from mid-Feb 2010 through mid-Mar 2010; Saturn will be proximate to the Sun from mid-September 2010 through mid-October 2010. Imaging of these planets will not be possible in these timeframes. ! Measuring the orbital precession of a moon requires many observations over a long period of time. The basic observational data is high precision imaging of the parent planet and the target moon at precise times. The geometry of the orbit can be determined directly from measurements off the images. The limitation on high precision measurements of moons from astronomical images is “astronomical seeing” [see, e.g., 6]. The Earthʼs atmosphere is turbulent, making images and precise locations fuzzy; this is the source of the familiar twinkling of stars that you can see at night. Modern technology allows high-resolution images to be captured using a technique known as “registered stacking”. Registered stacking takes a long sequence of images (for example, video [7,8]) and keeps only the best frames. The best frames represent the single images that occurred in an instant of atmospheric clarity. From a set of clear images stacked together, the precise location of the moons can be measured with respect to the parent planet. Orbit determination from photographic measurements can be accomplished using classical orbit fitting techniques such as the Gauss Method, which requires three points of reference (images), or the Lambert Method, which requires successive observations (images) from which position and velocity can be determined [9, 10].

Equipment The observational program described above will be carried out using the twenty-inch telescope mounted in the USU observatory on the Logan campus. The funding in this proposal will purchase the astronomical camera and software needed for these observations. Basic image analysis and orbit fitting can be accomplished in a standard desktop computing environment available through Dr. Larsonʼs research group. The astronomical camera to be purchased is the DFK 41AF02.AS, a CCD camera from Imaging Source. The camera has a 1280x968 resolution, with an output rate of fifteen frames per second and a maximum exposure of sixty minutes. These features will be ideal for the proposed project by allowing for enough resolution to properly image the gas giant planets and their moons as well as enough exposure time to capture the required number of frames for registered stacking techniques to be used.

Summary These observations will provide a new weak field test of general relativity from solar system observations of orbital dynamics. The observations required for this research project are enabled by modern technological innovations -- notably by the new 20” telescope located on the USU campus, and registered image stacking using a CCD camera (to be funded by this proposal). The anticipated duration of the work in this proposal is approximately one year for data collection and analysis. Final results are expected during Spring Semester 2011. The results from this research project will be presented in poster format at a forthcoming American Astronomical Society meeting (either AAS 217 in Seattle, 9-13 January 2011, or AAS 218 in Boston, 22-26 May 2011) and will also be written up for submission to an appropriate professional research journal. References

[1] Albert Einstein, “The Foundation of the General Theory of Relativity”, Annalen der Physik 49, 769 (1916). [2] Clifford M. Will, "The Confrontation between General Relativity and Experiment", Living Rev. Relativity 9, 3 (2006). URL (cited on 8 Feb 2010): http:// www.livingreviews.org/lrr-2006-3 [3] William A. Hiscock and Lee Lindblom, “Post-newtonian effects on satellite orbits near Jupiter and Saturn”, Astroph. J. 231, 224 (1979). [4] Starry Night, Simulation Curriculum Corp., http://www.starrynight.com [5] XEphem, Clear Sky Institute, http://www.clearskyinstitute.com/xephem/ [6] “Observing the Universe”, Andrew J. Norton, Ed., Cambridge University Press, Cambridge (2004). [7] Robert Reeves, “Introduction to Webcam Astrophotography”, Willmann-Bell, Virginia (2006) [8] Lynkeos, http://lynkeos.sourcefourge.net [9] A. E. Roy, “Orbital Motion”, Institute of Physics Press, London (1988). [10] Dan Boulet, “Methods of Orbit Determination for the Microcomputer”, Willmann-Bell, Virginia (1991).