11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST John Wilkin 609-630-0559 [email protected] IMCS Room 214C Lectures 1 and 2: Satellite orbits and Measurement Geometry Satellite Remote Sensing Systems The flow of information from land, ice and ocean surface to satellite to user depends on features of the Earth surface phenomena, the atmosphere, and the satellite observing system. 1. ocean and land phenomena affect: color, temperature, roughness, albedo, emissivity, terrain, vegetation canopy, wave height/sea level 2. water/land leaving signal WLR (water leaving radiance) and land surface reflectivity can depend on relative position of Sun and satellite therefore time-of-day and field-of-view affect signal 3. satellite sensor • the observation may be from a passive or active system11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST • measurement may be an image or point-wise data • scan geometry depends on satellite trajectory • remote sensing instruments are not in physical contact with the phenomena under investigation – properties are inferred from the received radiation 4. field of view and ground-track sampling frequency depend on orbital period, trajectory, and altitude 5. orbit determination and satellite pointing information determine the geographic location of observation (time, place, averaging period). (The range to data may be the observation of interest.) Satellite position Critical to several aspects of the data set acquired by the sensor: • Sub-satellite ground-track and pointing: data coordinates • Altitude and field of view (FOV) resolution errors, atmospheric interference • sun-satellite angle illumination of land/sea surface • satellite velocity and sensor image forming and scan pattern signal to noise • repeat period repeat sampling interval for time- varying phenomena Operational issues Higher altitude – more energy required from launch vehicle – less drag, more stable orbit On orbit, and getting to orbit – don’t smack into anything else Sun-satellite angle affects thermal state, available power, solar wind perturbations to orbit stability and electronics, ground communication Satellite position is determined principally by orbital physics, with influence from satellite dynamics (drag, roll, pitch, moment of inertia). The set of parameters that define an orbit are referred to as the satellite’s ephemeris.11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST Physics of satellite orbits 50 years before Isaac Newton, Johannes Kepler analyzed data on planetary movements and deduced that: 1. Planets move in elliptical orbits with the sun as one focus 2. the radius vector from the sun to the planet sweeps out equals areas in equal times 3. T2 : R3 ratio is constant for all planets, where T is orbital period and R is semi-major axis of the orbit Substitute satellite for planet and earth for sun in the above rules and they apply for artificial earth satellites. For planets, a convenient unit of time is Earth Years, and for distance a convenient unit is the Astronomical Unit (A.U.) being the distance from the Sun to Earth. Then, trivially, R3 = T2 (because both units = 1) For Mars, the orbital period is 1.88 Earth years, so R = T2/3 = (1.88)2/3 = 1.52 A.U. which is indeed the average radius of the Martian orbit. (see e.g. http://www.windows.ucar.edu/tour/link=/our_solar_system/planets_table.html) Newton discovered the laws of gravitation and explained planetary and satellite orbits in terms of the balance of forces: Gravity : centrifugal acceleration Newton: F = ma = mdvdt Gravity: Fgravity=GMmr2 where r is the separation distance of masses M and m G = 6.67 x 10-11 N m2 kg-2 Mearth = 5.976 x 1024 kg11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST An object of mass m falling in the Earth’s gravitational field at the Earth’s surface accelerates at a rate determined by ma =GMmrearth2a = g =GMearthrearth2 rearth = 6373 km Note: this is independent of mass m - remember Galileo  g = 9.81 m s-2 A satellite in permanent Keplerian orbit maintains a balance between gravity and centripetal force due to its circular motion. Centripetal acceleration =v2r v is the speed of the satellite r the radius of the orbit11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST Acceleration is the rate of change of velocity a =ΔvΔt v = v − sinθ,cosθ⎡⎣⎤⎦dvdt= v − cosθ,−sinθ⎡⎣⎤⎦dθdtanddθdt=vr (notice that vectors v and dv/dt are perpendicular) so it follows that the acceleration is dvdt=v2r−cosθ,− sinθ⎡⎣⎤⎦a =v2r and the acceleration is always perpendicular to the direction of v. To have a balance between gravitational force and centripetal force in a circular orbit means that: GMmr2=mv2rv =GMr Note that v does not depend on m The satellite velocity is set by the radius of the orbit, which is the radius of the earth plus the satellite altitude above ground. Altitude of the satellite (altitude = r – rearth), mass of Earth, and G, determine the satellite’s orbital period:11:670:451 / 16:712:552 | Remote Sensing Ocean & Atmosphere | John Wilkin | SST vT = 2πrT = 2πr /GMrT2=4π2r3GMT = 2πr3GM <<< Kepler T2 : R3 The ISS at altitude 360 km above the earth surface (the distance from D.C. to NYC) will have a period of T = 2π(6373 + 360)3x1093.986x1014= 5.498x103s (<< add radius of Earth 6373 km to get radius of orbit) = 91.6 minutes at a speed of 7.69 x 103 m s-1 = 17,200 m.p.h. D.C. to NYC is 360 km, which at the speed of the ISS takes 46 seconds. The characteristics of how an earth observing satellite samples the land/ocean surface and atmosphere depends on its orbit with respect to the Earth’s center of mass, and the rotation of the surface of the planet beneath this orbit (the ground track pattern, and repeat period). Often it is the pattern of the ground-track traced by the satellite that is a key factor in deciding a suitable orbit. However, the rotation of the Earth has nothing to do with the orbit of the satellite