John Wilkin 732 932 6555 x 251 609 933 7753 jwilkin rutgers edu Remote Sensing of the Ocean and Atmosphere IMCS Room 214C 11 670 451 16 712 552 Lectures 2 and 3 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 phenomena affect color temperature roughness height sea level 2 water land leaving signal WLR can depend on relative position of Sun and satellite Time of day and field of view affect signal 3 satellite sensor the observation may be from a passive or active system 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 1 satellite velocity and sensor image forming and scan pattern repeat period repeat sampling of 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 ephemeris is determined principally by orbital physics with influence from satellite dynamics drag roll pitch moment of inertia 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 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 2 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 m dv dt Gravity Fgravity GMm r2 where r is the separation of the two masses M and m G 6 67 x 10 11 N m2 kg 2 Mearth 5 976 x 1024 kg An object of mass m falling in the earth s gravitational field at the earth s surface accelerates at a rate determined by ma GMm 2 rearth GM earth a g 2 rearth 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 v2 Centripetal acceleration r v is the speed of the satellite r the radius of the orbit Acceleration is the rate of change of velocity a v t 3 v v sin cos dv d v cos sin dt dt these are perpendicular s r t t d v dt r so it follows that the acceleration is 2 dv v cos sin dt r a v2 r and the acceleration is always perpendicular to the direction of v directed away from the origin of the circle To have a balance between gravitational force and centripetal force in a circular orbit means that GMm mv 2 r r2 GM v r Note that v does not depend on m Altitude of the satellite determines its orbital period vT 2 r T 2 r GM r T2 4 2 r 3 GM T 2 Kepler r3 GM The ISS at altitude 360 km D C to NYC above the earth surface will have a period of 4 6373 360 3 x10 9 3 986 x1014 5 498 x10 3 s T 2 radius of Earth is 6373 km or 91 6 minutes at a speed of 7 69 x 103 m s 1 17 200 m p h The characteristics of how an earth observing satellite samples the land ocean surface and atmosphere depends on its orbit with respect to the Earth 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 itself which must be considered in a non accelerating Newtonian coordinate system fixed w r t the stars The three principal orbits employed for Earth observation are Geosynchronous Sun synchronous polar orbiting Near equatorial low inclination 5 Geometry of elliptical orbits Figures from Martin chapter 1 Kidder and Vonder Haar their figs 2 4 2 5 and Stewart his figs 15 1 15 3 Strictly speaking a satellite orbit is elliptical and described by 6 Keplerian elements though in practice most earth observing satellites are in near circular orbits described by 4 elements Orbit shape is defined by its eccentricity e semi major axis a from Stewart The location of the orbital plane is defined with respect to an inertial coordinate system i e one that is independent of the earth s rotation a 1 e 2 r Satellite position is defined in polar coordinates r 1 e cos where angle is called the true anomaly The true anomaly is sometimes is measured counterclockwise from perigee for elliptical orbits and always measured counterclockwise from the Ascending Node for circular orbits 6 Right ascension declination coordinate system z axis parallel to Earth rotation axis north pole south pole x axis toward point on the celestial sphere when the sun is at the vernal equinox March 21 So x axis lies in both the ecliptic and the satellite s orbital plane Satellite orbit is described by 3 angles i inclination angle between orbital plane Earth s equatorial plane i 90 prograde i 90 retrograde i is also the maximum latitude of the satellite ground track