Space platform and Orbits Introduction to Remote Sensing Instructor: Dr. Cheng-Chien LiuCheng-Chien Liu Department of Earth Sciences National Cheng Kung University Last updated: 11 October 2004 Chapter 2

Platform of remote sensing  Various platform Towers, balloons, model aircraft, kites, helicopter (Fig), light aircraft, jet aircraft, reconnaissance aircraft, low-earth orbit satellite, geostationary satellite, … Range and altitude (see Fig 10.1 in Rees 2001) Concept of multistage of remote sensing (Fig 1.21) Our focus

Aircraft  Characteristics Operation: convenient and flexible  Routes, time, speed, …  Restriction of weather condition Range of payload Altitude Spatial resolution  Disadvantages Duration Spatial coverage Position  GPS (global position system)  GCPs (ground control points) Motion  Fig

Satellite  Characteristics Temporally homogeneous observation Spatial coverage Stability  Disadvantages Expensive Flexibility Spatial resolution  Debate on the replacement of airborne remote sensing by satellite remote sensing

Launch of satellite  Traditional approach – rocket  New approach 1: space shuttle  New approach 2:  The X prize The X prize The X prize

Traditional approach – rocket  Fuel  Classical mechanics Increasing speed  v by burning a mass M f of fuel  where u is the speed of the exhaust gases relative to the rocket, M i is the initial mass

Traditional approach – rocket (cont.)  Placing a satellite in orbit Way 1: (see Fig 10.3 in Rees 2001)  Launch vertically upwards  Increase an orbit velocity Example  R = 7200 km  R E = 6400 km  GM = x m 3 s -2   v 1 = 3.7 m s -1   v 2 = 7.5 m s -1   v = 11.2 m s -1

Traditional approach – rocket (cont.)  Placing a satellite in orbit (cont.) Way 2: (see Fig 10.4 in Rees 2001)  Launch tangentially  Increase an circular orbit velocity Example  R = 7200 km  R E = 6400 km  GM = x m 3 s -2   v 1 = 8.2 m s -1   v 2 = 0.2 m s -1   v = 8.4 m s -1  Tangential speed of Earth’s surface = 0.5   v = 7.9 m s -1

Traditional approach – rocket (cont.)  Placing a satellite in orbit (cont.) Rationale of having a multi-stage rocket   v = 8 m s -1  u = 2.4 km  M f / M i = 96%  Payload < 4%

The Elements of a Satellite Orbit Source:

The Elements of a Satellite Orbit (cont.)  An ideal elliptical orbit Fig 10.5 in Rees 2001 Perigee P Apogee A Major axis, semi-major axis Minor axis, semi-minor axis Eccentricity e b 2 = a 2 (1 – e 2 ) Period GM = (  ) x m 3 s -2

The Elements of a Satellite Orbit (cont.)  An ideal elliptical orbit (cont.) Position of the satellite in the orbital plane Relationship between  and t Series expansion against e For most artificial satellite: e < 0.01 ∴   t

The Elements of a Satellite Orbit (cont.)  An inclined elliptical orbit Fig 10.6 in Rees 2001 Inclination  Prograde  Retrograde  Exact polar orbit  Near-polar orbit  Give the greatest coverage of the Earth’s surface  Widely used for low-orbit satellite  More expensive to launch  Ascending node  Ascending  Descending

The Elements of a Satellite Orbit (cont.)  Sub-satellite point Based on spherical trigonometry  Latitude b  Longitude l Fig 10.7 in Rees 2001  Typical sub-satellite tracks for circular orbits of inclination 60 0, 89 0,  Earth’s rotation  westwards drift of sub-satellite track

Effects of the Earth’s asphericity  Earth  oblate spheroid The gravitational potential  a e : the earth’s equatorial radius  J 2  : dynamical form factor  The most convenient way to describe mathematically the effect of this non-spherical Earth on the motion of a satellite is to write the gravitational potential as a sum of spherical harmonics

Effects of the Earth’s asphericity  Three effects Nodal period Precession (see Fig 10.8 in Rees 2001) Rotating the elliptical orbit in its own plane (Fig 10.9)

Special orbits  Geostationary orbits Geostationary orbits Geostationary orbits Place the satellite into a circular orbit above the equator Nodal period P n = Earth’s rotational period P E  Sidereal day = 24 /(1+1/365.24) = hr = s i = 0 0 e = 0 a = km h = km GOES-2 visible band (Fig 6.36)  Not the full coverage but just over 81 0  In practice,

Special orbits (cont.)  Geo-synchronous orbits Geo-synchronous orbits Geo-synchronous orbits Place a satellite in a geostationary orbit above a point that is not located on the equator Nodal period P n = Earth’s rotational period P E  Sidereal day = 24 /(1+1/365.24) = hr = s i  0 0 The sub-satellite path: figure-of-eight pattern Not used in remote sensing

Special orbits (cont.)  Molniya orbits Molniya orbits Molniya orbits Select orbital parameters  highly eccentric with apogee positioned above the desired point  spend longer on station than in the wrong hemisphere i = or Nodal period P n = ½ Earth’s rotational period P E  a = km  If P n = P E and small e  unhelpful large distance of apogee Example  e = 0.74  Perigee distance = 6900 km, apogee distance = km  Sub-satellite track of Molniya orbit (see Fig in Rees 2001)  On station for 8 hours  three satellite can provide continuous coverage

Special orbits (cont.)  Low Earth orbits Low Earth orbits Low Earth orbits Widely used  Increasing spatial resolution at the expense of reduced coverage Range  van Allen belt van Allen belt Sun-synchronous orbit  Precess about the Earth’s polar axis at the same rate (one revolution per year) that the Earth orbits the Sun  Mean angular speed  S = 2  per year =  s -1  Inclination and nodal period for circular sun-synchronous orbits (see Fig in Rees 2001)

Special orbits (cont.)  Low Earth orbits (cont.) Low Earth orbits Low Earth orbits Advantages of Sun-synchronous orbit  View a large fraction of the Earth’s surface  Cross the same latitude at the same local solar time

Special orbits (cont.)  Exactly repeating orbits

Homework  C-prize Describe an innovative way of remote sensing that could be deployed in the future Explain the feasibility of your idea  Derive all equations that were used for placing a satellite in orbit  The altitude of TERRA orbit is 705 km. Please calculate the required inclination to achieve a circular sun-synchronous orbit.