Remote Sensing of the Oceanand Atmosphere:

John L. Wilkin

Orbits and Measurement Geometry (1)

jwilkin@rutgers.eduIMCS Building Room 214C609-630-0559 (g-voice)

The flow of information from land or sea surface to satellite to user depends on features of the land/ocean phenomena, the observing system, and the intervening atmosphere.

(1) Ocean phenomena: color, temperature, roughness, height

(2) Water leaving signal: WLR can depend on relative position of sun and satellite, time of day, emissivity, reflectance

(3) Sensor: the data is a measurement or image

(4) resolution: FOV, aperture, scan geometry can depend on satellite trajectory and altitude (orbit), pointing

(5) Geolocation: position, time, pointing. Orbit affects repeat sample interval

(6) Position of the satellite, or range to target may be the actual data.

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

Johannes Kepler (1571 – 1630) German mathematician, astronomer and astrologer

1. Newton discovered the laws of gravitation and explained planetary and satellite orbits in terms of the balance of forces:

2. Centripetal acceleration

3. Gravity

Isaac Newton (1643 - 1727) English physicist, mathematician, astronomer, theologian)

F =ma=mdvdt

Fgravity =GMmr2

Galileo Galilei (1564 - 1642)Italian physicist, mathematician, astronomer, and philosopher

Galileo's pupil Vincenzo Viviani stated that Galileo had dropped balls of the same material, but different masses, from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass.

This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight.

There is no account by Galileo himself of such an experiment, and it is generally accepted that it was at most a thought experiment which did not actually take place.

Nov 5, 2007 view from Space Shuttle

Epoch (UTC): 10:07:53 AM, Monday, January 28, 2008

Eccentricity: 0.0005362

Inclination: 51.6418°

Perigee Height: 334 km

Apogee Height: 341 km

Right Ascension of Ascending Node:

22.2238°

Orbit Number at Epoch: 52631

Revolutions per Day: 15.77540422

v1

-v1

Δv

v2

v2

Δθ

ΔθΔs = rΔθ

change in velocity (acceleration) is perpendicular to the direction of travel

v =ΔsΔt

=rΔθΔt

=rdθdt

⇒dθdt

=v

r

Stewart, R. H., 1985, Methods of Satellite Oceanography, University of California Press, 360 pp.

x-axis

Right ascension - declination coordinate system

First Point of Aries: One of the two points on the Celestial Sphere where the Ecliptic and the Celestial Equator cross one another.

Ecliptic: An imaginary line that approximates the plane in which the planets (other than Pluto) orbit the Sun. From the perspective of an observer on Earth, the planets and the Sun will always remain close to this line.

When the Sun reaches the First Point of Aries, as it does once each year, an equinox occurs. (Northern hemisphere Vernal Equinox)

The First Point of Aries, which is actually in Pisces, defines the zero-point for Right Ascension.

Right ascension: the celestial equivalent of longitude (starting at the First Point of Aries)

Declination: the celestial equivalent of latitudeThe celestial north pole is at declination +90

http://spaceflight.nasa.gov/realdata/elements See graphics of orbital elements and data for ISS

Jason-1 launch from Vandenburg Air Force Base, CaliforniaOrbit: http://www.aviso.oceanobs.com/en/missions/current-missions/jason-1/orbit/index.html

Launch: http://www.youtube.com/watch?v=Z4WHOSF2Ktg

Topex/Poseidon launched with Ariane rockethttp://sealevel.jpl.nasa.gov/gallery/tiffs/videos/launch.mov

Pegasus vehicle aircraft launch http://www.youtube.com/watch?v=QRHiTvRHHd8

Other launches:

Delta-II (Themis):http://www.youtube.com/watch?v=p_pAhPecto0

Ariane launch failure:http://www.youtube.com/watch?v=kYUrqdUyEpI

Jason-2 OSTMhttp://www.youtube.com/watch?v=cf0loVEs_lo

OSTM / Jason-2 Boost Profile

Space craft separation:http://www.youtube.com/watch?v=1aBpcCVljt4

http://en.wikipedia.org/wiki/Hohmann_transfer

Maneuver to different inclination

Hohmann Transfer

On Jan 11, 2007, China tested anantisatellite rocket. The initial collisionadded 800 to 1000 pieces of space junkto the current total of detectable objects.

Kessler, D. J., and Burton G. Cour-Palais. "Collision frequency of artificial satellites – The creation of a debris belt." Journal of Geophysical Research Vol. 83 (June 1978): 2637-2646.

Collisions between existing debrisgenerate additional pieces of debris.There is concern that eventually a chainreaction will ensue (the Kesslersyndrome) littering the low earth orbit(LEO) with debris making it almostimpenetrable to new satellite launches forfear of collision.

How many detectable objects (> 4inches) are in orbit?

http://www.nytimes.com/2007/02/06/science/space/06orbi.html?emc=eta1

http://www.nytimes.com/2007/02/06/science/20070206_ORBIT_GRAPHIC.html

http://spaceflight.nasa.gov/realdata/elements See graphics of orbital elements and data for ISS

ostm-topex-5days-orbit animation

SeaWiFS daily coverage

seawifs_daily_coverage animation

Is this orbit prograde or retrograde?

Terra satellite, MODIS instrument, coverage of all instrument swaths during a single day ( 01/28/2006 )

Jason altimeter satellite

Equatorial separation of Jason groundtracks is 315 km

ENVISAT 35-day repeat

Sidereal day = time it takes for Earth to rotate through 360o This is slightly shorter than a solar day (24 hours)

There are 365.25 solar days in a year but 366.25 sidereal days

Sidereal day = 365.25/366.25*24 = 23.93 hours

sidereal

solar

http://en.wikipedia.org/wiki/Sidereal_time

Scan geometry

• zenith angle w.r.t. satellite nadir

• look angle and solar zenith angle w.r.t local vertical

• Fixed solid angle Field of View (FOV) such as for an optical lens, gives elliptical footprint off-nadir and varying spatial resolution in the scan

View satellite orbits and ground tracks at:http://science.nasa.gov/realtime/jtrack/Spacecraft.html

Internet resources on orbits and satellites

• http://science.nasa.gov/realtime/jtrack/Spacecraft.htmlShows ground tracks and 3-D orbits for all satellites

– Notice the clusters of satellites in the major categories or orbits• Geostationary• Polar orbiting (NOAA, Topex, ERS, Envisat)• Low Earth orbit (Iridium, HST, ISS)• GPS

– Unusual orbits (especially ground track)• Chandra• IMAGE• CRRES (in a geosynchronous transfer orbit)

• http://heavens-above.comShows predicted orbits and visibility magnitudes and star charts of pass trajectories for all satellites

– See Homework 1 http://tinyurl.com/11-670-451-homework-1

• http://spaceflight.nasa.gov/realdata/elements – See graphics of orbital elements and data for ISS

• Real-time satellite tracking at http://www.n2yo.com