Remote Sensing of the Ocean
and Atmosphere:
John Wilkin
jwilkin@rutgers.edu
IMCS Building Room 214C
732-932-6555 ext 251
609-933-7753 (cell/txt)
Orbits and
Measurement Geometry (1)
Johannes Kepler (1571 – 1630)
German mathematician,
astronomer and astrologer
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 semimajor axis of the orbit
Isaac Newton (1643 - 1727)
English physicist,
mathematician, astronomer,
theologian)
1. Newton discovered the laws
of gravitation and explained
planetary and satellite orbits
in terms of the balance of
forces:
2. Centripetal acceleration
F  ma  m
3. Gravity
Fgravity
dv
dt
GMm

r2
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.
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
Nov 5, 2007 view from Space Shuttle
Remote Sensing of the Ocean
and Atmosphere:
John Wilkin
jwilkin@rutgers.edu
IMCS Building Room 214C
732-932-6555 ext 251
or 609-933-7753 (cell)
Orbits and
Measurement Geometry (2)
Stewart, R. H., 1985, Methods of Satellite Oceanography, University of California Press, 360 pp.
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 latitude
The 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, California
Orbit: http://www.aviso.oceanobs.com/en/missions/current-missions/jason-1/orbit/index.html
Launch: http://www.youtube.com/watch?v=Z4WHOSF2Ktg
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 OSTM
http://www.youtube.com/watch?v=cf0loVEs_lo
Topex/Poseidon launched with Ariane rocket
http://sealevel.jpl.nasa.gov/gallery/tiffs/videos/launch.mov
Pegasus vehicle aircraft launch
http://www.youtube.com/watch?v=QRHiTvRHHd8
OSTM / Jason-2 Boost Profile
Space craft separation:
http://www.youtube.com/watch?v=1aBpcCVljt4
Hohmann Transfer
Maneuver to different inclination
http://en.wikipedia.org/wiki/Hohmann_transfer
http://www.nytimes.com/2007/02/06/science/space/06orbi.html?emc=eta1
On Jan 11, 2007, China tested an
antisatellite rocket. The initial collision
added 800 to 1000 pieces of space junk
to the current total of detectable objects.
How many detectable objects (> 4
inches) are in orbit?
Collisions between existing debris
generate additional pieces of debris.
There is concern that eventually a chain
reaction will ensue (the Kessler
syndrome) littering the low earth orbit
(LEO) with debris making it almost
impenetrable to new satellite launches for
fear of collision.
http://www.nytimes.com/2007/02/06/science/20070206_ORBIT_GRAPHIC.html
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.
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
ENVISAT
35-day repeat
Equatorial separation of
Jason groundtracks is 315 km
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 = 29.93 hours
solar
sidereal
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.html
Shows 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.com
Shows 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