1. Remote sensing platforms

3. Remote sensing platforms
launch
1972, Landsat MSS, TM, ETM+
1999, NASA flagship satellite “Terra” with 5 state-of-the-art sensors for studying the Earth’s atmosphere, land, ocean, life, and radiation
1999, the first high-resolution commercial satellite IKONOS
Ground-based
Airplane-based
Satellite-based

11. Orbits Sun-synchronous polar orbits Non-Sun-synchronous orbits
Most earth imaging satellites is polar-orbiting, meaning that they circle the planet in a roughly north-south ellipse while the earth revolves beneath them. Therefore, unless the satellite has some sort of "pointing" capability, there are only certain times when a particular place on the ground will be imaged
global coverage, fixed crossing, repeat sampling
typical altitude 500-1,500 km
example: Terra/Aqua, Landsat
Non-Sun-synchronous orbits
Tropics, mid-latitudes, or high latitude coverage, varying sampling
typical altitude 200-2,000 km
example: TRMM, ICESat
Geostationary orbits
regional coverage, continuous sampling
over low-middle latitudes, altitude 35,000 km
example: GOES.

12. Orbital Mechanics
Imagine planet without topography save for one very tall mountain… with a gun on it.
Fire gun, cannonball shoots out on ballistic arc:
Horizontal motion due to muzzle velocity.
Vertical motion due to gravity.
Faster horizontal motion -> cannonball travels farther before hitting ground.
Enough horizontal motion -> cannonball will “fall around world”, missing ground each time (orbit).

17. Orbital Mechanics
A spacecraft's periapsis altitude can be raised by increasing the spacecraft's energy at apoapsis. This can be accomplished by firing on-board rocket thrusters when at apoapsis.
A spacecraft's apoapsis altitude can be raised by increasing the spacecraft's energy at periapsis. This can be accomplished by firing on-board rocket thrusters when at periapsis.

18. Conic Sections
Ellipse: closed plane curve with property that sum of distances from two fixed points (foci) is constant.
Intersection of circular cone and plane cutting it.
Ellipses have (semi-)major and (semi-)minor axes.
Ellipse shape is determined by spacing of foci divided by major axis = eccentricity (e).
Circle is ellipse with e = 0

22. Kepler’s Laws
If two bodies interact gravitationally, each will describe an orbit that is a conic section about common mass of pair. (Shape)
A line joining two such bodies will sweep out equal areas in orbital plane in equal intervals of time. (Velocity)
For two such bodies, the sum of their masses times the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. (Orbital Parameters)

25. Ellpitical Orbit

26. 12 hour orbit (a = 26,000 km)
Molniya orbit
Note loitering over Europe and N. America

31. Orbital Mechanics
Newton’s 1st law describes how, once in motion, a body will remain in motion unless acted upon by an outside force.
Newton’s 2nd law describes how an orbit will be a circular path if there is an acceleration towards the center of the path e.g. gravity (leading to centripetal acceleration).

35. Circular Orbit

36. Circular Orbit

37. Circular Orbit

39. Circular Orbit For earth… … then for h = 570 km… gs = 9.81 m s-2
R = 6380 km
… then for h = 570 km…
v = 7.6 km s-1
T = 1 hr 36 min
Spacecraft will orbit 15 times per day

42. Orbital Mechanics
Geosynchronous orbit: special case of circular orbit where T = sideral day (rotation wrt vernal point).
For T = 86,164 sec, r = 42,180 km (or altitude of 35,800 km)

44. Figure “8” between latitude range +/- I
Geosynchronous Orbit

47. Geostationary Orbit

48. For I = 0 (equatorial orbit), satellite appears stationary over single point.
Geostationary Orbit

49. High Inclination Orbits
Polar orbits have I = 90

50. Orbital Mechanics
Orientation of orbit in space specified by relation to Earth’s equatorial plane and the vernal equinox.
Angle between orbit plane and Earth’s equatorial plane is the inclination (I).
Angle between vernal equinox and the node line is the orbital node longitude ().
Orbit variation largely due to precession e.g. rotation of orbit plane around polar axis because Earth is not perfectly round…

52. J2 =
(2nd zonal harmonic of geopotential

54. Sun-Synchronous Orbits
Terra (the spacecraft carrying ASTER) and most other remote sensing satellites are in sun-synchronous orbits.
These orbits are designed such to cross the equator at the same local time each day. They maintain a constant relationship between the orbital plane of the spacecraft, the Earth, and the Sun.
Orbit precession exactly compensates for Earth’s rotation around sun.
Constant node-to-sun angle.
Satellite passes over certain area at same time of day every time.
Terra’s orbit crosses the equator at 10:30am (local) and passes over the same point every 16 days.

57. Sun-Synchronous Orbit
I = 98 for Landsat altitude of 700 km
Note: these orbits require I > 90

59. Orbital Coverage
Nadir trace is ground track of point directly below satellite.
Governed by combined motion of spacecraft and planet.
If planet does not rotate, nadir trace will be a sine wave on a map between latitudes of +/- I.
If planet does rotate, there will be steady crrep of trace at rate proportional to ratio of orbital motion and planet rotation…

60. S = orbit step
(longitudinal difference between two successive equator crossings
Satellite makes L revolutions as planet makes N revolutions…
N = orbit repeat period.
L = revolutions per cycle.
N = 1 (exact daily repeat)
N = 2 (repeat every other day)
etc..

64. Landsat passes overhead at intervals of ~ 2 weeks

65. Orbits

66. FOV = 178 km Drifting coverage: Orbits on successive days
overlap allowing mapping of
contiguous strips
(e.g. 542 and 867 km)
Dispersed coverage:
Second day is about halfway
in the orbital step (e.g. 700 km)
Semi-drifting coverage:
Every 5 days orbit drifts
through whole orbital step
leaving gaps to be filled
later on (e.g. 824 km)

67. Orbit Selection

68. Common for planetary missions to accommodate wide range of objectives
Elliptical Orbits
Common for planetary missions to accommodate wide range of objectives
Imagers need low altitude
Global observations need high altitude
Low energy requirement to capture into elliptical orbit vs. circularization.

70. Planets orbit the Sun in ellipses
Kepler’s Law # 1
Planets orbit the Sun in ellipses
with Sun at one focus
circle ellipse x
focus x
Copernicus’s model of Earth orbiting the sun required circles, but Kepler couldn’t find any mathematical solution that used circles to predict motions
Ellipses were the key!

71. Conic Sections
Ellipse: closed plane curve with property that sum of distances from two fixed points (foci) is constant.
Intersection of circular cone and plane cutting it.
Ellipses have (semi-)major and (semi-)minor axes.
Ellipse shape is determined by spacing of foci divided by major axis = eccentricity (e).
Circle is ellipse with e = 0

76. Eccentricity and Elliptical Orbits
Position of a planet in its orbit is described by its distance from the Sun (r) and its angular distance around its orbit (h; true anomaly). For every h, the planet will lie a distance r from the Sun.
h is measured counterclockwise looking down from north

81. Kepler’s Law # 2 A line joining a planet to the Sun
sweeps out equal areas in equal times
as the planet travels around the ellipse
C D
close to sun
A B
far from sun
Kepler observed that planets moved faster when there were nearest the sun -- needed a theory to explain this
Rule - when orbit takes the planet closes to the sun, it travels the faster.
travels slowest
travels fastest
time to go from C D = time to go from A B

85. Kepler’s Law #2
fast
speed
slow
speed
equal area, equal times

86. Elliptical Orbits and Mean Motion
For nearly circular orbits change in r is negligible and r -> a. Also e -> 1 so square root term -> 1. Can simplify to find average orbital velocity (mean motion; n):

87. Kepler’s Law # 3 P2 ~ a3 orbital period orbital radius
P = orbital period (years), time to complete 1 orbit
a = orbital radius (AU, astronmomical unit)
*note: 1 AU is distance from Earth to Sun, 1.5x108 km
like lanes on a race track
Relates the distance an object is with how long it takes to make one full revolution.
Orbital period (P) is proportional to the orbital radius of the planet, period is measured in years, radius in AU, or astronomical units
The longer a planet takes to complete one orbit, the farther it is located from the central body its orbiting.
Think of this like runners on a race track -- the inside lanes are closest to the center (small a), and so runners in that track take less time.
Runners in the far outside lane take longer because they are farther out.

88. Elliptical Orbits, Orbital Period, and Mean Distance
P = period
a = semimajor axis
M1 = mass of Sun (dominant)
M2 = mass of planet (negligible)
G = gravitational constant
There is a linear relationship between the square of the period and the cube of the semimajor axis…

90. Newton’s Laws Describe classical mechanics
If a body is not accelerated, then its velocity stays constant. Inertia
The acceleration that a body experiences is equal to the force acting on it, divided by the body’s mass.
F = ma
If one body exerts a force on another, then the second must also be exerting a force on the first, but in the opposite direction. Equal and opposite
Description of gravitation (underlies Kepler’s Laws)

91. Newtonian Gravitation
FG = force of gravity
G = gravitational constant
M1, M2 = masses
r = distance between masses
Gravity is a “central force” e.g. it is directed towards the body being orbited.
Gravity gets larger as the mass of the body being orbited gets larger.
Gravity gets smaller as the distance increases. Inverse square law.

92. Orbital Mechanics
Newton’s 1st law describes how, once in motion, a body will remain in motion unless acted upon by an outside force.
Newton’s 2nd law describes how an orbit will be a circular path if there is an acceleration towards the center of the path e.g. gravity (leading to centripetal acceleration).

95. Orbital Mechanics
Imagine planet without topography save for one very tall mountain… with a gun on it.
Fire gun, cannonball shoots out on ballistic arc:
Horizontal motion due to muzzle velocity.
Vertical motion due to gravity.
Faster horizontal motion -> cannonball travels farther before hitting ground.
Enough horizontal motion -> cannonball will “fall around world”, missing ground each time (orbit).

99. Orbital Mechanics
A spacecraft's periapsis altitude can be raised by increasing the spacecraft's energy at apoapsis. This can be accomplished by firing on-board rocket thrusters when at apoapsis.
A spacecraft's apoapsis altitude can be raised by increasing the spacecraft's energy at periapsis. This can be accomplished by firing on-board rocket thrusters when at periapsis.

101. Circular Orbit

103. Orbital Mechanics
Geosynchronous orbit: special case of circular orbit where T = day
For T = 86,164 sec, h = 42,180 km (or altitude of 35,800 km)

104. For I = 0 (equatorial orbit), satellite appears stationary over single point.
Geostationary Orbit

106. Launching Spacecraft When a spacecraft is launched it must
have enough speed to overcome gravity
• Universal Law of Gravitation: Fg ~ M/R2
Fg ~ M Fg ~ 1/R2 M R V
Vesc = escape velocity
• The more massive a planet is (M),
the stronger gravity field (Fg) it will have
• The further a spacecraft is from a planet (R),
the weaker the gravity field (Fg) it will feel
Need high enough velocity (v)
to escape Earth’s gravity field
ESCAPE VELOCITY

107. Escape Velocity ve = escape velocity G = gravitational constant
M = mass of body
r = distance
Speed at at which the kinetic energy plus the gravitational potential energy of an object is zero. Therefore it is the speed needed for a body to break free of a gravitational field without further propulsion. Only applies to ballistic trajectories, not propulsive flight.

108. Energy of Orbits

109. Energy of Orbits
Total energy of a closed orbit is negative. At escape velocity, the total energy is zero. Total energy is always a constant.
Energy per unit mass of an orbiting body only depends on M (mass of parent body), r (distance from parent body), and a (size of orbit). It does not depend on m or the shape of the orbit.

111. Circular orbit and extremely eccentric orbit with the same semimajor axis (a) will have the same energy.

112. Most efficient way of transferring from one orbit to another.
If old and new orbits are circular, transfer orbit will have pericenter equal to semimajor axis of lower orbit and apocenter equal to semimajor axis of higher orbit. Semimajor axis for transfer is average of semimajor axes of two circular orbits.
Takes half a Hohmann orbit to do the transfer.

113. Speed of an orbit decreases as energy is added (higher orbits have lower velocity).
To move ahead of another spacecraft, you must lose energy.
To move behind another spacecraft, you must gain energy.

114. Normal perturbations change orbital inclination and cause precession

115. Transverse perturbations change orbital energy and therefore a and eccentricity.
Spacecraft will return to the point where perturbation applied.

116. Radial perturbation will change eccentricity and can change orbital velocity.