#### Artificial Satellite and Remote Sensing, Physics tutorial

The Orbit of the Earth:

The solar system has the given objects:

a. The sun

b. The eight planets (and the dwarfs like Pluto)

c. The satellites

d. The comets

e. The meteors

f. The interplanetary medium.

The earth is one of the eight planets in solar system. These eight planets are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. (Pluto is a dwarf). The orbit of the earth lies between orbits of Venus and Mars. To good approximation, orbit of the earth is the ellipse of small eccentricity. Elements of this orbit suffer changes because of the presence of moon and the other planets. Moon is a natural satellite of the earth. Certainly, it is the centre-of-mass of earth moon system which revolves about sun. It lies approx 1600 kilometers below surface of the earth.

Orbit of earth is very significant. For example, astrophysicists find it suitable to utilize data connected with orbit of earth to define the units of time and distance. Kepler's third law, for planet of mass m2 revolving above the sun of mass m1, defines that

k2(m1 + m2)T2 = 4π2a3

Taking solar mass, the mean solar day, and earth's mean distance from the sun as the units of mass, time and distance, respectively, the statement of this law becomes

k2(1 + m2)T2 = 4π2a3

Here, k2 is written for gravitational constant G ; m2, T and a are in units defined above. Quantity k is known as Gaussian constant of gravitation.

Satellites in Circular Orbits:

Relationship between Radius and Orbital Speed:

There are several satellites orbiting about earth. Some of the satellites move in about circular orbits. Such satellites are kept in their circular orbits by centripetal force given by gravity. To remain in circular orbit, satellite should have centripetal force F provided by

F = mv2/r

Here, m = mass of satellite

v = speed of satellite

r = radius of orbit of satellite

ME = mass of the earth.

As it is gravity alone which gives this centripetal force, it follows that F should be equivalent to gravitational force of attraction between earth and the satellite. This signifies that

F = GME/r2

When the right-hand sides of equations (1) and (2) are equated, you find that

mv2/r = GMEm/r2

Solving for v, you get

v = √GME/r

If satellite is to remain in the circular orbit of radius r, its speed should be equivalent to value of v in equation above.

Period of the Satellite:

The period T of the satellite is the time needed for satellite to move round its orbit. It is time taken for satellite to complete one orbital revolution. In all circular motions, linear velocity v and angular velocity ω are associated by expression

v = rω or, v = r(2π/T)

If substitute v from equation, we get

√GME/r = 2πr/T

Solving the expression for T, we get

T = (4π2r2/GME)1/2

T = 2π(r3/GME)1/2

Thus T = 2πr3/2/√GME

Equation given above represents Kepler's third law of planetary motion.

Synchronous satellites are very significant in field of communications. Generally, synchronous satellites are put in the circular orbit in plane of the equator. Period T is selected to be one day so that earth-based observer finds satellites at fixed positions in sky. Consequently, satellites can act as stationary relay stations for communication signals sent up from earth's surface. That is how digital satellite system works. All synchronous satellites move in their orbits with same orbital speed v.

Therefore, they should be placed at same height above surface of earth. Their orbital radius r is provided by

√GME/r = 2πr/T

Solving this expression for orbital radius r, you find that

r = [T√GME/2π]-2/3 Thus r = [T2(GME)/4π2]1/3

Remote Sensing:

Preliminary Remarks:

Remote sensing is very useful method. It allows man to obtain information about the object without making physical contact with that object. Remote sensing frequently engages use of aerial sensor methods to detect and categorize objects on different parts of earth.

As a discipline, remote sensing started as soon as humans developed flying objects. Today, artificial satellites have made it possible for discipline of remote sensing to suppose global dimension. Remote sensing makes it possible to gather data on hostile objects and unapproachable areas. For this motive, remote sensing methods may be used in making systematic aerial photographs for military surveillance and reconnaissance objectives. Also, space probes to other planets have given man with opportunity to conduct remote sensing studies in extraterrestrial environment.

Data Collection:

Orbital platforms collect and transmit data from appropriate regions of electromagnetic spectrum. By multispectral data collection method, scientists are able to reconstruct the correct image of object being observed. Satellite, aircraft, spacecraft, buoy, ship and helicopter images given data which may be examined to paint the comprehensive picture of things such as vegetation rates, erosion, pollution, forestry, weather, and land use.

Processing of Remote Sensing Data:

Data collected by remote sensing methods should be carefully and skillfully analyzed. Quantity of any remote sensing data is estimated in terms of its resolution. There are several kinds of resolution related with remote sensing data. Scientists are generally interested in spatial resolution, spectral resolution, radiometric resolution, and temporal resolution of remote sensing data.

Wavelength width (of different frequency bands recorded) gives a measure of spectral resolution. It is associated to number of frequency bands recorded by the particular orbital platform. For example, current land sat collection engages seventy bands ranging from a spectral resolution of 0.07 to 2.1μm. Many of these bands are in the infrared region of electromagnetic spectrum. Another example is hyper ion sensor on earth observing-1. This sensor resolves 220 bands from 0.4 to 2.5 μm with a spectral resolution of 0.10 μm per band.

Number of different intensities of radiation which a particular sensor is capable of distinguishing provides a measure of radiometric resolution. One of the factors affecting radiometric resolution is instrument noise. Temporal resolution is estimated by frequency of flyovers by satellite. Temporal resolution is applicable when time-series studies are needed.

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