Ch-02 Satellite Orbits & Trajectories2

7/29/2019 Ch-02 Satellite Orbits & Trajectories2

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Satellite Orbits & Trajectories

Chapter-2


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Satellites orbits

Satellite Orbits

GEO

LEO

MEO

HEO

HAPs

LEO 500 -1000 km

GEO 36,000 km

MEO

5,000 15,000 km


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Geostationary Earth Orbit (GEO)

These satellites are in orbit 35,863 km

Objects in Geostationary orbit revolve aroundthe earth at the same speed as the earth

rotates. This means GEO satellites remain in the same

position relative to the surface of earth.

now over 200 active commercialcommunications satellites in geostationaryorbit.


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Low Earth Orbit (LEO)

LEO satellites are much closer to the earth

than GEO satellites, ranging from 500 to 1,500

km above the surface.

LEO satellites dont stay in fixed positionrelative to the surface, and are only visible for

15 to 20 minutes each pass.

A network of LEO satellites is necessary for

LEO satellites to be useful


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LEO (cont.)

Disadvantages

A network of LEO satellites is needed, which can

be costly

LEO satellites have to compensate for Doppler

shifts cause by their relative movement.

Atmospheric drag effects LEO satellites, causing

gradual orbital deterioration.


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Medium Earth Orbit (MEO)

A MEO satellite is in orbit 8,000 km -18,000

km

MEO satellites are visible for much longerperiods of time than LEO satellites, usually

between 2 to 8 hours.

MEO satellites have a larger coverage area

than LEO satellites.

A.k.a. Intermediate Circular Orbits (ICO),


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Highly Elliptical Orbit (HEO)

Known as Molniya Orbit Satellites

Used by Russia for decades.

Molniya Orbit is an elliptical orbit. The satellite

remains in a nearly fixed position relative to earth

for eight hours.

A series of three Molniya satellites can act like a

GEO satellite. Useful in near polar regions.


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Other Orbits (cont.)

High Altitude Platform (HAP)

One of the newest ideas in satellitecommunication.

A blimp or plane around 20 km above the earthssurface is used as a satellite.

HAPs would have very small coverage area, butwould have a comparatively strong signal.

Cheaper to put in position, but would require a lotof them in a network.


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Orbiting Satellites: Basic Principles

The motion of natural and artificial satellitesaround earth is governed by two forces-

One of them is Centripetal force directed

towards the center of the Earth due togravitational force of Earth.

Other is Centrifugal force is the force exerted

during circular motion, by the moving objectupon the other object around which it is

moving.


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Here Satellite is

exertingcentrifugal force.

The force that is

causing circular

motions is

centripetal force.

These two forces

are explained

from Newtons

Law of motionand Gravitation.


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Newtons Laws of Motion

1st Law An object at rest will stay atrest, and an object in motion will stay inmotion at constant velocity, unless actedupon by an unbalanced force.

2nd Law Force equals mass timesacceleration.

3rd Law For every action there is anequal and opposite reaction.


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Newton's Law of Gravity

In the Principia, Newton defined the force ofgravity in the following way (translated from

the Latin):

Every particle of matter in the universe attractsevery other particle with a force that is directly

proportional to the product of the masses of the

particles and inversely proportional to the

square of the distance between them.


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Fg = The force of gravity (typically in newtons)

G = The gravitational constant, which adds the proper level of

proportionality to the equation. The value ofG is 6.67259 x 10-11 N * m2 / kg2, although the value will change if other units

are being used.

m1 & m1 = The masses of the two particles (typically in

kilograms) r= The straight-line distance between the two particles

(typically in meters)


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Newtonss 1st Law and You

Dont let this be you. Wear seat belts.

Because of inertia, objects (including you) resist changesin their motion. When the car going 80 km/hour is stopped

by the brick wall, your body keeps moving at 80 m/hour.


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Newtons 2nd Law

The net force of an object is

equal to the product of its mass

and acceleration, or F=ma.


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3rd Law

There are two forces

resulting from this

interaction - a force on

the chair and a force on

your body. These two

forces are called action

and reaction forces.

For every action,there is an equaland oppositereaction.


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German astronomer (1571 1630)

Spent most of his career tediouslyanalyzing huge amounts of observational

data (most compiled by Tycho Brahe) on

planetary motion (orbit periods, orbit radii, etc.)

Used his analysis to develop Laws ofplanetary motion.

Laws in the sense that they agree

with observation, but not true

theoretical laws, such as Newtons

Laws of Motion & Newtons Universal

Law of Gravitation.

Johannes Kepler


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Keplers Laws are consistent with & are obtainable fromNewtons Laws

Keplers First Law All planets move in elliptical orbits with the Sun at one

focus

Keplers Second Law The radius vector drawn from the Sun to a planet

sweeps out equal areas in equal time intervals Keplers Third Law

The square of the orbital period of any planet isproportional to the cube of the semimajor axis of theelliptical orbit

Keplers Laws


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The points F1 & F2 are each a focusof the ellipse

Located a distance c from the center Sum ofr1and r2 is constant

Longest distance through center isthe major axis, 2a

a is called the semimajor axis

Shortest distance through center isthe minor axis, 2b

b is called the semiminor axis

Math Review: Ellipses

Typical Ellipse

Theeccentricity is defined as e = (c/a) For a circle, e = 0

The range of values of the eccentricity for ellipses is 0 < e < 1

The higher the value ofe, the longer and thinner the ellipse


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The Sun is at one focus Nothing is located at the other focus

Aphelionis the point farthest away from the Sun The distance for aphelion is a + c

For an orbit around the Earth, this point is called theapogee

Perihelionis the point nearest the Sun The distance for perihelion is a c

For an orbit around the Earth, this point is called theperigee

Ellipses & Planet Orbits


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All planets move in elliptical orbits

with the Sun at one focus

A circular orbit is a special case of an elliptical orbit

The eccentricity of a circle is e = 0.

Keplers 1st Lawcan be shown (& was by Newton) to be a direct resultof the inverse square nature of the gravitational force. Comes out ofNs 2ndLaw + Ns Gravitation Law + Calculus

Elliptic (and circular) orbits are allowed for bound objects A bound object repeatedly orbits the center

An unbound object would pass by and not return These objects could have paths that are parabolas

(e = 1) and hyperbolas (e > 1)

Keplers 1st Law


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Orbital Parameters

The satellite orbit which in general is elliptical, is

characterized by a number of parameters. The following

are orbital elements and parameters.

Ascending and Descending Node

Equinoxes

Solstices

Apogee

Perigee


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Eccentricity Semi-Major Axis

Right Ascension of Ascending Node

Inclination Argument of the Perigee

True Anomaly of Satellite

Angles Defining Direction of Satellite

Orbital Parameters


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Ascending and Descending Nodes

The satellite orbit cutsthe equatorial plane at two points,

the first called the descending

node (n1), where satellite passes

From northern hemisphere to theSouthern hemisphere, and second

Called ascending node (n2), where

Satellite passes from southern to northern

Hemisphere.


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Equinox

An equinox occurs twice a year (around 20 March and 22 September), when the tilt of

the Earth's axis is inclined neither away from nor towards the Sun, the center of theSun being in the same plane as the Earth's equator. The term equinoxcan also be usedin a broader sense, meaning the date when such a passage happens. The name"equinox" is derived from the Latin aequus (equal) and nox(night), because aroundthe equinox, night and day are about equal length.


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Solstices

Solstices are the

times when theinclination angle is

at its maximum

(i.e 23.4 deg).

These also occurtwice a year on 21

June, called the

summer solstice

and21 December

called the wintersolstice.


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Apogee

Apogee is a pointon the satelliteorbit that is at thefarthest distancefrom the center ofthe Earth. The

apogee distance Acan be computedfrom the knownvalues of orbiteccentricity e and

the semi-majoraxis a as A=a(1+e)


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Perigee

Perigee is the

point on theorbit that is

nearest to the

centre of the

earth . The

perigee

distance P can

be computedby

P=a(1-e)


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The orbit eccentricity e is ratio of the distance between

the center of the ellipse and the center of the Earth tosemi-major axis of the ellipse. It can be computed by

e=

+

e=

2

e=

Where a and b are semi-major and semi-minor axes,

respectively.

Eccentricity


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Right Ascension of Ascending Node

The Right Ascension of the Ascending Node

(aW

) indicates the geocentric Right Ascension

(R.A. or a) of a satellite as it intersects the

Earth's equatorial plane traveling northward

(ascending). Its value can range anywhere

from 0 to 360 degrees.


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Inclination

A satellite orbit's Inclination (i) indicates the angle of the

satellite orbit plane measured from the Earth's equatorialplane. Inclination can range anywhere from 0 to 180 degrees.An orbit inclination of 0 to 90 degrees is called a progradeorbit. An orbit inclination of 90 to 180 degrees is called aretrograde orbit.
http://www.castor2.ca/03_Mechanics/04_Glossary/index.htmlhttp://www.castor2.ca/03_Mechanics/04_Glossary/index.htmlhttp://www.castor2.ca/03_Mechanics/04_Glossary/index.html


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Argument of the Perigee

The Argument of Perigee

(w) is defined as the anglewithin the satellite orbitplane that is measuredfrom the Ascending Node

(W) to the perigee point(p) along the satellite'sdirection of travel.

The value of the Argumentof Perigee can beanywhere from 0 to 360degrees.


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True Anomaly of Satellite

This parameter is used

to indicate the positionof the satellite in its

orbit. This is done by

defining the angle ,

called the true anomalyof the satellite, formed

by the line joining the

perigee and center of

the earth with the line

joining the satellite and

the center of the earth.


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Angles defining Direction of Satellite

The direction of the

satellite is defined bytwo angles, the first by

angle y between the

direction of the

satellite velocity vectorand its projection in

the local horizontal and

second by Angle Az,

between the north and

the projection of the

satellites velocity

vector on the local

horizontal.


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Ch-02 Satellite Orbits & Trajectories2

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