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Avila, Angelo G.
Veras, Charmaine J.
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An ORBIT is the gravitationally curved path of an object around a point in
space, for example the orbit of a planet around the center of a star
system, such as the Solar System. Orbits of planets are typically elliptical.
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The basis for the modern understanding of orbits was first formulated
by Johannes Kepler whose results are summarized in his three laws of
planetary motion.
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In the early 1600s, Johannes Kepler proposed three laws of planetary
motion. Kepler was able to described the motion of planets in a suncentered solar system.
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Kepler's three laws of planetary motion
are as follows:
 The Law of Ellipses
 The Law of Equal Areas
 The Law of Harmonies
“The orbit of every planet is an ellipse with the Sun at
one of the two foci.”
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Kepler's First Law - he found that the orbits of the planets in our solar
system are elliptical, not circular as had previously been believed, and
that the Sun is not located at the center of the orbits, but rather at
one focus.
Kepler's first law placing the Sun at the focus of an elliptical orbit.
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Mathematically, an ellipse can be represented by the formula:
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where (r, θ) are polar coordinates, d is the focal parameter, and ε is
the eccentricity of the ellipse.
For a planet r is the distance from the Sun to the planet, and θ is the
angle to the planet's current position from its closest approach, as seen
from the Sun.
At θ = 0°, perihelion, the distance is minimum.
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At θ = 90° and at θ = 270°,
At θ = 180°, aphelion, the distance is maximum
“A line joining a planet and the Sun sweeps out equal
areas during equal intervals of time.”
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Kepler's Second Law - he found that the orbital speed of each planet is
not constant, but rather that the speed depends on the planet's distance
from the Sun.
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The speed at which any planet moves through space is constantly
changing. A planet moves fastest when it is closest to the sun and
slowest when it is furthest from the sun.
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In a small time the planet sweeps out a small triangle having base
line and height
and area
and so the constant areal
velocity is
The planet moves faster when it is closer to the
Sun. The area enclosed by the elliptical orbit is
period satisfies
So the
“The square of the orbital period of a planet is
directly proportional to the cube of the semi-major
axis of its orbit.”
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Kepler's Third Law - he found that there is a universal relationship
between the orbital properties of all the planets orbiting the Sun.
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Unlike Kepler's first and second laws that describe the motion
characteristics of a single planet, the third law makes a comparison
between the motion characteristics of different planets. It provides an
accurate description of the period and distance for a planet's orbits about
the sun.
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Mathematically, the law says that the expression
has the same
value for all the planets in the solar system.
The modern formulation with the constant evaluated reads:
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T the orbital period of the star
 M the mass of the star,
 G the universal gravitational constant(6.67384 × 10-11 m3 kg-1 s-2) and
 r the radius, the semi-major axis of the ellipse.
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In the full formulation under Newton's laws of motion, should be
replaced by
, where
is the mass of the orbiting body.
Consequently, the proportionality constant is not truly the same for each
planet. Nevertheless,
for all planets in our solar system such that
variations in the proportionality constant are negligible.
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1. Using the values for Kepler’s Constant in the table. Find :
A. Determine the average Kepler’s Constant for anything orbiting our sun
B. Neptune has an average orbit of 4.5e12 m from the
sun. Determine how long it takes to complete one orbit.
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2. If the orbit of Mars is 1.52 times greater than the orbit of Earth,
Determine how much time it takes Mars to complete one orbit.
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The commonly used altitude classifications of geocentric orbit are Low
Earth orbit (LEO), Medium Earth orbit (MEO) and High Earth orbit (HEO).
Low Earth orbit is any orbit below 2,000 km. Medium Earth orbit is any
orbit between 2,000km-35,786 km. High Earth orbit is any orbit higher
than 35,786 km.
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Geocentric orbit: An orbit around the planet Earth, such as the Moon
or artificial satellites. Currently there are approximately 2,465 artificial
satellites orbiting the Earth.
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Heliocentric orbit: An orbit around the Sun. In our Solar System, all
planets, comets, and asteroids are in such orbits, as are many artificial
satellites and pieces of space debris. Moons by contrast are not in a
heliocentric orbit but rather orbit their parent planet.
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Areocentric orbit: An orbit around the planet Mars, such as
by moons or artificial satellites.
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Low Earth orbit (LEO): Geocentric orbits ranging in altitude from 0–
2000 km (0–1240 miles).
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Medium Earth orbit (MEO): Geocentric orbits ranging in altitude from
2,000 km (1,200 mi)-35,786 km (22,236 mi). Also known as
an intermediate circular orbit.
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Geosynchronous Orbit (GEO): Geocentric circular orbit with an altitude
of 35,786 kilometers (22,236 mi). The period of the orbit equals
one sidereal day, coinciding with the rotation period of the Earth. The
speed is approximately 3,000 meters per second (9,800 ft/s).
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High Earth orbit (HEO): Geocentric orbits above the altitude
of geosynchronous orbit 35,786 km (22,236 mi).
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A low Earth orbit (LEO) Objects below approximately 160 kilometers
(99 mi) will experience very rapid orbital decay and altitude loss. Objects
in LEO encounter atmospheric drag in the form of gases in
the thermosphere depending on orbit height. The altitude is usually not
less than 300 km for satellites, as that would be impractical due to
atmospheric drag.
All manned space stations to date, as well as the majority of
artificial satellites, have been in LEO. The orbital velocity needed to
maintain a stable low earth orbit is about 7.8 km/s, but reduces with
increased orbital altitude.
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Remember Kepler's second law: An object in orbit about Earth moves
much faster when it is close to Earth than when it is farther away. If the
orbit is very elliptical, the satellite will spend most of its time near
apogee where it moves very slowly.
The 'highly elliptical' term refers to the shape of the ellipse, and to the
eccentricity e of the orbit, not to the high apogee altitude.
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A geosynchronous orbit is an orbit around the Earth with an orbital
period of one sidereal day, matching the Earth's sidereal rotation
period. The synchronization of rotation and orbital period means that, for
an observer on the surface of the Earth, an object in geosynchronous
orbit returns to exactly the same position in the sky after a period of one
sidereal day.
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In this case, the satellite can not be too close to the Earth because it
would not be going fast enough to counteract the pull of gravity. The
space shuttle, in order to stay aloft, must circle the planet every 90
minutes.
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Inclined orbit: An orbit whose inclination in reference to the equatorial
plane is not zero degrees.
 Polar orbit: An orbit that passes above or nearly above both poles of
the planet on each revolution. Therefore it has an inclination of (or
very close to) 90 degrees.
 Polar sun synchronous orbit: A nearly polar orbit that passes
the equator at the same local time on every pass. Useful
for image taking satellites because shadows will be nearly the same on
every pass.
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Elliptic orbit: An orbit with an eccentricity greater than 0 and less than 1
whose orbit traces the path of an ellipse.
 Geosynchronous transfer orbit: An elliptic orbit where the perigee is
at the altitude of a Low Earth orbit (LEO) and the apogee at the
altitude of a geosynchronous orbit.
 Geostationary transfer orbit: An elliptic orbit where the perigee is at
the altitude of a Low Earth orbit (LEO) and the apogee at the altitude
of a geostationary orbit.
 Molniya orbit: A highly elliptic orbit with inclination of 63.4°
and orbital period of half of a sidereal day (roughly 12 hours). Such a
satellite spends most of its time over two designated areas of
the planet (specifically Russia and the United States).
 Tundra orbit: A highly elliptic orbit with inclination of 63.4° and orbital
period of one sidereal day (roughly 24 hours). Such a satellite spends
most of its time over a single designated area of the planet.
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A satellite is an artificial object which has been intentionally placed
into orbit. Such objects are sometimes called artificial satellites to
distinguish them from natural satellites such as the Moon.
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Satellites are used for a large number of purposes. Common types
include military and civilian Earth observation satellites, communications
satellites, navigation satellites, weather satellites, and research
satellites. Space stations and human spacecraft in orbit are also
satellites.
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Satellite orbits vary greatly, depending on the purpose of the satellite,
and are classified in a number of ways. Well-known classes include low
Earth orbit, polar orbit, and geostationary orbit.
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Geostationary orbits To an observer on the earth, a satellite in a
geostationary orbit appears motionless, in a fixed position in the sky. This
is because it revolves around the earth at the earth's own angular
velocity (360 degrees every 24 hours, in an equatorial orbit).
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A geostationary orbit is useful for communications because ground
antennas can be aimed at the satellite without their having to track the
satellite's motion. This is relatively inexpensive. In applications that
require
a
large
number
of
ground
antennas,
such
as DirectTV distribution, the savings in ground equipment can more than
outweigh the cost and complexity of placing a satellite into orbit.
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Low-Earth-orbiting satellites A low Earth orbit (LEO) typically is a
circular orbit about 200 kilometres (120 mi) above the earth's surface
and, correspondingly, a period (time to revolve around the earth) of
about 90 minutes. Because of their low altitude, these satellites are only
visible from within a radius of roughly 1000 kilometers from the subsatellite point. In addition, satellites in low earth orbit change their
position relative to the ground position quickly. So even for local
applications, a large number of satellites are needed if the mission
requires uninterrupted connectivity.
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Low-Earth-orbiting satellites are less expensive to launch into orbit than
geostationary satellites and, due to proximity to the ground, do not
require as high signal strength (Recall that signal strength falls off as the
square of the distance from the source, so the effect is dramatic). Thus
there is a trade off between the number of satellites and their cost. In
addition, there are important differences in the onboard and ground
equipment needed to support the two types of missions.
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Molniya orbits can be an appealing alternative in such cases. The
Molniya orbit is highly inclined, guaranteeing good elevation over
selected positions during the northern portion of the orbit. (Elevation is
the extent of the satellite's position above the horizon. Thus, a satellite at
the horizon has zero elevation and a satellite directly overhead has
elevation of 90 degrees.)
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The Molniya orbit is designed so that the satellite spends the great
majority of its time over the far northern latitudes, during which its
ground footprint moves only slightly. Its period is one half day, so that
the satellite is available for operation over the targeted region for six to
nine hours every second revolution. In this way a constellation of three
Molniya satellites (plus in-orbit spares) can provide uninterrupted
coverage.
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Anti-Satellite weapons / "Killer Satellites" are satellites that are
designed to destroy enemy warheads, satellites, and other space assets.
Astronomical satellites are satellites used for observation of distant
planets, galaxies, and other outer space objects.
Biosatellites are satellites designed to carry living organisms, generally
for scientific experimentation.
Communications satellites are satellites stationed in space for the
purpose of telecommunications. Modern communications satellites
typically use geosynchronous orbits, Molniya orbits or Low Earth orbits.
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Miniaturized satellites are satellites of unusually low masses and small
sizes. New classifications are used to categorize these satellites:
minisatellite (500–100 kg), microsatellite (below
100 kg), nanosatellite (below 10 kg).
Navigational satellites are satellites which use radio time signals
transmitted to enable mobile receivers on the ground to determine their
exact location. The relatively clear line of sight between the satellites and
receivers on the ground, combined with ever-improving electronics,
allows satellite navigation systems to measure location to accuracies on
the order of a few meters in real time.
Reconnaissance satellites are Earth observation satellite
or communications satellite deployed
for military or intelligence applications. Very little is known about the full
power of these satellites, as governments who operate them usually
keep information pertaining to their reconnaissance satellites classified.
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Earth observation satellites are satellites intended for non-military uses
such as environmental monitoring, meteorology, map making etc.
Tether satellites are satellites which are connected to another satellite
by a thin cable called a tether.
Weather satellites are primarily used to monitor Earth's weather
and climate.
Recovery satellites are satellites that provide a recovery of
reconnaissance, biological, space-production and other payloads from
orbit to Earth.
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Manned spacecraft (spaceships) are large satellites able to
put humans into (and beyond) an orbit, and return them to Earth.
Spacecraft including space planes of reusable systems have
major propulsion or landing facilities. They can be used as transport to
and from the orbital stations.
International Space Station as seen from Space.
Space stations are man-made orbital structures that are designed
for human beings to live on in outer space. A space station is
distinguished from other manned spacecraft by its lack of major
propulsion or landing facilities. Space stations are designed for mediumterm living in orbit, for periods of weeks, months, or even years.
A Skyhook is a proposed type of tethered satellite/ion powered space
station that serves as a terminal for suborbital launch vehicles flying
between the Earth and the lower end of the Skyhook, as well as a
terminal for spacecraft going to, or arriving from, higher orbit, the Moon,
or Mars, at the upper end of the Skyhook.
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A microwave link is a communications system that uses a beam of radio
waves in the microwave frequency range to transmit video, audio,
or data between two locations, which can be from just a few feet or
meters to several miles or kilometers apart. Microwave links are
commonly used by television broadcasters to transmit programs across a
country, for instance, or from an outside broadcast back to a studio.
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Involve line of sight (LOS) communication technology.
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Affected greatly by environmental constraints, including rain fade.
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Have very limited penetration capabilities through obstacles such as hills,
buildings and trees.
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Sensitive to high pollen count.
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Signals can be degraded during Solar proton events.
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In communications between satellites and base stations.
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As backbone carriers for cellular systems.
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In short range indoor communications.
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Telecommunications, in linking remote and regional telephone
exchanges to larger (main) exchanges without the need for
copper/optical fiber lines.