Avila, Angelo G.Veras, Charmaine J.

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.

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.

“The orbit of every planet is an ellipse with the Sun at one of the two foci.”

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.

Mathematically, an ellipse can be represented by the formula:

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.

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.”

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.

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.

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    So the period    satisfies

“The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.”

Kepler's Third Law - he found that there is a universal relationship between the orbital properties of all the planets orbiting the Sun.

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.

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:

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.

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.

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.

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.

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.

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.

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.

Areocentric orbit: An orbit around the planet Mars, such as by moons or artificial satellites.

Low Earth orbit (LEO): Geocentric orbits ranging in altitude from 0–2000 km (0–1240 miles).

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.

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).

High Earth orbit (HEO): Geocentric orbits above the altitude of geosynchronous orbit 35,786 km (22,236 mi).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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 sub-satellite 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.

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.

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.)

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.

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.

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.

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.

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 medium-term 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.

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.

Involve line of sight (LOS) communication technology.

Affected greatly by environmental constraints, including rain fade.

Have very limited penetration capabilities through obstacles such as hills, buildings and trees.

Sensitive to high pollen count.

Signals can be degraded during Solar proton events.

In communications between satellites and base stations.

As backbone carriers for cellular systems.

In short range indoor communications.

Telecommunications, in linking remote and regional telephone exchanges to larger (main) exchanges without the need for copper/optical fiber lines.