Long ago, people thought the Earth was flat. Many believed that you could sail to the edge of the Earth and fall off. We have long since dismissed this idea as we now know the Earth is a sphere. Right?

1. Lunar Synchronous Orbit
2. Synchronous Orbit Definition
3. Synchronous Orbit Calculation
4. Synchronous Orbit Elevation

Actually, the Earth really isn't a sphere - it is an oblate spheroid. Because of the rotation of the Earth on its axis, centrifugal force bulges the equator. In fact, the radius at the Earth's equator is about 21 km larger than the radius at the poles. See the below diagram to understand what we're talking about:

Oblate Earth

While a high inclination Sun-synchronous orbit around the Earth can always keep the Sun in view by slowly precessing around the Earth (once per year), there is no solution that could precess once per lunar month of about 27.3 days. Other articles where Synchronous orbit is discussed: celestial mechanics: Examples of perturbations:, geostationary satellites, which orbit synchronously with Earth’s rotation) are destabilized by this deviation except at two longitudes. If the axial asymmetry is represented by a slightly elliptical Equator, the difference between the major and minor axis of the ellipse is about 64 metres.

Now that we understand that our Earth is really more oblate than spherical, we need to ask ourselves some questions. How does this affect our orbits? There is a perturbing force based on this oblate Earth called 'J2 Perturbations.' But where does the term 'J2' come from? The term J2 comes from an infinite series mathematical equation that describes the perturbational effects of oblation on the gravity of a planet. The coefficients of each term in this series is described as Jk, of which J2, J3, and J4 are called 'zonal coefficients.' However, J2 is over 1000 times larger than the rest and has the strongest perturbing factor on orbits.

The two main orbital elements affected by J2 Perturbations are the Right Ascension of the Ascending Node (Ω) and the Argument of Perigee (ω). If we were to model the Earth as a perfect sphere with a uniform gravitational field, the RAAN and argument of perigee would not change. But since our Earth is not really a perfect sphere, it is important that we account for this perturbation.

J2 perturbations will move the RAAN over time at a constant rate depending on the orbit's size, shape, and inclination. Using this property of J2 perturbations, we can manipulate our orbit so that the RAAN changes at a rate of 360 degrees per year, keeping the orbit in the same orientation with respect to the Sun. This is called a 'Sun-Synchronous Orbit'. However, if we did not account for J2, would have the red orbit in the picture below:

Sun-Synchronous Orbit vs Non Sun-Synchronous Orbit

The green orbit on the other hand, does account for J2 and keeps the same orientation with respect to the Sun. The reason this is possible is because the orbit is designed to have the RAAN change 360 degrees per year. The formula for the change of RAAN over time is the formula below:

In this section, we will discuss: Razer orbweaver chroma profiles.

1.Calculating a Sun-Synchronous Orbit

2.Modeling a Sun-Synchronous Orbit

Calculating a Sun-Synchronous Orbit

First, we need to calculate exactly what the nodal precession rate is. We know it needs to be 360 degrees per year, but we need to convert it to radians per seconds.

360 deg/year = 0.98562625 deg/day = 11.4077116e-6 deg/s
11.4077116e-6 deg/s = 0.19910213e-6 rad/s

Next, we need to take the formula given above and solve for the inclination. When we do that, we get this formula:

This formula looks rather complex. However, we have all of the necessary variables so let's plug in our variables and calculate the result.

a = 7000 km

e = 0

dΩ/dt = 0.19910213e-6 rad/s

J2 = 1.08262668e-3

RE = 6378.1363 km

μE= 398600.442 km^3/s^2

i = 1.7082196041 rad = 97.87377 deg

Modeling a Sun-Synchronous Orbit

Let's model the orbit whose inclination we just calculated in FreeFlyer. For demonstration purposes, we will add in a Spacecraft identical to the Sun-Synchronous Spacecraft we've calculated, but simplify the force model to a point mass and see if there is any nodal precession.

•Open a new Mission Plan and save it as 'J2Perturbation.MissionPlan'

Adding in Spacecraft

•Create a new Spacecraft with the following Keplerian elements:

oA: 7000 km

oE: 0

oI: 97.87377 deg

oRAAN: 100 deg

oW: 0 deg

oTA: 0 deg

•To speed up simulation time, we will change the propagator. Go to the 'Propagator' section on the left-hand side of the Spacecraft object editor

•Change the Integrator Type to 'Bulirsch-Stoer VOP'

•Make sure the step mode is set to 'Variable Step Size'

Propagator Settings in the Spacecraft Editor

•Click 'Ok' to close the editor

•Right-click 'Spacecraft1' and click 'Clone'

•Open the newly cloned Spacecraft

•Rename it to 'Spacecraft2'

•Go into 'Force Model' on the left-hand side

•Change the 'Field Type' to 'Point Mass'

Force Model Settings in the Spacecraft Editor

•Press 'Ok' to close the editor

Adding a PlotWindow

•Create a PlotWindow through the object browser

•Double-click 'PlotWindow1' to open the editor

•Change the y-axis to 'Spacecraft1.RAAN'

Lunar Synchronous Orbit

•Click 'More' to add another line to the plot

•Change the new dropdown to 'Spacecraft2.RAAN'

•Click 'Ok' to close the editor

Building the Mission Sequence

•Drag and drop a 'While..End' loop onto the Mission Sequence

•Change the argument inside the while loop to '(Spacecraft1.ElapsedTime < TIMESPAN(500 days))

•Drag and drop a FreeForm script editor inside the loop

•Change the name of the FreeForm to 'Step and Update'

In this script, we will be stepping both Spacecraft with an epoch sync and updating the plot window. To do this, we write:

Audacity adobe. Your Mission Sequence should look something like this:

Mission Sequence Example

Save and run your Mission Plan, then try and answer these questions:

Look at the RAAN for Spacecraft1. The output should be like a saw wave. What is the period of this plot?

Did Spacecraft2's RAAN change? Games that dont workfree wii games. Why or why not?

See Also

•Interplanetary Topics

•Next Topic: Atmospheric Modeling

•Previous Topic: Multi-Body Effects

A synchronous orbit is an orbit in which an orbiting body (usually a satellite) has a period equal to the average rotational period of the body being orbited (usually a planet), and in the same direction of rotation as that body.^[1]

Contents

Simplified meaning

A synchronousorbit is an orbit in which the orbiting object (for example, an artificial satellite or a moon) takes the same amount of time to complete an orbit as it takes the object it is orbiting to rotate once.

Properties

A satellite in a synchronous orbit that is both equatorial and circular will appear to be suspended motionless above a point on the orbited planet's equator. For synchronous satellites orbiting Earth, this is also known as a geostationary orbit. However, a synchronous orbit need not be equatorial; nor circular. A body in a non-equatorial synchronous orbit will appear to oscillate north and south above a point on the planet's equator, whereas a body in an elliptical orbit will appear to oscillate eastward and westward. As seen from the orbited body the combination of these two motions produces a figure-8 pattern called an analemma.

Nomenclature

There are many specialized terms for synchronous orbits depending on the body orbited. The following are some of the more common ones. A synchronous orbit around Earth that is circular and lies in the equatorial plane is called a geostationary orbit. The more general case, when the orbit is inclined to Earth's equator or is non-circular is called a geosynchronous orbit. The corresponding terms for synchronous orbits around Mars are areostationary and areosynchronous orbits. ^{[citation needed]}

Formula

For a stationary synchronous orbit:

${\displaystyle R_{syn}=\sqrt[3]{\frac{G(m_2)T^2}{4{\pi }^2}}}$^[2]

G = Gravitational constant

m₂ = Mass of the celestial body

T = rotational period of the body

By this formula one can find the stationary orbit of an object in relation to a given body.

Orbital speed (how fast a satellite is moving through space) is calculated by multiplying the angular speed of the satellite by the orbital radius:^{[citation needed]}

Examples

An astronomical example is Pluto's largest moon Charon.^[3] Much more commonly, synchronous orbits are employed by artificial satellites used for communication, such as geostationary satellites.

For natural satellites, which can attain a synchronous orbit only by tidally locking their parent body, it always goes in hand with synchronous rotation of the satellite. This is because the smaller body becomes tidally locked faster, and by the time a synchronous orbit is achieved, it has had a locked synchronous rotation for a long time already.^{[citation needed]}

See also

• Tidal locking (synchronous rotation)

Related Research Articles

A geosynchronous orbit is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds. The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km (22,236 mi), and all geosynchronous orbits share that semi-major axis.

A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 kilometres above Earth's equator and following the direction of Earth's rotation.

A low Earth orbit (LEO) is an Earth-centered orbit with an altitude of 2,000 km (1,200 mi) or less, or with at least 11.25 periods per day and an eccentricity less than 0.25. Most of the manmade objects in outer space are in LEO.

Charon, also known as (134340) Pluto I, is the largest of the five known natural satellites of the dwarf planet Pluto. It has a mean radius of 606 km (377 mi). Charon is the sixth-largest trans-Neptunian object after Pluto, Eris, Haumea, Makemake and Gonggong. It was discovered in 1978 at the United States Naval Observatory in Washington, D.C., using photographic plates taken at the United States Naval Observatory Flagstaff Station (NOFS).

A natural satellite, or moon, is, in the most common usage, an astronomical body that orbits a planet or minor planet.

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

Tidal locking, in the best-known case, occurs when an orbiting astronomical body always has the same face toward the object it is orbiting. This is known as synchronous rotation: the tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon.

An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

A geocentric orbit or Earth orbit involves any object orbiting the Earth, such as the Moon or artificial satellites. In 1997 NASA estimated there were approximately 2,465 artificial satellite payloads orbiting the Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. Over 16,291 previously launched objects have decayed into the Earth's atmosphere.

A Sun-synchronous orbit is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time. More technically, it is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun.

Synchronous Orbit Definition

An areostationary orbit or areosynchronous equatorial orbit is a circular areo­synchronous orbit in the Martian equatorial plane about 17,032 km (10,583 mi) above the surface, any point on which revolves about Mars in the same direction and with the same period as the Martian surface. Areo­stationary orbit is a concept similar to Earth's geo­stationary orbit. The prefix areo- derives from Ares, the ancient Greek god of war and counterpart to the Roman god Mars, with whom the planet was identified. The modern Greek word for Mars is Άρης (Áris).

Nix is a natural satellite of Pluto, with a diameter of 49.8 km (30.9 mi) across its longest dimension. It was discovered along with Pluto's outermost moon Hydra in June 2005 by the Pluto Companion Search Team. It was named after Nyx, the Greek goddess of the night. Nix is the third moon of Pluto by distance, orbiting between the moons Styx and Kerberos.

The dwarf planet Pluto has five moons down to a detection limit of about 1 km in diameter. In order of distance from Pluto, they are Charon, Styx, Nix, Kerberos, and Hydra. Charon, the largest of the five moons, is mutually tidally locked with Pluto, and is massive enough that Pluto–Charon is sometimes considered a double dwarf planet.

A near-equatorial orbit is an orbit that lies close to the equatorial plane of the object orbited. Such an orbit has an inclination near 0°. On Earth, such orbits lie on the celestial equator, the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. A geostationary orbit is a particular type of equatorial orbit, one which is geosynchronous. A satellite in a geostationary orbit appears stationary, always at the same point in the sky, to observers on the surface.

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets, as well as natural satellites and minor-planet moons.

A geosynchronous satellite is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. Such a satellite returns to the same position in the sky after each sidereal day, and over the course of a day traces out a path in the sky that is typically some form of analemma. A special case of geosynchronous satellite is the geostationary satellite, which has a geostationary orbit – a circular geosynchronous orbit directly above the Earth's equator. Another type of geosynchronous orbit used by satellites is the Tundra elliptical orbit.

Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object. It may also describe other motions such as precession or nutation of an object's rotational axis. Prograde or direct motion is more normal motion in the same direction as the primary rotates. However, 'retrograde' and 'prograde' can also refer to an object other than the primary if so described. The direction of rotation is determined by an inertial frame of reference, such as distant fixed stars.

In celestial mechanics, the term stationary orbit refers to an orbit around a planet or moon where the orbiting satellite or spacecraft remains orbiting over the same spot on the surface. From the ground, the satellite would appear to be standing still, hovering above the surface in the same spot, day after day.

This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.

References

1. ↑ Holli, Riebeek (2009-09-04). 'Catalog of Earth Satellite Orbits: Feature Articles'. earthobservatory.nasa.gov. Retrieved 2016-05-08.
2. ↑ 'Calculating the Radius of a Geostationary Orbit - Ask Will Online'. Ask Will Online. 2012-12-27. Retrieved 2017-11-21.
3. ↑ S.A. Stern (1992). 'The Pluto-Charon system'. Annual Review of Astronomy and Astrophysics. 30: 190. Bibcode:1992ARA&A.30.185S. doi:10.1146/annurev.aa.30.090192.001153. Charon's orbit is (a) synchronous with Pluto's rotation and (b) highly inclined to the plane of the ecliptic.

Synchronous Orbit Calculation

• This article incorporatespublic domain material from the General Services Administrationdocument: 'Federal Standard 1037C'.

Synchronous Orbit Elevation