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Topic: Orbit equation

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  Earth's Orbit
If a plane containing an orbit crosses a reference plane, we call the points where the orbit crosses the reference plane the nodes of the orbit and the straight line passing through those points, the line on which the two planes cross each other, we call the line of nodes.
We define the nodes of the orbit with reference to the nodes of the Celestial Equator: the line of nodes of Earth's orbit consists of that straight line passing through the center of the sun that lies parallel to the straight line passing through the two points where Earth's Equator crosses the Ecliptic plane.
Equation 25, describing the path that the small body traces around the large one, also describes a conic section of eccentricity e.
www.bado-shanai.net /Astrogation/astrogEarthsorbit.htm   (1857 words)

 TeacherSource . Math . Orbiting the Earth | PBS
Perigee: for an object orbiting the earth, this is the point closest to the center of the earth.
Apogee: for an object orbiting the earth, this is the point farthest from the center of the earth.
These are circular orbits in which the time it takes to complete one orbit is the same as the 24 hours it takes the earth to complete one revolution.
www.pbs.org /teachersource/mathline/concepts/space/activity2.shtm   (568 words)

 Planetary orbit Summary
The third factor is the inclination of the orbit, or the angle between the plane of the orbit and the plane of Earth's orbit.
As an object orbits another, the periapsis is that point at which the two objects are closest to each other and the apoapsis is that point at which they are the farthest from each other.
The gravity of the orbiting object raises tidal bulges in the primary, and since below the synchronous orbit the orbiting object is moving faster than the body's surface the bulges lag a short angle behind it.
www.bookrags.com /Planetary_orbit   (4861 words)

 Orbits for Amateurs
Once Kepler understood that the orbit of Mars [and subsequently other planets] was an ellipse, mathematicians began to try to determine an equation which would describe the difference between M and the true anomaly [the actual position] ν, the position of the body on its elliptical orbit.
This is the obliquity [tilt] of the equator to the Ecliptic.
The equation of the center is the amount the Kepler's Equation adds to M to yield ν.
www.frostydrew.org /observatory/courses/orbits/booklet.htm   (9399 words)

 PHYS 510 - Assignment 4, Spring 2006
This equation can then be numerically integated to get the equation of motion for a particular orbit with a given energy E and angular momentum l.
The outgoing orbit is symmetric to the incoming orbit with respect to the turning point.
The unbounded orbit is with one extension and the bounded orbit is with 20 extensions.
complex.gmu.edu /www-phys/phys510/assignments/assign_04/assign_04.html   (985 words)

 A Detailed Classical Description of the Advance of the Perihelion of Mercury
This means that the forces acting on the mass orbiting on an ellipse, and the velocity must be compatible with the constant (radius of) curvature R of the ellipse.
Equation 32 uses the circumference of a circle equal to the perimeter of an ellipse having a small eccentricity.
Equation 81 shows that the advance of the perihelion of Mercury, calculated above with a small eccentricity is mathematically identical to equation 5.45 in section 5.10 of [1].
www.newtonphysics.on.ca /MERCURY/Mercury.html   (9400 words)

 Waves in Dark Matter   (Site not responding. Last check: 2007-09-17)
The equation also fits into a picture where the wave velocity is proportional to the reciprocal of the square root of the density of the medium, as with sound waves.
Equation (1) does not describe the locations of all the sun's planets exactly perhaps because matter was distributed around the solar system in a different manner when the satellites and planets were placed.
Equation (1) does describe the locations of Mercury and Venus exactly because the solar wind had cleared the region of the less dense matter when they were placed.
www.chatlink.com /~oedphd/plants/Darkmatter.html   (5819 words)

 Solution for timelike orbits and precession   (Site not responding. Last check: 2007-09-17)
This equation is solved by choosing a particular integral of the form [ Assignment 7 ]:
The orbit of the planet is thus only approximately an ellipse.
This is the famous perihelion precession  of planetary orbits.
www.mth.uct.ac.za /omei/gr/chap8/node10.html   (175 words)

 Earth Orbits
The circular orbit is a special case since orbits are generally ellipses, or hyperbolas in the case of objects which are merely deflected by the planet's gravity but not captured.
Setting the gravity force from the univeral law of gravity equal to the required centripetal force yields the description of the orbit.
The orbit can be expressed in terms of the acceleration of gravity at the orbit.
hyperphysics.phy-astr.gsu.edu /hbase/orbv.html   (424 words)

 [No title]
The equivalence of electromagnetic and mechanical phenomena is recognized in Bohr’s theory of atomic structure.
Our first indication is that the magnitude of the invariant velocity is equal to that of the electron in the first Bohr orbit.
If both the speed of light and the velocity in the first Bohr orbit are invariant then their ratio is also.
wbabin.net /babin/dvp.htm   (765 words)

 Aerospaceweb.org | Ask Us - Space Shuttle Speed in Orbit
The one equation that is at the heart of orbital mechanics is Newton's second law of motion.
The reason the speed is constant is because the orbiting object is always accelerating toward the center of the primary body while moving in a straight line.
Note how simple this equation is. It says that the velocity of an object in a circular orbit is proportional to nothing more than the mass of the primary body and the radius of the circular orbit.
www.aerospaceweb.org /question/spacecraft/q0164.shtml   (1074 words)

 Troubled Times: Orbit   (Site not responding. Last check: 2007-09-17)
Although the mechanics of the outgoing orbit is different than the incoming phase of the orbit, before passage of the Sun, we can still use the exponential function to explain the movement of the 12th planet out of in the inner part of the solar system.
Due to the premise, that most of the orbital variables, the repulsion and gravitational forces emanating from the Sun, the planets, and too a lesser degree the Dark One effecting the 12th planet's path as it moves around the backside of the Sun, occur after Earth passage.
The (k) rate, representing incoming acceleration in the exponential equation changes a from a positive value when the 12th planet hurtles towards the Sun, to a negative value as the combined forces of gravity from both binary stars erodes the 12th planet's forward momentum.
www.zetatalk.com /theword/tword03e.htm   (649 words)

The average inclination of the Moon's orbit to the plane of the ecliptic,
Equation for determining age of formation of rock from ratio of isotopes.
When equation (2) is satisfied, the perturbation produces a large change in the orbital properties of the object being acted on.
www-astro.physics.uiowa.edu /~srs/2961_05/Formulary/Formulary.html   (912 words)

 Dr. Dobb's | Orbit Propagation | April 15, 2003
For orbit prediction, exact expressions are available for the solutions of objects moving in two-body or Keplerian motion, which involves modeling the motion of an object being accelerated only by the gravitational force from a second object.
When you want to model the orbit motion precisely, you must use a numerical method, because orbiting objects are subject not only to the point-mass gravitational force, which produces their Keplerian motion, but also to a range of other forces that perturb or modify this motion.
The eccentric anomaly E is defined (for elliptical orbits) by circumscribing a circle around the ellipse, then dropping a perpendicular from a point p on the circle so it passes through the current position of the object on the ellipse (see Figure 4).
www.ddj.com /dept/cpp/184402360?pgno=10   (2741 words)

 Planetary orbits
Since we are only interested in the orbit's shape, we can set this quantity to zero without loss of generality.
is termed the eccentricity of the orbit, and is a measure of its departure from circularity.
107 illustrates the relationship between the aphelion distance, the perihelion distance, and the semi-major and semi-minor axes of a planetary orbit.
farside.ph.utexas.edu /teaching/301/lectures/node155.html   (693 words)

 Geosynchronous and geostationary orbits
A geostationary orbit is one where the orbit has the same period as its primary's rotation period, and remains stationary over a single point on the Earth's surface.
A geosynchronous one only has the first restriction; that is, geosynchronous orbits can be elliptical, but geostationary ones have to be circular and stationed over the equator.
Now all you have to do is find an orbit where these conditions is satisfied (all you're interested in his how high up it is).
www.alcyone.com /max/writing/essays/geostationary-orbits.html   (320 words)

 SparkNotes: Orbits: Orbits
The particle is trapped at the very bottom of a potential well, and the radius does not change as it goes around the orbit, hence forming a circle.
Note that we could have derived this directly by summing the potential energy we found for a circular orbit with the kinetic energy (Gravitational Potential Energy).
In the parabolic case the particle barely has enough energy to make it to infinity, but the hyperbolic orbit makes it with energy to spare.
www.sparknotes.com /physics/gravitation/orbits/section1.html   (633 words)

 Fundamentals of Orbital Mechanics
The square of the period of a planet's orbit is proportional to the cube of the semi-major axis of its orbit.
The total energy of a spacecraft in orbit is the sum of its kinetic energy (due to its energy of motion in its orbit) and its potential energy (due to the gravitational pull of the Sun).
From this equation we see that a circular or elliptical orbit has negative total energy, which means that the potential energy due to the Sun exceeds the kinetic energy of the spacecraft - the spacecraft is in a "bound" orbit.
www.projectrho.com /rocket/Orbits.htm   (3602 words)

 The Relativity Dilemma
There is no doubt that Einstein’s energy-velocity equation is valid and indisputable, and one of the greatest achievements in science.
The circumference of the innermost atomic orbit as determined by Louis de Broglie’s wave equation is
It is remarkable that Mach’s Principle has to be invoked in order to explain relativistic atomic orbits when Mach himself did not believe in atoms while Einstein, on the other hand, who was first to prove that atoms exist (Brownian movement and the photoelectric effect) chose to abandon Mach’s Principle.
www.wbabin.net /wahlin/wahlin.htm   (1479 words)

 Lecture 6 - Orbital Mechanics II: The Barycenter (9/29/98)
Because of Newton's third Law of reaction, if the Earth is made to orbit because of the gravitational force between the Earth and Sun, then the Sun must also orbit by the equal and opposite force.
Because the forces are equal, then the accelerations are inversely proportional to the masses, and we would expect the two bodies to each orbit a point on the line between them, but closer to the more massive body (the Sun).
The relative distances from the center of mass are inversely proportional to the respective masses.
www.aoc.nrao.edu /~smyers/courses/astro11/L6.html   (481 words)

 Elliptic orbit - Wikipedia, the free encyclopedia
Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.
In astrodynamics or celestial mechanics an elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1.
Specific energy of an elliptical orbit is negative.
en.wikipedia.org /wiki/Elliptic_orbit   (426 words)

 Space Exploration Technology: The Missing Zero in Zero Gravity
What the equation says is that the force of gravity between two objects depends on their respective masses and the distance separating them.
For the equation, the distance is expected to be in meters rather than kilometers, so we need to multiply the radius by 1000.
The only difference between this equation and the previous one is that my distance from the surface of the Earth has been increased by the amount h.
www.astrodigital.org /space/zgr.html   (1025 words)

 Apollo 13 and Vector Calculus
Using equation (1) it can be shown (see your calculus textbook) that a particle, or a relatively small object like a spacecraft, orbits the earth in a plane curve given in polar coordinates by
You may recognize this as the general equation of a conic section with eccentricity e.
It is known that the constants p and e in equation (2) are given by
www.math.iupui.edu /m261vis/A-13.html   (865 words)

 No Title
To do this, we use the circular orbit equation, or a generalization of this equation.
It is a relation between V, the speed at which the star moves, M the mass of the massive star, and R, the radius of the circular orbit.
The speed of the little star in its orbit is 283 kilometers per second.
www-astro.physics.uiowa.edu /~srs/lec12/lec12.html   (687 words)

 No Title
Obtain orbits for small energies as well as for energies large enough for the pendulum to go over the top.
Square well orbits (Related to Scheck 2.18) Solve for the orbits of a particle of mass m in a a square well potential of depth W and radius R.
What are Lagrange's equations for this system and their physical significance.
www.physics.orst.edu /~rubin/COURSES/ph621/problems/problems.html   (2638 words)

 Orbit   (Site not responding. Last check: 2007-09-17)
As the planet moves around its orbit during
motion changes from an elliptical orbit to a
orbit Lyapunov orbit Milankovitch cycles N-body problem Orbit
orbit.supercomputerconsulting.net   (72 words)

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