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Topic: Orbit mathematics


  
  Orbits
An elliptical orbit is described by several parameters: the length of its semimajor axis, its eccentricity, its inclination, its period, the location of its nodes, and the location of its apsides.
The length of the orbit’s semimajor axis is the average distance from the planet to its primary.
The inclination of an orbit is the angle between the plane of the orbit and a reference plane.
library.thinkquest.org /29033/begin/orbits.htm   (1054 words)

  
 Hohmann Transfer
Since the point in an orbit where the engines are fired automatically becomes a point in the new orbit (or the burn point becomes the intersection of the old and new orbits), this firing must occur where the current orbit and the desired orbit intersect.
So, if the satellite is in an orbit inclined 28.5 degrees to the equator the firing must occur at one of two points during each orbit revolution where the spacecraft is directly over the equator.
Velocity in inclined orbit: 7.726 km/sec at 28.5 degrees to equator.
liftoff.msfc.nasa.gov /academy/rocket_sci/satellites/hohmann.html   (852 words)

  
 [No title]
The sizes of the orbits and the orbital speeds are all to scale, but the sizes of the Sun and planets are not.
But they model all the orbits on the orbital plane of the Earth and ignore the fact that the planes of the orbits differ from the plane of the Earth from about 1 to 3.5 degrees (except for Mercury’s orbit which deviates by 7 degrees).
The parameter i represents the angle between the plane of the orbit of the comet or asteroid and the plane of the Earth's orbit.
www.nd.edu /~learning/orbital   (1712 words)

  
 Orbits
In 1684 Wren, Hooke and Halley discussed, at the Royal Society, whether the elliptical shape of planetary orbits was a consequence of an inverse square law of force depending on the distance from the Sun.
When he computed the orbits for three comets which had appeared in 1537, 1607 and one Halley observed himself in 1682, he found that the characteristics of the orbits were almost identical.
Lagrange published further major papers in 1783 and 1784 on the theory of perturbations of orbits using methods of variations of the arbitrary constants and, in 1785, applied his theory to the orbits of Jupiter and Saturn.
www-groups.dcs.st-and.ac.uk /~history/HistTopics/Orbits.html   (4387 words)

  
 Weightlessness in Orbit
But for certain, the orbiting astronauts weigh something; that is, there is a force of gravity acting upon their body.
Many students believe that orbiting astronauts are weightless because they do not experience a force of gravity.
One might respond to this discussion by adhering to a second misconception: the astronauts are weightless because the force of gravity is reduced in space.
www.glenbrook.k12.il.us /gbssci/phys/Class/circles/u6l4d.html   (2541 words)

  
 Basic Concepts of Chaos - Chaos - IMO
The orbit of a seed is defined as the sequence of values (points on the number line) that satisfy the equation x
The lowest possible n for such an orbit is called the prime period of the orbit.
Using 5 as the seed, for example, the orbit is {5, 25, 625, 390625, 152587890625,.
library.thinkquest.org /2647/chaos/concepts.htm   (1265 words)

  
 Isaac Newton (1642 - 1727)
The moon's orbit relative to the earth is nearly a circle; and as a rough approximation, taking it to be so, he knew the distance of the moon, and therefore the length of its path; he also knew that time the moon took to go once round it, namely, a month.
This led Newton to repeat, with Picard's data, his calculations of 1666 on the lunar orbit, and he thus verified his supposition that gravity extended as far as the moon and varied inversely as the square of the distance.
This book is given up to the consideration of the motion of particles or bodies in free space either in known orbits, or under the action of known forces, or under their mutual attraction; and in particular to indicating how the effects of disturbing forces may be calculated.
www.maths.tcd.ie /pub/HistMath/People/Newton/RouseBall/RB_Newton.html   (8709 words)

  
 [No title]   (Site not responding. Last check: 2007-10-12)
Any closed path followed by a particle or body, such as the orbit of a celestial body under the influence of gravity, the elliptical path followed by electrons in the Bohr theory, or the paths followed by particles in a circular particle accelerator.
] One of the tracks on a primary body's surface traced by a satellite that orbits about it several times in a direction other than normal to the primary body's axis of rotation; each track is displaced in a direction opposite and by an amount equal to the degrees of rotation between each satellite orbit.
] The direction that the path of an orbiting body takes; in the case of an earth satellite, this path may be defined by the angle of inclination of the path to the equator.
www.accessscience.com /Dictionary/O/O10/DictO10.html   (1631 words)

  
 Orbit
For the planetary orbits you computed in the previous suggestion, you can also get an estimate of the period of the orbit if you choose to output "position vs time" or "velocity vs time" in the choice box that is the last option in the parameter window.
But for the planet to repeat the same orbit over and over again requires in addition that the velocity of the planet at the end of one orbit should be the same as its starting velocity.
One of the most remarkable things about orbits in Newtonian gravity is that planetary orbits close, which means that when the planet has gone exactly once around the central mass, it returns to the same radial distance and has the same velocity as when it started.
www.gravityfromthegroundup.org /programs/Orbit.html   (8539 words)

  
 Orbital Mechanics
) is a nondimensional parameter of the orbit.
In this case, the transfer orbit's ellipse is tangent to both the initial and final orbits at the transfer orbit's perigee and apogee respectively.
When transferring from a smaller orbit to a larger orbit, the change in velocity is applied in the direction of motion; when transferring from a larger orbit to a smaller, the change of velocity is opposite to the direction of motion.
www.braeunig.us /space/orbmech.htm   (6414 words)

  
 Description -- Mathematics and Science Initiative
It is essential to develop a new generation of citizens who have the mathematical and scientific skills to create and understand new strategies and technologies to keep America safe and prosperous.
To increase the number of new teachers with strong backgrounds in mathematics and science, the campaign will work with colleges of arts and sciences, colleges of education, teacher training programs, school districts, and states to ensure strong content knowledge in both today's and tomorrow's teachers through professional development programs known to boost student achievement.
Research will aim to: identify workforce requirements and citizenship needs related to mathematics and science, better understand student learning in mathematics and science, explain successful interventions, and develop and apply valid assessment tools to measure progress and need.
www.ed.gov /inits/mathscience/describe.html   (711 words)

  
 Basics of Space Flight Section I. The Environment of Space
To launch a spacecraft from Earth to an outer planet such as Mars using the least propellant possible, first consider that the spacecraft is already in solar orbit as it sits on the launch pad.
This existing solar orbit must be adjusted to cause it to take the spacecraft to Mars: The desired orbit's perihelion (closest approach to the sun) will be at the distance of Earth's orbit, and the aphelion (farthest distance from the sun) will be at the distance of Mars' orbit.
In a gravity-assist trajectory, angular momentum is transferred from the orbiting planet to a spacecraft approaching from behind the planet in its progress about the sun.
www2.jpl.nasa.gov /basics/bsf4-1.htm   (1848 words)

  
 Planet X, Mathematics & Astronomy
Occasionally the orbit of a Kuiper Belt object will be disturbed by the interactions of the giant planets in such a way as to cause the object to cross the orbit of Neptune.
Anderson concluded that the tenth planet must have a highly elliptical orbit, carrying it far away to be undetectable now but periodically bringing it close enough to leave its disturbing signature on the paths of the outer planets.
She also points out that these resonant orbits tend to put the objects farthest from the ecliptic at perihelion (when they are brightest) so that searches need to cover a broad band of latitudes in order to avoid a selection bias in sampling the KBO population.
www.bibliotecapleyades.net /cosmic_tree/nemesis.htm   (7979 words)

  
 Spin-Orbit Duality
We were told that the earth never set from their vantage point, due to the moon being in orbit around the earth.
If we see a planet spinning to the right, with a satellite orbiting to the left, the differential movement will be the sum of the two.
The details given here relate to all moving objects, from the orbits and spins of elementary particles via the behaviour of the gyroscope to the dynamics of the largest galaxies.
www.wehner.org /agrav   (1520 words)

  
 The Guardians.com Teachers' Area
The 16th Century scientist Johannes Kepler proved that objects orbit in an elliptical fashion, and while Kepler's laws may be introduced here, it is probably best to consider circular orbits, which are just a special case of Kepler.
Circular orbits can be used to demonstrate many of the basics of circular measure and calculation.
He originated a mathematical system, known as Eratosthenes' sieve, for determining prime numbers, and determined the inclination of the ecliptic to the celestial equator.
www.theguardians.com /space/orbitalmech/gm_em701.htm   (1077 words)

  
 Illuminations: Mars Earth Orbit - Actual
The center of the Earth's orbit is approximately the Sun; the center of Mars' orbit is about 22 million miles from the Sun.
Consequently, the orbits of the two planets are closer to one another on one side of the Sun than on the other side.
The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring mathematics learning of the highest quality for all students.
illuminations.nctm.org /ActivityDetail.aspx?ID=119   (517 words)

  
 Bowdoin: David Francis: Ask A Nerd   (Site not responding. Last check: 2007-10-12)
The elliptical nature of Earth's orbit is due entirely to the original force which tossed it away from the solar disc (now the sun).
If the momentum of this toss had been greater, the Earth's orbit would have been more highly elliptical, or it might have been tossed completely out of the solar system forever.
If it had been a slightly less violent toss, Earth's orbit might have been perfectly circular (and it really is very close to being circular) or if it had been even less violent, it might have spiraled right back into the disc and never become a planet at all.
www.bowdoin.edu /~dfrancis/askanerd/orbits   (712 words)

  
 Stick Software (Mac OS X Shareware) : Fractal Gallery (Mandelbrot Orbit Traps)
Conceptually, an orbit trap is an object that is "placed" into the same mathematical environment as the fractal itself.
Due to the nature of the mathematics, the orbit trap object is copied many times, while being scaled, rotated, and stretched in all sorts of ways.
In more mathematical terms, an orbit trap is a test that can be applied to complex numbers.
www.sticksoftware.com /gallery/mandelorbit.html   (286 words)

  
 1 Iteration
In mathematics this process is most often the application of a mathematical function.
As another example, for c = 0, the orbit of the seed 0 is quite different: this orbit remains fixed for all iterations.
and we see that this orbit tends to infinity in the complex plane (the numbers comprising the orbit recede further and further from the origin).
math.bu.edu /DYSYS/FRACGEOM/node1.html   (689 words)

  
 NASA Quest > Space Team Online   (Site not responding. Last check: 2007-10-12)
In higher orbits, spacecraft travel slower because the force of gravity is less.
In the lower orbit, the spacecraft will not only travel faster than the higher spacecraft, but the orbit has a smaller circumference as well.
The curve of the orbits resembles a sine curve.
quest.arc.nasa.gov /space/teachers/liftoff/math.html   (1378 words)

  
 Newtonian Gravitation and the Laws of Kepler
From Kepler's 1st Law the orbit is an ellipse with the Sun at one focus; from Newton's laws it can be shown that this means that the magnitude of the force must vary as one over the square of the distance between the planet and the Sun.
The orbits of some of the planets (e.g., Venus) are ellipses of such small eccentricity that they are essentially circles, and we can put artificial satellites into orbit around the Earth with circular orbits if we choose.
For a given central force, increasing the velocity causes the orbit to change from a circle to an ellipse to a parabola to a hyperbola, with the changes occurring at certain critical velocities.
csep10.phys.utk.edu /astr161/lect/history/newtonkepler.html   (874 words)

  
 Elliptic Orbits
Visualizing the orbit of the spaceship going to Mars, and remembering it is an ellipse with the sun at one focus, the smallest ellipse we can manage has the point furthest from the sun at Mars, and the point nearest to the sun at earth.
Although the elliptic orbit touching the (approximately) circular orbits of earth and Mars is the most economical orbit of getting to Mars, trips to the outer planets can get help.
In the sun’s frame, the gravitational pull on the spaceship from Jupiter was strongest as the spaceship swung behind Jupiter, and this pull accelerated the spaceship in the same direction Jupiter moves in the orbit, so the spaceship subsequently moves ahead of Jupiter, having gained enough energy to move further out in the solar system.
galileo.phys.virginia.edu /classes/152.mf1i.spring02/EllipticOrbits.htm   (1152 words)

  
 SignOnSanDiego.com > News > Science -- NASA spacecraft prepares to enter orbit around Mars
Besides the orbiting satellites, two rovers – Spirit and Opportunity – have been rolling across opposite ends of the planet since 2004 searching for evidence of ancient water.
Once in orbit, the spacecraft is expected to photograph Mars' surface for evidence of water-altered rocks and scout for future landing sites to send robotic and perhaps human explorers.
Two of the last four orbiters that flew to Mars in the past 15 years lost their signal before or during orbit insertion – a “sobering” track record, according to Fuk Li, who heads the Mars program at JPL.
www.signonsandiego.com /news/science/20060310-0953-marsorbiter.html   (620 words)

  
 Orbit - OneLook Dictionary Search
Orbit, Orbit, Orbit, Orbit, Orbit : InfoVisual Visual Dictionary [home, info]
Phrases that include Orbit: geosynchronous orbit, geostationary orbit, electron orbit, celestial orbit, hyperbolic orbit, more...
Words similar to Orbit: ambit, area, arena, compass, domain, field, orbital, orbited, orbiting, range, reach, revolve, scope, sphere, circle, encircle, eye socket, orbital cavity, path, more...
www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=Orbit   (454 words)

  
 Problems
Determine the minimum energy required to place a large (five metric ton) telecommunications satellite in a geostationary orbit.
A satellite of mass m is in orbit about the earth, which has mass M and radius R.
The satellite is initially in an elliptical orbit as shown in the diagram to the right [magnify].
hypertextbook.com /physics/mechanics/orbital-mechanics-2/problems.shtml   (427 words)

  
 EUVE Orbit Lesson Plan   (Site not responding. Last check: 2007-10-12)
An orbit is the path or trajectory traveled by one object with respect to another and, in our case, it describes the EUVE satellite's revolution about the Earth.
Then, the student may choose a time step or interval of a few minutes to a few months, plot the data for 50 or 100 time steps, and figure out if his or her parameter choices are reasonable.
Students should be able to successfully describe and draw an orbit path on a world map given at least 10 sets of coordinates.
cse.ssl.berkeley.edu /lessons/indiv/lesdel/details.html   (1581 words)

  
 Temporal Epoch Calculations by James Q. Jacobs
In previous epochs the duration of solar and lunar orbit and the apparent position of the moon and sun, for example solstice rise/set azimuths, were different than today.
Mathematics and astronomy are universal languages, accessible to analysis.
Now, at the level of science, the astronomer's chair is an ellipse on a spinning earth, and the moon is a constant foresight to the cosmos, albeit a very peripatetic one.
www.jqjacobs.net /astro/epoch_2000.html   (4871 words)

  
 Round and Round They Go
As you introduce students to the orbits of the planets around our Sun, it is important that they understand more than just the order based on distances.
The orbital path (for this exercise, assume all orbits are circular) is simply 2 times pi times r, where r is the distance from the planet to the Sun.
You can have your students investigate this concept using their string apparatus as a pendulum to see that only the length of the swing arm (not the amount of mass of the bob) affects the period of time it takes the bob to complete one swing).
starchild.gsfc.nasa.gov /docs/StarChild/teachers/orbiting.html   (1356 words)

  
 SignOnSanDiego.com > News > Science -- NASA's new Mars probe sends back first view from orbit
The crisp test image from the Mars Reconnaissance Orbiter was taken late Thursday at an altitude of 1,547 miles, the space agency said Friday, showing a 30.9-mile-by-11.7-mile area of the planet's mid-latitude southern highlands.
When the spacecraft is in its final “mapping orbit,” the spatial resolution will be nine times higher, he said.
The main purpose of initial images, however, is to calibrate the camera, which has 10 side-by-side charge-coupled devices, or optical sensors.
www.signonsandiego.com /news/science/20060325-0202-ca-marsorbiter.html   (542 words)

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