If the average distance is the distance as measured between the orbiting body and the primary focus... then how does the average depend on the angle (what, angle?, where'd that come from) you measure over?
|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
|WikiProject Physics||(Rated Start-class, Low-importance)|
Confusion or me being dumb
Forgive me, it's late, I may be missing something obvious, but it seems like the mathematical and astronomical definitions given in this article are contradictory. If the semi-major axis is half the largest diameter of the ellipse ie. the largest radius, then surely this is the same as the aphelion point of an orbit, not a sort of 'average orbital radius'? Trent 900 23:12, 9 April 2007 (UTC)
- The semi-major axis is measured from the center of the ellipse, while the aphelion and perihelion distances are measured from the focus. The foci are offset from the center of the ellipse by an amount directly proportional to the eccentricity ( i.e offset=e*a). Norbeck (talk) 08:16, 13 July 2010 (UTC)
time of year
Is it true that the earth and sun are 1 AU apart at the same two antipodal points of the calendar year? If so then when, would be a good piece of information here. MotherFunctor 17:23, 27 April 2007 (UTC)
If you ignore the precession of the equinoxes (which define the tropical year), precession of the axial tilt (which affect sidereal year) and the precession of perihelion (which affects the anomalistic year)... which I think are reasonable assumptions to make in the short term...
... then no, the distance of 1 AU is achieved at some point in time, T days into the year, and again at -T (that is, T days before the start of the year). Anomalistic year, that is (since Im using perihelion as a reference point). The same is true for any arbitrary distance you want to pick, not just 1 AU. These points T and -T are not 180 degrees apart (neither by ellipse center nor by foci) due to the fact that the orbit is not a perfect circle.
derivations instead of relations please
There are no references on how to derive these relations, neither are they derived here, only presented i.e. for ellipse a=-mu/2epsilon ... —Preceding unsigned comment added by 126.96.36.199 (talk) 13:42, 22 April 2011 (UTC)
Error in equation
Error in equation
The equation for angular momentum is incorrect.
(I will try to find a source for the correct equation, simply removing the division in the sqrt should fix it.)
This is only my second edit (prompted by trying for hours to get the wrong equation to work in my computer program) so I do not yet know how to change equations, and do not have a good source for my equation in the meantime I will add a note below the equation. — Preceding unsigned comment added by Paul Torry (talk • contribs) 00:05, 2 December 2012 (UTC)
Image thumbnail not readable
While the image itself (if you click on the link to it) is perfectly readable, the thumbnail size in this page is not. I have 0 experience with images on wikipedia - is there a good way to fix this? Like a smaller image to begin with, or an SVG instead? I may be able to do the heavy lifting if someone points me in the right direction. I've perused Wikipedia:Extended_image_syntax, which led me to the belief that increasing the thumbnail size to 2.5x is sometimes OK, and I "Be'd Bold" to make that change, but it's quite a size difference so if there's a better way, let me know. RobI (talk) 15:40, 29 April 2013 (UTC)
I don't want to come off sounding harsh, but I am rather perplexed reading these pages dealing with with orbital geometry. This particular page and specifically this section of this page comes to epitomize my disgust. Whoever is writing this stuff does not appear to come from a background of physics, astrophysics or astronomy and it makes following these pages a magnitude more difficult.
Gravitationally defined (astronomical) orbits are created by the warping of space-time by massive objects (yeah-yeah fancy talk but that is as simple as it gets), in each system the most massive of these objects are the closest object to, and typically cover one, orbital focal point (see introduction illustration; exceptions are balance binary star systems). Because of the perturbations that exist in most space (i.e three body problems) even the most perfect circular orbits become elliptical over astronomical time frames. Within systems, smaller objects periodically advance and retreat on primary focal points. When one assumes the perspective of the massive center, there are two natural positions (nodes) within these elliptical orbits. The first node, called the periapsis (Pe) , is the point of closest approach to the systems center. At this point the orbiting object is no longer advancing on or retreating away from the systems center, but Pe also has the highest orbital and angular velocities. In addition the proxi-periapsis region primarily defines the stability of the orbit, because if at periapsis the object can interact with the atmosphere (e.g. Aerobreaking as an example), liquids (e.g. moon/earth tidal effects) or terrain of the massive center, then orbit is subject to rapid change . The second apsis, Apoapsis (Ap) has opposing statistics, being furthest away and having the lowest velocities. Since Ap has the lowest kinetic energy perturbations of the Pe (e.g. Aerobraking) can have assymetrically large affects on Ap. Because of its low kinetic energy at Ap, for highly eccentric orbits the Ap is the point in an orbit where it is easiest to alter inclination (all other parameters being held equal), periapsis and eccentricity. If the Ap is near the boundary of influence of system other objects can result in ejection from the system. For these reasons stable orbits are frequently denoted by Pe, and Ap as well as period as these parameters are 'reasonably' static (for discussions of how these change see Precession). Since Pe lies along the axis from the elliptical center through the focal point (being the closest point to the primary focal point) it is at the end of the semi-major axis. Likewise Ap being furthest away is by definition closest to the secondary focal point and is on the same line through the elliptical and system center as Pe. Consequently Ap to Pe length define the longest axis (by definition the major-axis) of the orbit. Therefore it is quite natural and simple to define the major axis in terms of these two nodes.
Major-axis (2a) = rPe + rAp and semi-major axis = 2a/2
Simple enough. No need to introduce values that are defined 'behind the curtain'. The semi-major axis is simply the arithmetic mean of the radii at closest and furthest nodes from the systems gravitationally defined center. Since radii of these two apsis is generally taken as their default values the equation can be simplified.
a = (Pe + Ap)/2
This makes defining the semi-minor axis so much easier. The semi-minor axis is the geometric mean of the same two radii.
b = (Pe * Ap)0.5
This [Astronomy-section] ill-defined value for eccentricity, e, is quite simply the relative half-range of radii deviation,
e = (Ap - Pe)/major-axis
Notice that I did not need to use l, a or b to define e. latus-rectum like e definitions are often obscure to the people who examine natural orbital statistics. These values are twice removed from the most basic statistics and should be defined last. IN this case on l requires the apriori definition of a or b, and that is for solely for ascetics.
l = b2/a
it could have been written as:
l = 2 (Pe * Ap)/(Pe + Ap)
Here's is the point: either out of ignorance or sophistry the editors of these astronomy sections for geometric definitions have apparently obfuscated very simply defined orbital statistics, defacto have hidden the very simplist definitions behind parameters that often hardest to extract. Most oddly, the terms periapsis and apoapsis are not even mentioned. The same problem exists for many of the geometry pages in which gravitationally defined orbital mechanics are mentioned. I don't have the time to edit all these various pages and I'm not going to engage in edit wars with mathematical ex-spurts. So take this advise or leave it.--PB666 yap 13:52, 10 June 2014 (UTC)