Semi-major axis, vs aphelion, vs mean orbital distance?

The website Swinburne University of Technology (AU) gives the definition of semi-major axis as: ...half of the longest diameter of an ellipse.This website give the definition of semi-major axis as: Half of the major axis is called the semi-major axis, and the semi-major axis is also the average sun-planet distance.But the average sun-planet distance should be the average of the semi-major and semi-minor axes. I've also seen the mean orbital distance described as the semi-major axis in many other places, not just the one cited, so that seems t...Read more

orbital elements - Why is it impossible to estimate the inclination of an exoplanet with the Radial Velocity Method?

The formula of the radial velocity is:$$v_i= V - K(\sin(f_i+\omega)\ + e\sin\omega),$$ with$$K = \frac{m_p}{m_s+m_p}\frac{na\sin i}{\sqrt{1-e^2}}.$$Being $V$the systematic velocity of the system,$m_p$ the mass of the planet, $m_s$ the mass of the star, $n = \frac{2\pi}{P}$ the mean motion and $P$ is orbital period of planet, $a$ the length of the semi-major axis of the planet, $i$ the inclination of the orbital plane with the ecliptic,$e$ the eccentricity of the planet, $f_i$ the true anomaly at time $t_i$ and $\omega$ the longitude of periastr...Read more

orbital elements - Where to look for historical or reconstructed orbit data for early NASA missions - Mercury-Atlas 6 for example

After reading this answer I decided that for my own use I'd like to plot the orbit of Mercury-Atlas 6, the spacecraft piloted by John Glenn on February 20, 1962. This thorough answer lists fourteen (14) ground stations plus two additional radar tracking stations for telemetry and/or voice communication, spread out - roughly along the general path that the spacecraft wold follow.Wikipedia lists some parameters for an elliptical orbit in geocentric (inertial) coordinates. From these I should be able to find an ellipse whose ground track comes clo...Read more

orbital elements - different ways to calculate satellite height

I found 2 formulas for calculating height. First is:height = magnitude(satillate_position_vector) - Earth_radiusSecond is:height = Semimajor_axis * (1 - eccentricity) - Earth_radiusWhich of them is correct for calculation? And if them both correct then which of these formulas is used for. Because results are different even if I use satillate_position_vector for calculating orbital elements like Semimajor_axis and eccentricity....Read more

orbital elements - Generating JPL HORIZONS parameters for use with JPL HORIZONS itself

I want to be able to calculate RA/Dec for a given body with JPL HORIZONS, using a heliocentric specification of the orbital elements for a small solar system body (say, Apophis), but instead of using the name of the body, using its parameters. I cannot find exactly what is the expected input.Furthermore, I want to be able to use JPL HORIZONS to generate those orbital elements, in the right format, for a known body (say, again, Apophis), so that it is clear what to provide for any other case.Hope that makes sense…...Read more

orbital elements - Is it possible to plot the ground track of a satellite with just azimuth & elevation angles without range?

I came across this question on StackOverflow about Satellite Trajectory plot. In the code mentioned in the question, the user takes only the Azimuth & Elevation angles (radians) & converts them into cartesian (x, y) coordinates & plots the Satellite trajectory onto a polar plot. However, to convert from Spherical to Cartesian coordinates, one needs Range, Azimuth & Elevation. But the formula used in the code is$$ x = \frac{(\pi/2) - Elevation} {(\pi/2)*cos(Azimuth - (\pi/2))} $$$$ y = \frac{Elevation - (\pi/2)} {(\pi/2)*sin(A...Read more

orbital elements - How are military satellites with (apparently) classified TLEs still showing up on sat map websites?

As I first noted in this comment I couldn't get TLEs for the recently launched OFEQ-11 spy satellites from When I looked at Search Resuls: OFEQ 11 Satellite details 2016-056A NORAD 41759 - I got a map that showed it over it's "target area." At the bottom of the page it lists what appear to be Two Line Elements, and if I plug them into SkyField using Tel Aviv coordinates, indeed those TLEs put OFEQ-11 above the horizon at the same time.n2yo:But the link where n2yo says it's getting the data is now empty http://nssdc.gsf...Read more

orbital elements - Why is the sidereal period of the Earth 362.392667 days?

Using JPL's Horizons API I can look at the orbital elements for the EM Barycenter wrt the Solar System Barycenter at J2000. The output looks like this:Watch for the PR (Sidereal orbit period) underlined in red. It is supposed to be 362.392667 days, but the sidereal year is supposed to be only about 20 minutes longer than the ~365 day tropical year.What's going on?EDIT: Mercury's page (below) is even more confusing. Even though the system is supposed to be simpler (no satellites), the same page shows 87.969257 days for the sidereal period on the...Read more

orbital elements - Why is argument of periapsis defined in terms of longitude of ascending node?

According to the Keplerian system of orbital elements, a reference direction is given; the longitude of the ascending node is an angle with respect to that direction, and the argument of periapsis, specifying the orientation of the axes of the ellipse, is given relative to the LAN.For a low-inclination, high-eccentricity orbit, the longitude of ascending node may be very uncertain (becoming undefined in the purely theoretical zero-inclination case) even though the orientation of the ellipse as projected to the reference plane is clear.Why is th...Read more

orbital elements - TA of the intersection of 2 orbits with different AoP

Two orbits are given with the same orbital elements, except the argument of perigee (AoP). How to calculate the true anomaly (TA) of the intersection of the orbits?Currently, I calculate it numerically, going through the [0,360] interval. DefinitionsAoP is the angle from the ascending node to the periapsis. TA is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse....Read more

orbital elements - How to obtain the initial positions and velocities of an inclined orbit?

I have (x,y,z) initial positions and (vx,vy,vz) initial velocities in a coplanar orbit with respect to the reference frame. If I change the inclination of this orbit with the angle i, how I can calculate the new (X,Y,Z) and (VX,VY,VZ) without having argument of periapsis and Longitude of ascending node (the calculation for new (X,Y,Z) is here: but it needs both argument of periapsis and Longitude of ascending node)....Read more