12

Your concerns are all perfectly valid - giving just a number doesn't tell a lot. So, in all proper publications, the reference system has to be mentioned. Typically, the reference is the body the spacecraft is mainly influenced by. I.e. in a Earth orbit it is the center of Earth, in lunar orbit the Moon. For interplanetary probes in transit it's usually the ...


9

Yes. This is a classical astrodynamics problem of orbit determination. The technique you would use is called Gauss' method. It allows you to determine an approximate orbit from three timed observations of azimuth and elevation. The details are well-described in the link, but are too lengthy to reasonably list here.


9

There are many different coordinate systems (X, Y, Z axes as you refer to them). The center of the Earth is often used as the origin "center" of the coordinate system, at least for calculations concerning the space in the vicinity of Earth. There are many such Earth-centered coordinate systems as well. In the Space Shuttle Program we used the "Mean of 50" ...


8

The standard for any tidally locked body, of which Europa is a member, is to have the 0 longitude be the point at the center of the planet-facing side. That being the case, the middle of the map should be the portion facing Jupiter, the edges the part that never faces Jupiter. See Wikipedia for the referenced quote below: Tidally-locked bodies have a ...


8

What you are looking for is called orbit determination, and in particular batch least squares orbit determination. To learn about it I can recommend Statistical Orbit Determination by Bob Schutz, Byron Tapley and George H. Born. I understand that you want to try to do it yourself. Nevertheless, if at some point you are looking to do it with software, it is ...


8

This is a low accuracy approximation. You can tell by the bottom row and right column of the transformation matrix. There is no allowance for precession, nutation, or polar motion in this simple model of Earth's rotation. The current angle between the Earth's rotational axis and the J2000 Z axis is currently over a tenth of a degree, and growing, thanks to ...


6

An LVLH frame is easy to construct. One construction: Let $\boldsymbol r$ and $\boldsymbol v$ denote the spacecraft's position and velocity with respect to the center of the planet as expressed in an inertial frame. Construct $\hat {\boldsymbol x}$ as the unit vector directed along the spacecraft position vector: $\hat {\boldsymbol x} = \boldsymbol r/||\...


6

The Explanatory Supplement to the Astronomical Almanac has all the equations you need. Take a look at chapters 3 and 4. Keep in mind you need some clear definitions of what you mean by ECEF and ECI. Most people utilize WGS84 for ECEF, but that is not a requirement. Similarly ECI could be J2000 or ICRF In general you will need 4 steps to convert from ECI ...


5

For the H-1 engines of Saturn I/IB, it appears that at some point in development, the origin was ...almost... at the bottom of the engines, according to this drawing I found linked from AlternateWars: That drawing shows "approximation" for the station 0/station 1 reference for the bottom of the engine bell, while another Rocketdyne document has the bottom ...


5

Galactic centre: -29.01° declination and 17.76 hours right ascension, Voyager 1 12.44° declination and 17.163 hours right ascension, missing by ~40° Voyager 2 −55.29° declination and 19.888 hours right ascension, missing by ~50° Pioneer 11 -8.80° declination and 18.83 hours right ascension, missing by ~30° Pioneer 10 25.99° declination and 5.2 hours ...


5

While this answer was written for a different question/project, it points out that the Two Line Element sets and the SGP4 propagator work together and each is designed specifically to work only with the other. The elements of a TLE are not exactly Keplerian orbital elements, even though the parameter names overlap with Keplerian element names. This is ...


5

I'm sorry, I should have included more explanatory links in what I wrote earlier. When reading what I put together below, please keep in mind that each of these paragraphs is normally an entire grad school course in mathematics. I have attempted to clarify my meaning, but if I haven't succeeded, please note that it took me several years to understand all ...


4

Here is information on an open source Java package that has code for TLE propagation: https://www.orekit.org/forge/projects/orekit/wiki/Tle It also contains classes for all the components you need to get your range/angles to the satellite. Look at the topocentric frame interfaces in the javadoc; it's got interfaces to get the azimuth/elevation/range: ...


4

Are you modeling drag? If you are not, you don't even need to model the Earth's rotation because the J2 effect depends on latitude only. This is a low fidelity simulation (there are lots of effects other than J2; e.g., drag, third body effects, higher order gravity terms, solid body and ocean tides, solar radiation pressure, relativistic gravity, ...) But ...


4

You must be using a computer from the 1960s to have even the most precise IAU earth orientation computation take "5-10 seconds". That said, computing the Earth's orientation using an extremely accurate algorithm at some epoch time and then rotating the Earth by $2\pi$ radians per sidereal day ($7.29211585275553\times10^{-5}$ radians per second) about the ...


3

Given either geocentric latitude, longitude, and radius or geodetic latitude, longitude, and altitude, the computation of Earth-centered, Earth-fixed cartesian coordinates is fairly simple. For geocentric coordinates $R,\theta,\lambda$, one uses $$ \begin{aligned} R\ &\text{is the radial distance from the center of the Earth} \\ \theta\ &\text{is ...


3

No, you would need to know the range to the satellite as well. Think of it this way - if you draw a diagram of what you describe above, the vector representing the line of sight from your ground position to the satellite (az, el) would cross a swath of longitudes, except for the trivial case where el=90


3

In section 3 of your reference, it states The EROS-A legacy pass-file contains all metadata in one file, but requires a lot of exceptional processing associated with [sic] customized coordinate system (so-called Q-frame). Satellites usually have many frames associated with different aspects of the body of the satellite. For instance, there will be at ...


3

I know this is an old question but for funsies, here's a quick script. This question was asked when the .subpoint() feature wasn't supported in Skyfield to grab the long/lat for a satellite orbit projected onto the Earth. Here's a quick script that shows how to use Skyfield's built in functions with plotting using cartopy to build the map and projections. ...


3

SOFA The IAU’s Standards of Fundamental Astronomy (SOFA) library has a ANSI C and FORTRAN version. See the documentation on the C2T06A function for converting from ECI to ECEF. note: You must look up what are called Earth Orientation Parameters (EOP) if you wish to convert ECI coordinates to ECEF. You can find them here.


3

How can Earth-Centered Inertial (ECI) coordinates be inertial if Earth's orbital motion is always accelerating? It is true that "Earth-Centered Inertial" is a bit of a misnomer. What this means is that one has to account for the fictitious acceleration that results from the acceleration of the frame of reference. Unlike the fictitious accelerations that ...


3

I believe this constitutes an answer - after acquiring a copy of the Fundamentals of Astrodynamics (1st edition), I've found that the above coordinate transformation is extremely similar to one mentioned in the book that is used for the same purpose, located on page 77: $\begin{bmatrix} \text{a}_\text{U} \\ \text{a}_\text{V} \\ \text{a}_\text{...


3

The transformation in the related question and the transformation in this question make the same low fidelity approximation, which is that precession, nutation, and polar motion can be ignored. This is probably fine for a low fidelity approximation of a satellite's orbit (e.g., two line elements). For applications where satellite position determined from two ...


3

In the Earth Centered Inertial frame (ECI, often called EME2000), a spacecraft could indeed pass through the Z-axis (formed from X=0 and Y=0). However, as with all orbital dynamics, it would not remain in that position unless there was active thrusting. It is possible for a spacecraft to stay in close proximity of the Earth's pole (north or south) with ...


3

note: based on comments below it's clear now that there are several problems, so this is currently a partial answer. I think I have it (at least partly) figured out one problem with the current plots, but there is still a bug in your analysis because Earth's analemma as defined in your link should range between +/- 23.4 degrees and yours goes from -24 to -...


3

If you want to understand how GPS works, a good first step would be to learn how LORAN worked. https://en.wikipedia.org/wiki/Loran-C In a nutshell, pairs of transmitting stations would send out synchronized radio signals, and by measuring the difference between the time of arrival of the signals from the two towers, a ship's navigator could know that they ...


2

I am not aware of any particular standard for the primary body, however for the Pluto system, in this image the 0,0 point is on the opposite side of the hearth: And in this image, the hearth is shown to also be at the opposite side from Charon. So I assume you are right.


2

I find the accepted answer unclear, so I'll try: The two maps in discussion use coordinate systems based on the convention that 0 longitude is the point directly facing Jupiter, but they have chosen to put that point on the far right-hand edge of the map. Dyfed Regio is on Europa's Trailing and Anti-Jovian hemispheres (not the Sub-Jovian). Note that the ...


2

At the bottom of your linked web page is the sentence: If you need really accurate data for a planet or asteroid, try the JPL HORIZONS System. (These guys were navigating spacecraft through the solar system when I was still playing with GI Joe!) ...which is indeed an excellent answer to your question! A step-by-step example of how to obtain "rectangular ...


2

$lon_{Sat}=f(lon, lat, ht, el, az)$ Where: $lon$ Receiver longitude $lat$ Receiver latitude $ht$ Receiver height in metres (does not have a major effect but adding for completeness) $el$ Satellite elevation in degrees $az$ Satellite azimuth in degrees $a = 6377.301243$ (Semi-Major Axis of Earth in Kilometres) $f = \frac{1}{ 298.257223563}$ (Flattening of ...


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