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14

NOTE: This answer was provided for a different, very basic question which didn't specify the WGS84 ellipsoid; it's illustrative of the basic principle as applied to a spherical Earth. Still, not bad for an answer written a year and a half before the question was asked... At any latitude, the Earth completes one rotation per day. At the equator, the ...


14

Like the SSRMS itself, it's rather complicated. The "control panel" is called the Robotics Workstation (RWS). There are two of them onboard the ISS. One is in the US Lab, the other in the Cupola. An RWS consists of four main parts. 1) The Display and Control Panel, which has hardware switches for Camera routing and control Joint selection for single ...


9

There are some subtleties here. The fields where the concept of nadir are most important are nadir-pointing Earth observation satellites, satellites formation flying, and rendezvous and proximity operations. The latter two almost inevitably use some form of a local vertical / local horizontal frame (aka a Hill frame), in which vertical (i.e., nadir and ...


8

All velocities are relative. In this case, the orbital velocity is in an Earth-Centered Inertial (ECI) framework, so it's relative to a non-rotating set of axes whose orientation is fixed with respect to the stars, and with it's center at the center of the earth.


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 ...


7

Is this method correct ? Not quite. You are assuming that $\hat r$ and $\hat v$ are orthogonal. A quick check shows that this is not quite the case. The ISS's orbit is not quite circular. This means that while your $\hat y$ points in the right direction, it is not a unit vector. You can make it a unit vector by dividing by the magnitude. Then you can ...


6

According to Wikipedia's Geographic_coordinate_conversion#From_geodetic_to_ECEF_coordinates The 3D cartesian coordinates $X, Y, Z$ in Earth-centered, Earth-fixed coordinates assuming an ellipsoidal shape is given by: $$X = \left(N(\phi) + h \right) \cos\phi \cos\lambda $$ $$Y = \left(N(\phi) + h \right) \cos\phi \sin\lambda $$ $$Z = \left(\frac{b^2}{a^...


6

The problem is solved using the Skyfield and Astropy packages in python. import skyfield.sgp4lib as sgp4lib from astropy import coordinates as coord, units as u from astropy.time import Time # time- J2000 date # p,v- vectors, result of SGP4 in TEME frame date= datetime.datetime(2000, 1, 1, 12, 0) + datetime.timedelta(days=time - 2451545) # ...


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 ...


5

Looks right to me to a first approximation. One useful sanity check is that X comes out close to V (because the orbit is close to circular and thus V was already almost perpendicular to R to begin with). Another is to note that the ISS was about to cross the equatorial plane (the ITRF $z$ coordinate of R is almost zero) and moving in a direction a little ...


5

It really depends on how pedantic you want to be. In the most extreme phrasings, there is a frame centered on the earth which is inertial, sometimes marked as "Earth inertial" and there is a frame centered on the earth which is fixed to the geoid of the Earth, sometimes marked as "Earth fixed." The key attribute of frames is that, within ...


5

Going backwards, and starting with 3. In my experience the two are used interchangeably. The Wikipedia article on frame of reference implies that coordinates are the orthogonal directions, while a frame of reference has a defined origin. The AGI help reference for STK treats the two terms as interchangeable. So the answer to 1 and 2 yes, they are both ...


5

The LVLH can be realized using the position and velocity vectors in the ECI frame. Other treatments are possible, but they would involve transformation of the vectors to the right frame. Conversion from ECI seems the most straightfoward, and aligned with the definition you provide above! Assume the following notation for the LVLH axes vectors, expressed in ...


5

I have published a julia package called SatelliteToolbox.jl that has all the conversions related to IAU-76/FK5 model (ITRF, MOD, TOD, GCRF, PEF, etc.) and now I also added the support for TEME. However, you need to use the master branch because it is not released yet. To install the package from master, you can do this: Pkg.add("SatelliteToolbox") Pkg....


5

Oh, on the surface you're overcomplicating things. When you dig deeper, specifically for numerical calculations, you're just seeing the top of an iceberg. And bringing KSP up is a good example: numerical precision, especially on interplanetary scales, is a huge problem. KSP deals with many of these problems by resetting the origin of the system of ...


4

Linear speed in circular motion depends on angular velocity (here: 1 rotation per day, for all latitudes) and radius of the circle - distance from the axis of rotation. $ v = \omega r$ If $\alpha$ is your latitude, the radius of the circle you make with each revolution of Earth, is $r$. As you can see above, basic trigonometry, ${r \over R} = cos \alpha$. ...


4

In the ISS Operations community, "zenith" and "nadir" are commonly used to refer to the Z axis directions relative to the ISS, instead of specifically Earth-pointing directions. (Although they got these names because the ISS does normally fly in an attitude that points the so-called nadir direction at the earth). Here's an example from a crew procedure ...


4

It's not about the frames; you just haven't fully constrained the orbit that results from the burn. I was able to get the DVs to match using your script by just adding an inclination constraint. The partials and initial guesses and such will be different when you use a VNB frame vs EME2000.


3

In the language of the International Earth Rotation Service's Technical Note 36, a "reference system" is a mathematical definition of the relationships between the coordinates, and a "reference frame" is a physical realization of a theoretical system. For example, the ITRS (International Terrestrial Reference System) is just a set of ...


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

Skyfield, at http://rhodesmill.org/skyfield (note the similarity to the location for PyEphem, not a coincidence) does exactly what you are asking for. You give it a TLE and you get coordinates in ICRF (or a variety of other options). However, you won't get better than several kilometers from TLEs, they are simply not that accurate to begin with, nor is the ...


3

The OP's question can be restated as "Are satellite velocities stated in an ECEF (Earth Centered, Earth Fixed) frame, or an ECI (Earth Centered Inertial) frame?" As indicated by David Hammen's answer to What is the frame of reference for orbital speed?, the choice of frame of reference is somewhat arbitrary. However, partly by convention, orbital velocity ...


3

Second question first: About the difference between GCRS and ITRS: is GCRS an ECI frame, and ITRS is an ECEF frame? Correct. What is the difference between GCRS and J2000 frames? Which is commonly used worldwide in satellite communications? The difference is small. The GCRF frame is essentially the ICRF frame, but with a slightly different ...


3

I'm not a specialist, but here are my guesses: the geocentric equatorial frame makes it easier to express $\mathbf{v}_{rel}$, the spacecraft's velocity relative to the atmosphere, in terms of $\mathbf{r}$ and $\mathbf{v}$: $$\mathbf{v}_{rel} = \mathbf{v} - \boldsymbol{\omega}_E\times \mathbf{r}, $$ where $\boldsymbol{\omega}_E$ is the angular velocity of ...


2

You are correct - and the choice is pretty simple (although might not be if your satellite is to interact with different bodies). There's a number of celestial coordinate systems, and they differ by a couple features. And the choice is based on where you go and what is your observation target. If your satellite is to observe Earth, Equatorial system is ...


2

Let us note $^A\vec\gamma$ a vector of magnitude $|\vec\gamma|=\gamma$ defined in the frame $A$. Let $A$ and $B$ be two distinct frames, $|^A\vec\gamma| = |^B\vec\gamma|$. Moreover, it may be useful to recall the definition of an inertial frame: it is a frame whose acceleration is nil. Finally, let's recall the transport theorem, as per "Analytic mechanics ...


2

Tarlan is spot on with his answer but I wanted to tag along for those not using python or using some other software not being discussed here. The general consensus is that converting directly between inertial frames gets messy and non-trivial. As a result it would be best to get TEME into a fixed/pseudo-fixed frame before converting it to your inertial ...


2

If you have a direct cosine matrix (also called a "rotation matrix") which converts from ECI to LVLH, then the transpose of that matrix will perform the opposite rotation: LVLH to ECI.


2

Am I wrong? Yes, I am wrong! The way the SOHO A and B pair move roughly symmetrically ahead and behind the Earth is by being in orbits similar to that of Earth but slightly closer and farther from the Sun. Thus when seen the GIF in the question which is in a frame that moving along with the Earth (but not rotating) at ~30 km/s it looks like A and B are ...


2

You can get the rotation matrices from J2000 to ECEF using SPICE, specifically SPICE's pxform function. Someone else asked about this same topic in another question here (Is it posible to convert JPL Horizons Vectors to ECEF?) where I showed which SPICE kernels to use in order to calculate ECEF vectors at given times. JPL has different kernels for different ...


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