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The lowest orbit achieved would probably be PFS-2, a small satellite deployed from Apollo 16's service module. It was intended to go into a 55x76-mile orbit (88.5x122 km), but due to variations in the Moon's gravity field, it made passes of six miles (9.6 km) or less before crashing into the Moon's surface. There are very few stable low orbits around the ...


17

"Lowest possible lunar orbit..." As pointed out in comments and in answers to the linked questions Are low, polar lunar orbits in general relatively stable? Moon orbit station-keeping delta-V budget What's the floor for stable retrograde lunar orbits? Besides Luna, what celestial bodies exhibit lumpy gravity? very close orbits around any body ...


6

Field of view. Landsat satellites by design have a rather narrow field of view (185 km across) so as to reduce issues with off-nadir resolution while Amazonia-1 by design has a much wider field of view (850 km) so as to reduce the time delay between repeated observations of the same locale. The key sensor on Amazonia-1 is the Advanced Wide Field Imaging ...


4

Yes, they're all just forms of the same relation that are specific to different values of eccentricity. This is one of the few topics treated in greater detail in Richard Battin's An Introduction to the Mathematics and Methods of Astrodynamics (chapter 4, pages 141–173) than in Vallado, including more biographical anecdotes about the mathematicians who ...


4

The current best ephemerides available is the JPL DE440 as described in Park et al. 2021 (paywalled) and available from the JPL ftp site. This is an incremental improvement over the previous DE430 ephemeris (detailed in the freely available IPN Progress Report 42-196). The main changes are that there is a longer baseline of spacecraft position data to fit to,...


4

Landsat orbits repeat their ground tracks almost exactly every sixteen days. Each Landsat sees some part of the Amazon three to six times per day, as the ground tracks @Alfonso Gonzalez posted show, but the interval between one Landsat swath of some part of the Amazon and the next image of the same part of the Amazon by the same Landsat imager, for greatest ...


3

Sun-synchronous orbits are useful for global coverage since they are near polar orbits. Attached is the plot of the groundtracks of Amazonia-1 and Landsat-7 for a 24 hour period. So in one day, each of the satellites makes 2 passes over the Amazon. However the Amazon is massive, and the flyovers are on the order of tens of minutes, so full coverage of the ...


3

Here's a partial answer until you add more information as requested in comments thanks to the numerical imprecision of Python I don't think you are anywhere near the limit of Python's floats. Instead let's remember that Keplerian orbits are theoretical approximations only. The biggest deviations come from Earth's equatorial oblateness as expressed by $J_2$ ...


2

$\newcommand{\r}{\mathbf{r}}$ $\newcommand{\i}{\mathbf{i}}$ Lagrange's set of solutions for the three-body problem is more general than just the points, which are special cases of a broader family of possibilities. The conditions under which they exist are very restrictive, but less so than the standard assumptions you list. Everything here is for the full ...


2

$$ \newcommand{\d}{\partial} \newcommand{\r}{\mathbf{r}} $$ Yes, there are many other terms involving higher powers of $\omega$, though the powers of $\omega$ are more often encountered as $\cos 2 \omega$, $\sin 3 \omega$, etc., and the size of most of them is usually ignorable, because they are multiplied by things which are small, like $J_2$ cubed or $J_5$....


1

Maybe, depending on your definition of "orbit". The lowest possible orbit around the Moon is a highly elliptical orbit where the orbiting body just barely avoids grazing the surface at its lowest point. This would mean that the Apollo landers, during their descent to the Lunar surface, would have been in such an orbit, since the landing process ...


1

The process of converting between Keplerian / classical orbital elements to ECI state vector is outlined in a number of books, a popular one being "Orbital Mechanics for Engineering Students" by Howard D. Curtis. I'll give a brief summary here: The orientation of the orbital plane is described by the right ascension, inclination, and argument of ...


1

Start by thinking of it in terms of Euler rotations. Using Ampere's hand / right-hand rule, "start" with your hand aligned with the "origin" ECI frame. Imagine that your right-hand is centered on the Earth, so a spacecraft will be in orbit around your hand. Specifically, its furthest distance from the origin is the semi-major axis, but ...


1

In addition to the argument about the earth rotating, it is also possible because you don't release the ball from your head, you release it from your hand. By the rules of 2-body problem orbits, the orbit will always intersect with the release point. This point is in front of you. So in theory one could have an elliptical orbit which is at a higher ...


1

A circle is a subset of ellipse, and a circular orbit can (on a theoretical, magical, non-rotating, vacuum Earth) be thrown. A slightly slower orbit might reasonably be thought to hit your knees (to avoid hitting the antipodal soil), but it would no longer be circular but again elliptical, with a greatly shifted major axis, since you would be releasing it at ...


1

The terms radial and tangential are relative to the central body NOT the instantaneous vector, so if the radial velocity is nonzero, then the tangential component is orthogonal to that and parallel to the planet's horizon. It is Vtangent * R that is the angular momentum that is conserved in a Kepleran orbit. Momentarily at apogee and perigee Vtan = V.


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The answer given before seems to work great, I am just here to give a different answer if you're more interested in learning about the software that goes into numerically propagation trajectories and 3D plotting The general procedure to go about solving this problem would be: Convert from TLE to state vector (position and velocity). There's a few equations ...


1

Spacecraft Maneuvers as Intellectual Property? Wow! I was thinking the same thing until I realized every orbital maneuver patent I was looking at was actually a process or method patent of the underlying calculations and software. Do we see patents on the use of actual orbital maneuvers themselves in which the patent holds regardless of the algorithm used ...


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