23

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 ...


18

"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 ...


12

I've got a set of Keplerian orbital elements $e_0$, $a_0$, $i_0$, $\omega_0$, $\Omega_0$, and $\theta_0$, and I'd like to get to a different orbit with orbital elements $e$, $a$, $i$, $\omega$, $\Omega$, and $\theta$. How do I calculate (a) the amount of delta-v I'll need for this maneuver or set of maneuvers, and (b) which maneuver or set of maneuvers I ...


11

I'm assuming atmosphere isn't a consideration. The azimuth angle (north-east-south-west orientation) doesn't matter at all for this question -- it determines the orientation of the ellipse, but has little effect on its shape, and none on the perigee-apogee question. If the elevation angle is zero -- i.e. you're throwing it with a perfectly horizontal ...


9

What you're looking for is Lambert's problem, which is used both for trajectory design and orbit determination, and to produce porkchop plots. Your hunch that this is not a simple problem is correct. pykep has a solver for Lambert's problem that supports multiple revolutions as well as solvers for various related problems such as low-thrust trajectories.


7

This is a case of an answer originating before a question. Originally a spin-off problem from this question asking about satellite footprints, it doesn't fit very well as an answer there. Hence this separate question and answer. As it turns out, this has a straightforward geometric solution from observer latitude $\phi$ and inclination $i$: $$r_P < \frac{...


7

You don't have enough information. You need a minimum of one more value to determine the true anomaly such as the time of perihelion passage. In general six values and a timestamp are needed to fully specify a Keplerian orbit. The reason six values and a timestamp are needed in the general case is that the two body problem is a second order differential ...


5

Do you really want to compute a new TLE, or just a new orbit? The TLE format itself is a significant problem, so it's best to avoid if possible. If you just need to look for changes in the orbit state, you should use SGP4 to convert into position and velocity, propagate the state with and without the maneuver using something other than SGP4, and convert ...


5

All orbits about the Earth except for polar orbits will see their line of nodes precess due to the Earth's equatorial bulge. The effect is strongest for near-equatorial orbits and for objects in low Earth orbit. In the case of the International Space Station, this nodal precession causes the ISS's right ascension of ascending node to decrease by about 5° per ...


4

This answer doesn't talk about how to do it Python at all: rather how to deal with the rotation. I think once you can do that then turning the maths into Python is simple. Initially I'll assume that you are computing positions in terms of three orthogonal axes, and the positions look like $(x, y, z)$, and you're just projecting these down onto the $(x, y)$ ...


4

Start with answers to How can I plot a satellite's orbit in 3D from a TLE using Python and Skyfield? Plotting in 3D makes my head hurt too, but for some reason I like it when my head hurts. If you like you can paste python into your question; blocks of text that are indented by 4 spaces appear as a "code block". You can have a look at the 3d plotting in ...


4

There is a gray area here, but probably yes. If it were called a "suborbital flight" the assumption would be that the orbit's path would intersect the surface of the Earth. Since the perigee of your orbit is in the denser part of the atmosphere but does not intersect the surface, if it weren't for the drag force the spacecraft would continue to ...


4

I'd always imagined its orientation would be fixed in inertial space, but now I'm inclined to say no? Trust your inclination! If Earth had perfect spherical symmetry then the smaller effects like gravity from the Sun and Moon and some other smaller effect would still perturb the ISS' orbital parameters (in addition to the big one - drag - which will pull it ...


3

Your user need to supply you with information about mean anomaly at fixed time (epoch) $M(t_0)$, and then mean anomaly at the moment $t_1$. Or about known mean motion $n$ instead of current mean anomaly $M(t_1)$. You can also get the mean motion as square root of gravitational parameter $\mu$ divided by cube of semi-major axis, and also as $2\pi$ divided by ...


3

Work in progress, new figures will follow. I took the orbit data of Hayabusa2 we got to plot the magenta ellipse. I used the initialValues.a Semimajor axis and initialValues.e Eccentricity. The two red dots are the foci of the ellipse. The blue dot is the one position of Hayabusa2 we got, only x and y were used. Sun is at the center x = 0 and y = 0, of ...


3

Is it possible to represent an orbit with just a periapsis position and 2 angular velocities? This works, except for singularities at the poles. In general, an epoch time and six scalar values that completely represent the state at the epoch time are needed. Only five scalar values are needed if the epoch time is known to be the periapsis time. For example, ...


3

I find these terms easiest to explain using an analogy. Let’s take these 5 points in the x,y plane: (1,1) (2,3) (3,4) (4,4) (5,3) We can perform the following operations on them in a Jupyter Notebook and produce a simple plot: %pylab inline x = array([1, 2, 3, 4, 5]) y = array([1, 3, 4, 4, 3]) fig, ax = plt.subplots() ax.plot(x, y, 'ko') ax.set(xlim=[0,6], ...


3

I will use a series of images of the Earth taken by the Apollo 11 crew during the flight to the Moon. I use the formulas developed by tfb to determine the percentage of the visible Earth. Image AS11-36-5325 from a distance of 18,700 km showing 37.3 % using a 80 mm lens Image AS11-36-5330 from a distance of 87,000 km showing 46.6 % using a 80 mm lens Image ...


3

This is not an answer as such, but an attempt to provide the mathematical apparatus you need to think about this (and it was way too long for a comment). There are two sensible things that might be meant by 'seeing the entire Earth': one is that the Earth would be visible in the field of view of a human eye; the other is that you can see a given amount of ...


2

Crew Dragon with Falcon Heavy can theoretically be sent to a lunar free return trajectory, so pretty much any apogee could be done. As for just a Falcon 9, it's hard to know for certain. Putting in a desired orbit of 2000 km with the NASA Performance Vehicle Calculator, I got the following plots. Note that 9000 km is the launch mass of Crew Dragon. The ...


2

Partial answer (to What is the maximum apogee a Space Shuttle (and which one of the five space-flying Shuttles?) ever reached ) The maximum altitude reached by a shuttle orbiter on an unclassified1 mission was on STS-82 (Discovery) after the 3rd reboost of Hubble. This resulted in a 335.1 X 321.0 NM orbit. (620.6 x 594 km) 1 Published orbits for the ...


2

You can download TLE data for each of these orbit regimes separately with the click of a link at https://www.space-track.org/#recent after registering and agreeing to the terms of the site. The definitions used there are: HEO: Eccentricity > 0.25 GEO: 0.99 <= Mean Motion <= 1.01 and Eccentricity < 0.01 MEO: 600 minutes <= Period <= 800 ...


2

You're in luck that you have the mean anomaly, that makes the calculations much easier. The mean anomaly is the angle expressing the fraction of the orbital period that has been covered since perihelion (and not the "real" angle between perihelion, the Sun and the object. That's the true anomaly and harder to calculate). So given a mean anomaly in ...


2

You need to learn a little about the many ways in which orbit data can be represented, starting from a basic tutorial like https://en.wikipedia.org/wiki/Orbital_elements One of the important things to keep in mind is there are no more than six independent numbers out of that set, but not just any six can be chosen. If you input values for too many, things ...


2

I found some information about correcting the azimuth for Earth rotation in an old package of notes. Unfortunately I don't remember all the assumptions that are baked into this, but you might be able to try it out in your simulation and see if it gives better results. Also this was for SRB sep, not for MECO.


2

Short answer, yes. Long answer: There are 6 keplerian orbital elements (but note that these parameters are not the only way to describe an orbit). Semi-major axis, eccentricity, inclination, argument of periapsis, right ascension, and true anomaly. Here is a surface level explanation of each: Semi-major axis describes the "size" of the orbit. In ...


2

Hohmann transfers only describe transfers between 2 circular orbits. So if you're looking to find when would be a good time to leave Earth to get to Ceres using Hohmann transfers, you don't take into account the gravity of the Earth, you only imagine transferring from one circular heliocentric orbit to another circular heliocentric orbit, like in this case ...


2

In practical terms, these hypothetical single-element manoeuvrers are not useful, as one cares very little for what intermediate path one takes through empty space, while the propellant consumption is an absolute bottleneck. Argument of periapsis can be changed the way you describe, by applying zenith thrust at apoapsis or nadir thrust at periapsis: $$...


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

It looks like there is not a possible answer to this question: the available data are not enough to plot a 3d orbit. Although there are apparently 6 orbital elements, they are actually just 5; indeed these three data are provided: - "e": 0.187058473659886 - "a": 1.19403253275367 - "q": 0.970678629676518 But: periapsis ...


Only top voted, non community-wiki answers of a minimum length are eligible