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In many cases, propellant is only dumped when the spacecraft’s mission is complete, so any minor changes to trajectory caused by the dump are unimportant. If you must avoid any trajectory or attitude change due to a propellant dump, the most straightforward way is to have multiple vents pointing in opposite directions, so the propulsive forces cancel out.


18

The asteroid belt isn't nearly as dense as popular media makes it out to be. An answer from the Dawn Mission's FAQ, specifically "What is the average distance between individual asteroids? (6/13/10)", helps here. Asteroids are not distributed uniformly in the asteroid belt, but could be approximated to be evenly spaced in a region from 2.2 AU (1 AU ...


15

The asteroid belt is roughly 6 Astronomical Units wide, and so when it is drawn only 600 pixels wide with each asteroid a handful of pixels wide, you end up with each asteroid being five times bigger than the Sun! I've borrowed a small piece of the image used in @jos' excellent answer to show what I mean. As pointed out in this answer, Wikipedia says: ...


6

It seems that rectangular coordinates in Earth-centered inertial frame is a viable choice. The relative spherical coordinates may be susceptible to singularity during the lift-off (i.e initial conditions such as velocity and flight path angle are 0 m/s and 90 degrees, respectively). From page 42 of Ezgi Civek Coskun's 2014 Ph.D. Thesis Multistage Launch ...


6

“Sailing a rhumb line” means holding a constant compass bearing. For short distances, this stays close to a great circle path.But at longer distances and/or higher inclinations, the rhumb-line path “tends north” of a great circle as shown in the Questions globular image. For a fast, short launch, a rhumb-line trajectory has the advantage of simplicity. As ...


5

The telescope was placed into a heliocentric orbit when its helium supply was depleted On 29 April 2013, ESA announced that Herschel's supply of liquid helium, used to cool the instruments and detectors on board, had been depleted, thus ending its mission. At the time of the announcement, Herschel was approximately 1.5 million km from Earth. Because ...


5

Yes, in fact it did slow down with time, until it approached close enough that the Moon pulled it faster. That happened at a point very close to the Moon. In a diagram on this page, for Apollo 8 we can see that point was just after the second full day, and the speed was about 3578 km/hr. Borman, Lovell and Anders were the first humans to leave the Earth’s ...


5

For some reason, I saw, or read this question as simply asking "How fast can you get to Mars if fuel is no expense". So this answers that question. I don't mind deleting it if that is considered appropriate. Anyway, it depends what you mean by "if fuel is no expense". If you are assuming something more or less along the lines of current rockets, but are ...


4

In the video Arianespace TV VS 21 Live Launch English after the spacecraft has entered "cruise" in LEO, the announcer says: Once the frigate is sent an “Engine off” we enter what we call the ballistic phase, and ballistic is probably a word I’m guessing that you’ve heard quite a lot over the years, and I believe, correct me if I’m wrong, that it means ...


4

I assume Apollo's velocity slowed down after it left Earth orbit, for how long was it decelerating. A pretty good analogy for TLI is throwing a baseball straight up into the air. The "throw" is the TLI burn; as soon as the ball leaves your hand it begins to slow down, trying to fall back towards Earth. The peak altitude of the "throw" is around where the ...


4

It will depend on many factors, but so long as you are NOT using a mono-propellant, then you can simply allow your fuel to run through the system normally (but without lighting it/mixing with oxidiser). This will still result in a slight thrust, but several orders of magnitude less than a 'proper' burn. If this is done through thruster nozzles, it should be ...


4

Here's a quick visual analogy. Imagine you want to "hop a train"; jump onto a flatcar as it is rolling along the tracks. The traditional approach is to run in the same direction the train is going, and then when you get beside the car make sure your speed matches, grab it, and jump on. It's dangerous, but very doable. Your suggested approach is to run in ...


3

To reach one body in space from another, you need to consider their speeds, not just their positions. To leave Earth going the other direction, you need to cancel out Earth's orbital velocity around the sun (about 30km/s), and then when you reach Mars you need to turn around and match Mars's velocity. This is much more expensive in fuel than more direct ...


3

Some good practices I'm aware of are: As you mentioned, maneuvers are simulated before they are commanded and their effect is evaluated on ground so that thruster parameters and tank filling are updated, so if anything funny is happening during maneuvers this can be identified. If propulsion is electric (which is still not so common), then thrusting is ...


3

From https://old.math.tsu.ru/50gagarin/moon.doc ...перелеты в рамках проекта США Аполлон (1968-1972), а также проекта СССР автоматической экспедиции по забору и возврату Лунного грунта (Луна-16, 20, 24, 1970-1976), они имели близкие траектории, лишь полеты советских КА с Луны на Землю удалось осуществить без коррекции траектории. translation - ......


3

Looks like they've used some figures that are very close to the sample calculations shown in the original paper with Katherine Johnson, which is available from NASA archives. The figure is for the distance of the vehicle from the center of the earth at the time of the retro rocket firing (or burnout) which initiates reentry. They've changed the original ...


3

Bennu's hill sphere is 29.5 km roughly. The orbit is roughly circular, about 1.75 km above the center, or about 1.5 km above the surface of the asteroid. It is well inside of the Hill Sphere. This doesn't even compare to Dawn, which orbited about 35 km above the surface at closest, and that was with a very eccentric orbit. Hayabusa 2 isn't really orbiting ...


2

Let's start with the easy bits. The distance from the center of the Moon at the far point. The max distance that the Moon was from Earth was actually at the exit point. The exact distance involves some complex geometry. Another thing to keep in mind is the Earth and Moon are not exact spheres, the radius can vary quite a bit. The Earth's actual radius can ...


2

[ This is going to be a draft answer as I learn more and get more time to fill it out and edit with symbolic math -- right now its going to be super rough and this answer will evolve a lot over time ] Basic Simplified Problem The generic problem is to take a spacecraft from a set of initial conditions $\vec{r}(0), \vec{v}(0), m(0)$ to a set of terminal ...


2

India's Chandrayaan-2 was launched into an initial Earth orbit with a perigee of 170 km and an apogee of 40,400 km. Whether you count it as LEO depends on your definition of LEO. Some would count it because the perigee intersects the altitudes for LEO. Others would not count it because of its high apogee and high eccentricity. As described in this answer ...


2

If you look at a pure definition from Webster's the answer is ambiguous with respect to in-orbit flight: of or relating to the science of the motion of projectiles in flight In most contexts I've seen, ballistic usually implies intersecting the central body. However orbiting satellites in low orbit (where atmospheric effects are noticeable) have a ...


2

SPICE has multiple tools for constructing and using piecewise Lagrange and Hermite polynomials because those techniques are textbook. In contrast, techniques for constructing piecewise Chebyshev approximations are anything but textbook. SPICE supports one very specific format of using (but not constructing) piecewise Chebyshev polynomial approximations. That ...


2

Most rocket companies use several coordinates systems for launch vehicles during ascent. Generally a local ground fixed reference frame centered at the launch pad is used along with an Earth Centered Inertial frame (ECI) and Earth Centered Earth Fixed Frame (ECEF).


1

The figure-8 is probably not the most efficient way to get to Mars, but it's likely how we're going to go. As an example of a mission that didn't use it, India's MOM (Mars Orbiter Mission) spent a lot of time in earth orbit, slowly raising its orbit every time it passed perigee. This allowed, for example, a smaller rocket engine. There is a concept called ...


1

Let's think this through. Some potential scenarios: The service module to rupture at the same time as the CM. It seems unlikely that anything that killed a service module could have been survivable from reentry that also caused a puncture, but... The worst case for this scenario is probably near that of Apollo 13, a few hours extra. Apollo 13 was about 87 ...


1

Draw triangle $PFG$ where $G$ is the second focus of the ellipse. You know the following: $|PF|$ = distance from planet to $F$. $|PG|$ = major axis minus $|PF|$. Sum of distances definition of an ellipse. $|FG|$ = major axis times eccentrity. Knowing all three sides of this triangle you calculate the angles from trigonometric laws. Next draw the ...


1

It turns out this isn't actually that complex. The trick is to use a rotation matrix. The rotation matrix is described here in the paper cited: The correct transform for the ICRF/J2000.0 is known in the paper as the $GEI_{J2000}$. There are actually two transforms that are required. Transform from HGI to $HAE_{J2000}$. The values are $E(\Omega (T_0=0),i,0)$...


1

Apollo 11 first entered a 103 nautical mile orbit, and midway through orbit 2 was boosted onto lunar trajectory. This was 2hrs 50mins into the mission, so from this point onwards, mission control were not considering orbits of the Earth. Apollo 11 passed 22k nautical miles at 5hrs and 22 minutes into the mission. 2:54 p.m.- The spacecraft is reported 22,...


1

This I believe is in reference to John Glenn's flight. It seems that this is some real numbers, but simplified in a way that doesn't let everything be seen. The speed is almost orbital. I believe what is actually being calculated is the location where a very late abort would put John Glenn landing, although it is somewhat difficult to tell from the limited ...


1

As such, I was wondering if there is a way to accurately track both position and velocity for the launch vehicle's ascent to orbit. If possible, have more accurate actuators and reference models. Improves the tracking of states easier. But since there is a relationship between position and velocity you cannot properly control both. The reason is simple: If ...


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