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27 votes
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How can we determine the most appropriate central body for orbit propagation?

Several years ago I had an intern investigate this very problem. A good intern task is an interesting but nonessential problem. This qualified as such; he even managed to turn that internship work as ...
David Hammen's user avatar
24 votes

Does the speed of ISS slow down at the time of a spacewalk or does it become stationary?

Let's look at Newton's first law: Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force ...
Polygnome's user avatar
  • 6,956
20 votes
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How to choose the best direction to leave Earth's sphere of influence?

Your intuition is quite correct. The Hohmann transfer orbit is a bi-tangential orbit, so at the point where the spacecraft leaves Earth, it is travelling in parallel to us. In the case of Mars, we ...
SE - stop firing the good guys's user avatar
15 votes

How does a Mars lander reach a chosen landing site?

There are typically five planned trajectory correction maneuvers on the way to Mars, referred to as TCM-1 to TCM-5. (Also there is a slot for an emergency TCM-6 a few hours before entry, but it is not ...
Mark Adler's user avatar
  • 58.2k
14 votes

What are the practical uses of a state transition matrix?

From the top of my head I could think of the following practical applications for state transition matrices. Note that the application referred to in the question is captured in point 3. Also, I don't ...
jochim's user avatar
  • 391
13 votes

Why are uncertainties of orbital state vectors provided as covariance matrixes?

The full covariance matrices are useful because you need the whole matrix if you want to apply a change of coordinates (as David Hammen's answer alludes to). For a state vector $x$ covariance matrix $...
Ludo's user avatar
  • 14.4k
12 votes
Accepted

Why is there a singularity in Lambert solutions for transfers of pi-multiple degrees?

An integral multiple of 180° means that the initial point $r_1$, the central point, and the target point $r_2$ all lie on the same line. This in turn means the cross product between the displacement ...
David Hammen's user avatar
11 votes
Accepted

How important is plume impingement in rendezvous operations?

NOTE: My answer applies specifically to Space Shuttle (STS) operations. In general, it is quite safe to say that it is never desireable that the chaser plume the target to any significant degree ...
Digger's user avatar
  • 4,185
11 votes
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Why are uncertainties of orbital state vectors provided as covariance matrixes?

But under what circumstances or for what purpose could such information be used? If you transform the 6x6 covariance matrix to the nominal perifocal (PQW) frame, the information contained therein ...
David Hammen's user avatar
11 votes

Object slowest at periapsis - despite correct position calculation

If I understand correctly, your $p, q$ are essentially cartesian coordinates, and you're trying to get the velocity components in those two orthogonal directions. However, you're taking the derivative ...
uhoh's user avatar
  • 149k
10 votes
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Why is FORTRAN recommended for astrodynamics rather than MATLAB?

As many of the comments have already mentioned, there are several different reasons people might recommend the use of Fortran over Matlab. One of the most straightforward answers is that a lot of ...
Chris's user avatar
  • 643
10 votes

What can one do as an individual to help support the development of skyhooks?

Assuming your question is addressing this point: it seems like no one is actively pursuing this technology I think there are multiple reasons for this It's too early for orbital-lift infrastructure. ...
Dragongeek's user avatar
  • 19.1k
10 votes

Why is there no difference between a transfer orbit delta-V and a capture orbit delta-V for Earth?

To begin with, you are correct that the perspective of the map is from the Earth's point of view. I also believe that a different map would be needed for people interested in traveling from Mars to ...
phil1008's user avatar
  • 5,634
9 votes
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Object slowest at periapsis - despite correct position calculation

As uhoh said, the velocity is the derivative of the position w.r.t. to time, not true anomaly. I.e., if we denote time by $t$, the components of the velocity vector are $\left(\frac{dp}{dt}, \frac{dq}{...
Litho's user avatar
  • 2,050
8 votes
Accepted

What is the amount of Delta-V required to enter lunar orbit following Trans-Lunar Injection?

Strictly speaking, the minimum ∆v is zero: from a ballistic capture trajectory, marginally stable lunar orbits at about 20,000 km altitude can be reached for zero or nearly-zero ∆v cost; an orbiter ...
Russell Borogove's user avatar
8 votes

How is the trajectory of spacecraft transferring between planets monitored?

In most missions, and especially interplanetary missions, spacecraft position and velocity is determined by calculating the range (i.e. straight-line distance) and range rate between the spacecraft ...
ChrisR's user avatar
  • 6,180
8 votes

How can we determine the most appropriate central body for orbit propagation?

A common approach is to calculate the sphere of influence of the celestial objects whose gravity you're accounting for in your propagation. $$ r_{SOI} \simeq a \left( \frac M m \right)^{\frac 2 5}$$ ...
ChrisR's user avatar
  • 6,180
8 votes

Are there any sources with high-confidence state vectors for GRAIL-A?

Partial answer too long for several comments: tl;dr: The drift you are seeing is just as likely (if not more) to be a difference in your acceleration models as it is an "inaccuracy" (...
uhoh's user avatar
  • 149k
8 votes

How to build an orbit propagator?

RK4 is far from the best numerical integration techniques to use for orbit propagation. This is particularly the case for non-circular orbits. The key problem with using RK4 is that it discards ...
David Hammen's user avatar
7 votes

notation to describe an elliptical orbit? (3000km x 40000km)

That's a common convention. The smaller number is the periapsis altitude, the larger is the apoapsis altitude, normally both given as height above a planetary surface rather than radius from ...
Russell Borogove's user avatar
7 votes

How big a nuke would be needed to break Phobos out of orbit?

Simply to lift get Phobos out of Mars orbit you would need to increase its orbital velocity by a factor of $\sqrt{2}$ (this is generally true for any object in circular orbit). Phobos orbits at about ...
Steve Linton's user avatar
  • 19.6k
6 votes
Accepted

How to derive the polar form of the equations of motion?

There's probably a simpler way to do it, but here is how you can obtain these equations from the basics. Let's start with equations in Cartesian coordinates: \begin{align} \dot{x} & = v_x;\\ \dot{...
Litho's user avatar
  • 2,050
6 votes

What liquids last the longest in space?

Just to propose something specific in an answer: I would first guess Gallinstan (by mass: 68.5% Ga, 21.5% In, 10.0% Sn), at least if we're talking about near-room-temperature applications: Supposedly, ...
Mr. Nichan's user avatar
6 votes
Accepted

Does Kepler's Method for Determining Time of flight between two True Anomalies break down with eccentricities approaching 1?

As noted in the comments, both methods potentially break down. Kepler's method is mathematically exact, but as formulated here it becomes ill-conditioned as the eccentricity approaches 1. The mean ...
Oscar Lanzi's user avatar
  • 8,525
6 votes

Where can one find the accelerations due to high-order terms of the geopotential model?

In Vallado's Fundamentals of Astrodynamics and Applications, Section 8.6.1: Gravity Field of a Central Body, he derives the equations to calculate perturbations due to aspherical bodies. In Section 8....
Paul W's user avatar
  • 721
6 votes

Why are uncertainties of orbital state vectors provided as covariance matrixes?

The full covariance matrix is useful in itself for much more than just drawing ellipsoids, and it can be a lot bigger than 6x6. Covariance is essential to the basic operations of orbit determination, ...
Ryan C's user avatar
  • 7,972
6 votes
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Why is the eccentricity vector used to describe near-circular orbits?

The question is "how are singularities avoided for $e→0$ by defining $(e_x,e_y)$, which is still a function of $ω$, thus still affected by the singularity?". (Worth noting first is that here ...
terry-s's user avatar
  • 1,092
6 votes
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Conversion of velocity vectors between ICRF frames with different central objects

Assuming Newtonian mechanics are in play, velocities, like displacements, are three dimensional vectors. (There is no reason to go full-bore general relativistic with regard to behaviors in the solar ...
David Hammen's user avatar
6 votes
Accepted

How to plot a satellite's orbit around Earth in MATLAB?

Like the comment above mentions, you wouldn't need mass of the satellite unless its a Deathstar. Also, you would need the initial values of elements you want to propagate. Since you mention that you ...
pathfinder_EOS's user avatar
6 votes
Accepted

Is there an accepted method to compare orbits?

You have several options, but you are still required to define what "close enough" means. Here are at least two I can think of, but first we need to address the big problem: since the ...
Michael Stachowsky's user avatar

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