27 votes
Accepted

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 ...
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 ...
  • 6,830
23 votes

Orbiting Earth before heading to Moon

Going from Earth's surface direct to Moon orbit without stopping in LEO would offer negligible savings -- depending on your assumptions, maybe 20 m/s worth of ∆v (and 2-3 hours worth of consumables).1 ...
20 votes
Accepted

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 ...
16 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 ...
  • 57.9k
15 votes

What are the choices today for orbital mechanics simulation software?

Orekit is the best space mechanics tool I know. Developed in Java (cross-platform), Orekit is a space dynamics open source library, based on Common Apache Math. Despite the fact it has no ...
13 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 ...
  • 381
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 $...
  • 12.8k
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 ...
11 votes

Orbiting Earth before heading to Moon

The wikpedia page says orbiting Earth was necessary "to verify readiness of spacecraft systems", but I'm curious how this affected fuel requirements and other aspects of navigation. The use of a ...
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 ...
  • 3,140
11 votes
Accepted

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 ...
10 votes
Accepted

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 ...
  • 633
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 ...
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 ...
  • 5,925
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. $$ r_{SOI} \simeq a \left( \frac M m \right)^{\frac 2 5}$$ ...
  • 5,925
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 ...
7 votes
Accepted

What is the difference between Space Dynamics & Astrodynamics in the engineering perspective?

Vallado begins [1] by borrowing Griffin and French's definition of astrodynamics as "...the study of the motion of man-made objects in space, subject to both natural and artificially induced forces." ...
  • 811
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 ...
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{...
  • 1,845
6 votes
Accepted

How to find orbital elements of a binary system

Make the stationary center of your coordinate system the stationary center of mass of the two bodies (called the "barycenter"). Then by conservation of momentum, the total momentum of the system will ...
  • 57.9k
6 votes
Accepted

Calculate time to impact on elipisoid Earth

In the general case you will need to solve numerically for the radii at which the orbit intersects the ellipsoid. Then you can solve analytically for the times at which the orbit is at those radii. ...
  • 57.9k
6 votes

Orbiting Earth before heading to Moon

Achieving orbital velocity on earth's surface is not practical due to earth's atmosphere. First a ship must get above the atmosphere and then achieve orbital velocity. Once altitude is gained, the ...
  • 15.2k
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, ...
  • 261
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 ...
  • 7,890
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....
  • 711
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, ...
  • 6,022
6 votes
Accepted

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 ...
  • 752
6 votes
Accepted

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 ...
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 ...

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