27

Here are the options I'm aware of off the top of my head: AGI/STK (Systems Toolkit) — PC, free Orbit Reconstruction, Simulation and Analysis (ORSA) — Linux/Mac/PC, free (last version 2011-02-17)


23

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 According to Apollo By The Numbers and Bob Braeunig's simulations, the ∆v budget for launch to orbit plus trans-lunar injection for the Apollo missions ...


23

Apart from these serious software mentioned above there is an interesting game with quite realistic orbital calculations, quite suitable for teaching kids about space: Kerbal space program. As for AGI non-free version is a lot more powerful.


23

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 impressed. In modern mathematical speech, this can be stated more precise. In an inertial frame of reference, an object either remains at rest or continues to ...


16

Shameless plug for Tudat (TU Delft Astrodynamics Toolbox)... If you're looking for something that allows you a lot of freedom to set up and play with simulations, you might want to consider an open-source C++ project I've been working on for the last few years as part of my PhD. Most of the graduate students in my group use it, so a lot of effort has gone ...


14

As far as games/simulations go, I have stumbled upon Orbiter. Seems to have quite a few add-ons and a forum. Unfortunately, works under Windows only.


13

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 expected to be used.) Also I sometimes refer to launch as TCM-0. That's the really, really big TCM. TCM-0 provides the energy to place the aphelion of the ...


11

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 parking orbit most likely saved fuel compared to a direct translunar insertion. A direct insertion into a translunar trajectory would have saved a tiny amount of ...


11

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 visualisation tool so far, the different force model it contains make it a really good choice if your plan is to solve accurate flight dynamics problem. Orekit includes ...


10

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 during rendezvous/proximity operations. A cursory overview of the Space Shuttle Orbiter's Reaction Control System (RCS) is shown below (page taken from a 2002 ...


10

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 explain the theory of state transition matrices, as that is already done here. 1. Covariance propagation The position and velocity of the spacecraft is ...


10

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 legacy (read: validated) code is written in Fortran, and depending on your job function, learning to use Fortran might make you more productive - for instance, if ...


10

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 vector from the central point to the initial point and from the central point to the final point is zero. Note that except for these special cases, the cross ...


8

PyEphem: PyEphem provides scientific-grade astronomical computations for the Python programming language. Given a date and location on the Earth’s surface, it can compute the positions of the Sun and Moon, of the planets and their moons, and of any asteroids, comets, or earth satellites whose orbital elements the user can provide. Additional functions are ...


8

It is theoretically possible, but such a satellite would probably not be in a stable orbit. Such a system is not known in the Solar system and due to gravitational perturbations it would not last long. Popular Science Astro


8

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 and several ground stations. There are several techniques for computing the range and range rate. They depend on a number of factors: Is the satellite ...


7

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 barycenter.


7

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." Vallado uses this definition because other related subjects - e.g., orbital dynamics, attitude dynamics - don't solely encapsulate what astrodynamics is. In the ...


7

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 can then descend to a lower orbit at leisure using low-thrust high-efficiency ion engines. More generally, low energy transfers allow a tradeoff between travel ...


7

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 2.1 km/s (Wikipedia) relative to Mars, so this is a delta-V of $2.1 \times (\sqrt{2} -1)$ which is about $0.9 km/s$. It's mass, same source is about $10^{16}kg$ ...


6

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 always be zero. If the net momentum of the two bodies is not zero, then first subtract the velocity of their center of mass from both to make it stationary. ...


6

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 most efficient way to achieve orbital velocity is by a horizontal burn. You could do the major burn along a non zero flight path angle but then the vertical ...


5

Edit -- I was wrong. I've asked around. John Schilling and Henry Spencer tell me altitude of apoapsis and periapsis is what's usually used to describe elliptical orbits about a planet. These guys know a lot more about space than I do. Please disregard what I said earlier. I would chastise your prof for ambiguous notation. Most instances I've seen the first ...


5

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. That is, if you ignore $J_2$. Since you made it an ellipsoid, you have introduced a $J_2$, so you will no longer be in a Keplerian orbit. To take $J_2$ into ...


5

You should write everything in vector form and then it is just a matter of applying a couple of formulas. 1) Use the given position and velocity values to write the position and velocity vectors, $\vec{r}$ and $\vec{v}$ 2) Compute $\vec{h} = \vec{r} \times \vec{v}$ (where $\times$ is the cross product) 3) Compute the eccentricity $\vec{e} = \dfrac{1}{\mu}(...


5

Here's a few other things out there as well depending on what you're looking for... WEB While not a simulator for orbital mechanics, I found this Trajectory Browser from Nasa to be interesting. More game-like is the LEO launcher app and the launch simulator. There's the JPL 3d simulator and the Near-Earth-Object Simulator (both web based). There is also ...


5

The general term for figuring out the position/velocity of a spacecraft is Orbit Determination. It's based on Estimation Theory, and the most common techniques are Batch Least Squares (BLS) and Extended Kalman Filtering (EKF). A simple description of Orbit Determination is that we predict the motion of the spacecraft as best we can, but then we also take ...


5

NASA JPL optical design team, including Scott Basinger and Mayer Rud and co-investigator Grover Swartzlander at the Rochester Institute of Technology Center for Imaging Science think so! They call them "orbital rainbows" when used as distributed mirrors for a giant telescope. JPL: Glitter Cloud May Serve as Space Mirror YouTube: Orbiting Rainbows: A Space ...


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