28

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)


22

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 ...


22

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.


15

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 ...


9

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 ...


9

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 ...


9

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 ...


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

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

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


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

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 ...


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 ...


6

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 ...


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. ...


5

iTraject might be very useful for learning orbital mechanics. Its numerical solver makes it very flexible. It also uses very precise astronomical algorithms for celestial positions. You can actually set your initial date, predict when your vehicle will be in Moon's SOI with analytical calculations, and make a flyby around the Moon. Moreover, you can get ...


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

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

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

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

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 ...


4

Two possibilities: An SEL2 infrared telescope From the point of view of a space craft at Sun Earth L2, the sun, earth and moon all dwell in the same region of the sky. A small shade could shield heat from all three sources. This leaves almost a full 4 pi steradians of 4 K sky an infra red scope can radiate heat into. An EML2 asteroid mining test bed ...


4

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{y} & = v_y;\\ \dot{v_x} & = \frac{F_x}{m};\\ \dot{v_y} & = \frac{F_y}{m}. \end{align} The relations between Cartesian and the polar coordinates are \...


4

Is it possible to drive artificial satellites in a free-return trajectory around the Sun? No. Getting a satellite close in to the Sun takes a lot of energy. Parker Solar Probe used the biggest rocket available to get a really high-speed launch, and then: Parker Solar Probe will use seven Venus flybys over nearly seven years to gradually shrink its ...


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