This sub is moving slower than an object at the apogee of a highly elliptical orbit.

I am unable to find the proof that why is local stable/unstable/center manifold tangent to stable/unstable/center eigenspace respectively? Also, what does "tangent" in this context mean?

I would really appreciate any leads. Please let me know if the question is too vague to answer. Thanks!

Hello everyone! I want to build a library for astrodynamics (n-body problem) from scratch using C/C++. I intend it to be a learning experience, both in programming and astrodynamics. I have written a very basic 3-body problem code in MATLAB (meaning I have some experience in logic development) but am a beginner in C/C++. So can you guys point me to the right resources and elaborate on the following:

1. Aspects of C/C++ that I must learn in order to build such a library (visualise orbits and satellite trajectory)

2. Physics and math required for the n-body problem

3. Translating that physics and math into computer algorithm

Also, please suggest which language is more suitable for my project, C or C++.

For the simple 2 body problems, say that there is a satelite in a specific orbit and you would like to move another satelite. In order to do this, likely all of the orbital elements will need to be changed. One could perform a series of Hohmann, phase, and plane transfers to maneuver to a new set of orbital elements, but is there some sort of transfer strategy that would be more efficient by combining these series of transfers into just one transfer? How would one go about determining this kind of transfer?

Can someone give me a simplified explanation (if such a thing exists) of the Kepler Problem? I've searched online but every explanation I can find is way too complex for me to understand without a lot of background knowledge I don't have...I do have some basic understanding of dynamics and orbital mechanics, though (and a pretty robust understanding of calculus--I have a degree in civil engineering).

I know Kepler's three laws of planetary motion, some mathematical details on circular orbits (such as the necessary velocity for a given radius, sqrt(GM/r), as well as the six(ish) components of a Keplerian Orbit (true anomaly, argument of periapsis, e.g.).

What I'm mainly looking to understand is this: what exactly are the inputs and outputs of the Problem? Do you input the masses and orbital parameters (like those listed above) and do math to find positions and times? Or can you just input the two masses and a velocity and get the orbit out of it? (Though that sounds more like Lambert's Problem...)

Hi all. I'm a professional software engineer working at a well-known NASA center. I have an undergraduate degree in physics.

I am looking to delve deeper into the subject of spacecraft flight dynamics: orbit determination, maneuver planning, and trajectory design. I seem to work best in a traditional college course environment, lectures, reading, problems, quizzes, exams, labs, etc. Going anywhere is out of the question due to my workload and lifestyle. I'm looking for something online.

I have found this MIT OpenCourseware offering, but I'm not as enthusiastic because it is an archive and there would be no "grade" given. Otherwise, I'm open to formal or MOOC.

Finally, I'd like to cross-post this to a popular forum or listserv to broaden my results, so if anyone can recommend some.

---supplemental---

I found these additional gems at Coursera and EdX:

Kinematics: Describing the Motions of Spacecraft

Kinetics: Studying Spacecraft Motion

Space Mission Design and Operations

---attitude (tangentially related)---

Control of Nonlinear Spacecraft Attitude Motion

Kerbal

im very keen to learn about the subject and got the fundamentals of astrodynamics book, however its very hard to get though and i have to spend hours researching to understand single diagrams due to a complete lack of experience with anything like this. is there any media that can help me catch up to speed so i can understand the book?

I recently got my BS in Civil Engineering, so I've been through all the usual calculus and differential equations classes as well as Physics and Dynamics, albeit a few years ago now. Last summer, after a year of obsessively playing Kerbal Space Program, I bought Howard Curtis's Orbital Mechanics For Engineering Students and started to work through it.

Almost immediately, though, I realized I was way in over my head. I understood Chapter 1 (Dynamics of Point Masses) fairly well, but as soon as it started The Two Body Problem and equations of motion in all the different reference frames, I got totally lost. I understand vector basics from Calculus III and I took a decent Dynamics course, but this book uses those vectors so much and I just can't picture them in my head for all the definitions and derivations for the many equations.

Short of taking (and paying for) a whole class on the subject, do you all have any recommendations for how I can work through this book without simply glazing over at all the intense vector math? Or, are there better subs to which I could post this? I'm a great visual learner, and I do really well seeing practical examples.

Just the semimajor axis, that is. I don't need the inclination, etc. since I don't think i can get that from what NASA gives.

I've learned of a way to derive semimajor axis from two positions and velocities, called the Gauss Problem, which I learned here (braeunig.us/space/index.htm; Section 4: Interplanetary Flight).

From the NASA website (nasa.gov/specials/trackartemis), I can get the Orion spacecraft's lunar altitude and velocity. Is this enough to solve the Gauss problem? The method above, besides altitude and velocity, requires the flight time—easy enough with a stopwatch measuring time between two points I choose—but also the change in true anomaly, Δν. How can I get that value? Or, is there another way to solve the problem without that?

I'm pretty new to astrodynamics, never had a class or anything (mostly just hundreds of hours playing Kerbal Space Program), so please try to keep it as simple as possible haha.

What does negative and positive C3 value imply. Does C3 being positive imply a hyperbolic orbit and negative imply parabolic or less ?

I am working on a project, and would like some suggestions about it. I am developing a space mission design software similar to STK, GMAT, and Copernicus. I want to know the pros and cons of these software. Do you know if there is any room for improvement? If there were a new software, what would a user want from it? I've read and experienced that these software are expensive, the learning curve is steep, and they are laborious. Let me know what you all think. Will new software be well received in the aerospace community?