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Question about orbital mechanics
I am writing a program that simulates a planetary system (a star and a group
of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? -- Robert Heller -- 978-544-6933 Deepwoods Software -- Custom Software Services http://www.deepsoft.com/ -- Linux Administration Services -- Webhosting Services |
#2
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Question about orbital mechanics
On May/15/2016, 8:39 PM, Robert Heller wrote :
I am writing a program that simulates a planetary system (a star and a group of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? I'm not sure of what exactly is the question here. I think that what you want to do is compute the trajectory of the spacecraft by numerical methods, probably the Runge-Kutta method. Wikipedia gives a good explanation of that method (use RK4): https://en.wikipedia.org/wiki/Runge-Kutta_methods You would probably also want to implement a method to figure out which planet can safely be ignored in your computations. If you want to compute the trajectory of a spacecraft near Jupiter, you can safely ignore Mercury. In fact you can probably ignore all the planets other than Jupiter. But exactly under which conditions you can ignore which planets depends on what precision of the trajectory you want. In most cases, you can ignore all planets but the one with the greatest gravitational pull on the spacecraft, but if you want very precise trajectories under some planetary configurations that won't be enough. As I said up there. I'm not really sure of what you want, if this doesn't answer your question, or if you want more details. Please say so. Alain Fournier |
#3
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Question about orbital mechanics
Robert Heller writes:
I am writing a program that simulates a planetary system (a star and a group of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? I'm not familiar with the software you're using, but the trajectory of every body in the system is dependant on every other body. If ORSA simplifies this to your spacecraft being in orbit around one other body, it isn't going to be accurate enough to be of any use in most circumstances. But, if you must assume you're only in orbit around one, it'll be the one exerting the most force, ie the one for which M/r^2 (the mass of the body divided by the distance from your spacecraft to that body squared) is greatest. |
#4
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Question about orbital mechanics
On May/16/2016 at 6:50 AM, Joe Pfeiffer wrote :
Robert Heller writes: I am writing a program that simulates a planetary system (a star and a group of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? I'm not familiar with the software you're using, but the trajectory of every body in the system is dependant on every other body. If ORSA simplifies this to your spacecraft being in orbit around one other body, it isn't going to be accurate enough to be of any use in most circumstances. But, if you must assume you're only in orbit around one, it'll be the one exerting the most force, ie the one for which M/r^2 (the mass of the body divided by the distance from your spacecraft to that body squared) is greatest. No that wouldn't be the best choice. Here on Earth, the gravitational force of the Sun is stronger than the gravitational force of the Moon. The Sun has about 27 million lunar mass and the distance from the Earth to the Sun is about 389 times the distance from the Earth to the Moon. So the gravitational force of the Sun is about 27,000,000/(389^2) ≈ 323 times the gravitational pull of the Moon. Yet, when we look at tides, clearly the Moon has a greater effect. I think you would want to use the body for which M/r^4 is the greatest, but I'd have to do some computations to be sure, it might be M/r^3. The reason for this is that, if we take again the example with the Sun and the Moon, the Moon's motion is already affected by the Sun. So if you compute your motion relative to the Moon, the action of the Sun on you is in good part already taken into account by computing your motion relative to the Moon instead of the Sun. But as you have already pointed out, you really would want to do computations using more than one body for this. Alain Fournier |
#5
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Question about orbital mechanics
Alain Fournier writes:
On May/16/2016 at 6:50 AM, Joe Pfeiffer wrote : Robert Heller writes: I am writing a program that simulates a planetary system (a star and a group of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? I'm not familiar with the software you're using, but the trajectory of every body in the system is dependant on every other body. If ORSA simplifies this to your spacecraft being in orbit around one other body, it isn't going to be accurate enough to be of any use in most circumstances. But, if you must assume you're only in orbit around one, it'll be the one exerting the most force, ie the one for which M/r^2 (the mass of the body divided by the distance from your spacecraft to that body squared) is greatest. No that wouldn't be the best choice. Here on Earth, the gravitational force of the Sun is stronger than the gravitational force of the Moon. The Sun has about 27 million lunar mass and the distance from the Earth to the Sun is about 389 times the distance from the Earth to the Moon. So the gravitational force of the Sun is about 27,000,000/(389^2) ≈ 323 times the gravitational pull of the Moon. Yet, when we look at tides, clearly the Moon has a greater effect. But what's relevant to his question isn't tides, it's the earth's orbit -- and the sun clearly has a greater effect than the moon on that! If I were calculating forces on me, the planet would dwarf the forces of either the sun or the moon. It does turn out my answer was wrong anyway -- if I didn't miss a decimal somewhere, the sun exerts roughly twice as much force on earth's moon as the earth does, but you'll get a more accurate model of the moon's orbit calculating it as orbiting the earth (of course). Though, of course, the orbit around the earth is a pretty minor perturbation compared to the orbit around the sun! I think you would want to use the body for which M/r^4 is the greatest, but I'd have to do some computations to be sure, it might be M/r^3. The reason for this is that, if we take again the example with the Sun and the Moon, the Moon's motion is already affected by the Sun. So if you compute your motion relative to the Moon, the action of the Sun on you is in good part already taken into account by computing your motion relative to the Moon instead of the Sun. But as you have already pointed out, you really would want to do computations using more than one body for this. Alain Fournier |
#6
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Question about orbital mechanics
On May/18/2016 at 6:58 AM, Joe Pfeiffer wrote :
Alain Fournier writes: On May/16/2016 at 6:50 AM, Joe Pfeiffer wrote : Robert Heller writes: I am writing a program that simulates a planetary system (a star and a group of planets in orbit about it). I am writing the program in Tcl and I have ported a C program, Stargen (http://www.eldacur.com/~brons/NerdCo.../StarGen.html), to generate the planetary system and part of the ORSA (http://orsa.sourceforge.net/), to perform orbital calculations. At this point I can generate a planetary system and compute the orbits of the planets. I want to add in spacecraft, but I am not sure how to determine a spacecraft's orbit -- for a given position and velocity, which planet (if any) would the spacecraft be in orbit about? I don't know if I should create a 'body' (an ORSA data type/class), with a given mass, position, and velocity for the spacecraft and then compute this body's orbit with each planet and the star (the ORSA library has a method which computes the orbital parameters given a pair of bodies). How do I tell which is the most likely orbit? I'm not familiar with the software you're using, but the trajectory of every body in the system is dependant on every other body. If ORSA simplifies this to your spacecraft being in orbit around one other body, it isn't going to be accurate enough to be of any use in most circumstances. But, if you must assume you're only in orbit around one, it'll be the one exerting the most force, ie the one for which M/r^2 (the mass of the body divided by the distance from your spacecraft to that body squared) is greatest. No that wouldn't be the best choice. Here on Earth, the gravitational force of the Sun is stronger than the gravitational force of the Moon. The Sun has about 27 million lunar mass and the distance from the Earth to the Sun is about 389 times the distance from the Earth to the Moon. So the gravitational force of the Sun is about 27,000,000/(389^2) ≈ 323 times the gravitational pull of the Moon. Yet, when we look at tides, clearly the Moon has a greater effect. But what's relevant to his question isn't tides, it's the earth's orbit -- and the sun clearly has a greater effect than the moon on that! If I were calculating forces on me, the planet would dwarf the forces of either the sun or the moon. It does turn out my answer was wrong anyway -- if I didn't miss a decimal somewhere, the sun exerts roughly twice as much force on earth's moon as the earth does, but you'll get a more accurate model of the moon's orbit calculating it as orbiting the earth (of course). Though, of course, the orbit around the earth is a pretty minor perturbation compared to the orbit around the sun! Yes exactly. I was about to write something around those lines. I myself thought that my tide example was poor and using the Moon's orbit around the Earth is a much better image of why you don't necessarily want to use the body exerting the biggest force. Alain Fournier |
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Question about orbital mechanics
In article ,
Alain Fournier writes: But as you have already pointed out, you really would want to do computations using more than one body for this. In principle, you need to take all bodies in the system into account. Depending on the accuracy desired and on the masses and distances, you may be able to ignore some of the least massive. If you want to know which single body is the most influential, look at references for "Hill Sphere." -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
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Question about orbital mechanics
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#9
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Question about orbital mechanics
On May/29/2016 at 6:18 PM, Joe Pfeiffer wrote:
(Steve Willner) writes: In article , Alain Fournier writes: But as you have already pointed out, you really would want to do computations using more than one body for this. In principle, you need to take all bodies in the system into account. Depending on the accuracy desired and on the masses and distances, you may be able to ignore some of the least massive. If you want to know which single body is the most influential, look at references for "Hill Sphere." Thank you! I hadn't encountered that term (no, I'm not even an amateur astronomer), and what I found made for some interesting reading. Yes it is interesting. But I'm not sure if it is the best answer for the question this thread is concerned with. The Hill Sphere indicates the region where a satellite will orbit the planet. But for computing a spacecraft trajectory, you might prefer to use for a while a planet centric system rather than a Sun centric system even if you are outside the Hill Sphere. The spacecraft will move further away from the planet so that won't last long and you will go back to the Sun centric system. But the planet centric system might be a better approximation of the trajectory for a while. But that is being somewhat pedantic. If you are not to far from the limit of the Hill Sphere, either inside or outside, I simply wouldn't use a single body system as an approximation and go to a multi-body system. Alain Fournier |
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