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Question about orbital mechanics



 
 
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  #1  
Old May 16th 16, 01:39 AM posted to sci.space.tech
Robert Heller
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Posts: 17
Default 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?

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  #2  
Old May 16th 16, 11:50 AM posted to sci.space.tech
Alain Fournier[_3_]
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Posts: 548
Default 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  
Old May 16th 16, 11:50 AM posted to sci.space.tech
Joe Pfeiffer
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Posts: 23
Default 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  
Old May 17th 16, 03:25 AM posted to sci.space.tech
Alain Fournier[_3_]
external usenet poster
 
Posts: 548
Default 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  
Old May 18th 16, 11:58 AM posted to sci.space.tech
Joe Pfeiffer
external usenet poster
 
Posts: 23
Default 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  
Old May 19th 16, 02:12 AM posted to sci.space.tech
Alain Fournier[_3_]
external usenet poster
 
Posts: 548
Default 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

  #7  
Old May 29th 16, 11:52 AM posted to sci.space.tech
Steve Willner
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Posts: 1,172
Default 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

  #9  
Old May 31st 16, 03:12 AM posted to sci.space.tech
Alain Fournier[_3_]
external usenet poster
 
Posts: 548
Default 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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