Hi, I'm new to this forum and I've got a question.
In all articles I've found about the two body problem, they first start off by writing the distances between the masses as one function r(t) and one function R(t) (which is just simple the position of the reference frame).
*note: i use initial position and speed to calculate the orbit equation*
Then they go to the central force problem and solve the equation of the orbit of a reduced mass (μ). This is a pretty complicated calculation, but eventually they all end up with the same polar equation:
[itex]r(θ) = \frac{p}{1+ε*cos(θ-θ0)}[/itex]
where:
[itex]p = L^2 / k[/itex] and [itex]L[/itex] is the angular momentum which is the cross product of speed and position wich is equal to [itex]L= r * v * sin(α)[/itex] where r and v are absolute values (the length's of the vectors). k is some constant [itex]G*M[/itex] in this case.
ε and θ0 can be expressed with the same values r, v and α, shown on this site http://upload.wikimedia.org/wikipedi..._Mechanica.pdf page 242 (it's in Dutch, sorry). I evuentually ended up making a 'geogebra applet' which calculates the path with the orbit equation of the reduced mass.
Now I want to go back to the two body problem, but I don't know which values r, v and α to use. Which values should I use??
Any help would be appreciated!
(if anybody is interested, I will post the geogebra file too)
Thanks in advance,
physics2.0
In all articles I've found about the two body problem, they first start off by writing the distances between the masses as one function r(t) and one function R(t) (which is just simple the position of the reference frame).
*note: i use initial position and speed to calculate the orbit equation*
Then they go to the central force problem and solve the equation of the orbit of a reduced mass (μ). This is a pretty complicated calculation, but eventually they all end up with the same polar equation:
[itex]r(θ) = \frac{p}{1+ε*cos(θ-θ0)}[/itex]
where:
[itex]p = L^2 / k[/itex] and [itex]L[/itex] is the angular momentum which is the cross product of speed and position wich is equal to [itex]L= r * v * sin(α)[/itex] where r and v are absolute values (the length's of the vectors). k is some constant [itex]G*M[/itex] in this case.
ε and θ0 can be expressed with the same values r, v and α, shown on this site http://upload.wikimedia.org/wikipedi..._Mechanica.pdf page 242 (it's in Dutch, sorry). I evuentually ended up making a 'geogebra applet' which calculates the path with the orbit equation of the reduced mass.
Now I want to go back to the two body problem, but I don't know which values r, v and α to use. Which values should I use??
Any help would be appreciated!
(if anybody is interested, I will post the geogebra file too)
Thanks in advance,
physics2.0