Register to reply 
Turn a sinusoid into a elliptic orbit 
Share this thread: 
#1
Sep2013, 11:38 AM

P: 366

I am trying to get my head around these equations. I am not sure they are correct. My logic is an orbit exists at a starting point (x0,y0,z0) with a starting velocity at time zero (vx0,vy0,vz0) changing with time (dx/dt, dy/dt, dz/dt). The gravity is (d^2x/dt^2, d^2y/dt^2, d^2z/dt^2). How do you turn a sinusoid into a elliptic orbit?
x = (1 / 2 * G * M / r ^ 2 * Cos(h) * Cos(p)) * t ^ 2 + vx0 * t + x0 y = (1 / 2 * G * M / r ^ 2 * Sin(h) * Cos(p)) * t ^ 2 + vy0 * t + y0 z = (1 / 2 * G * M / r ^ 2 * Sin(p)) * t ^ 2 + vz0 * t + z0 where r=(x^2+y^2+z^2)^0.5 h=atan(y/x) p=acos(z/r) 


#2
Sep2013, 07:38 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,739

You know how this works if the plane of the orbit is the xy plane right? However, I think you have been too general in your setup. Gravity is usually a central force  always directed to some point  with a magnitude that depends on the distance to that center. You write that down and apply Newton's Laws. There are several possible shapes  the stable ellipse is usually quite tricky to hit on by trail and error. 


#3
Sep2213, 02:11 AM

P: 366

Which is the correct postulation in Newtonian 2 Body solution:
h=atan(y/x) p=acos(z/r) or h=atan(vy/vx) p=acos(vz/vr) where vr = (vx^2+vy^2+vz^2)^0.5 


#4
Sep2213, 03:28 AM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,739

Turn a sinusoid into a elliptic orbit
Depends what you want h and p to represent.
The former are the angles to the position and the second to the velocity. They do not appear to represent any kind of postulates, and are not specific to the twobody problem. 


#5
Sep2213, 06:37 AM

Mentor
P: 15,147

The correct solution was found by Kepler. Why do you persist in avoiding that solution? 


#6
Sep2213, 06:46 AM

Mentor
P: 17,202




#7
Sep2313, 04:56 AM

P: 366

Then how do you find the equations for x,y,z, xdot, ydot, zdot, rdot thetadot, phidot, xdoubledot, ydoubledot, zdoubledot, rdoubledot, thetadoubledot, and phidoubledot with nonuniform acceleration?



Register to reply 
Related Discussions  
Elliptic orbit of a Satellite  Introductory Physics Homework  20  
Elliptic orbit of earth round the sun  Astronomy & Astrophysics  1  
Elliptic orbit proofs  Advanced Physics Homework  0  
Circularelliptic orbit  Advanced Physics Homework  8  
Elliptic orbit from empty focus  Advanced Physics Homework  0 