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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: kepler on 26/09/2016 02:37:28

Title: How does one calculate velocity when using spherical coordinates?
Post by: kepler on 26/09/2016 02:37:28

Hi,

I have a little doubt. I have, refered to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values in 3D dimensional space). I can easely calculate the polar coordinates (longitude and latitude - along with distance). My doubt is: how do I calculate the longitude and latitude speed in degrees/radians given the cartesian values? Is it the same way? I'm sorry for this stupid doubt....

Kind regards,

Kepler

Title: Re: Cartesian positions and velocities
Post by: chiralSPO on 26/09/2016 03:54:46

Yes, that's somewhat tricky!

It is certainly possible to calculate velocities using polar (spherical) coordinates, but it ends up (as far as I know) essentially involving a conversion from spherical to cartesian coordinates. This is fairly easy to do if the radius is not changing, just the latitude and longitude are changing with time--you can essentially convert from degrees (or radians) per unit time to distance per unit time (in the simplest case, where an object is moving in a great circle, the velocity and angular velocity are related only by the radius)

It gets more complicated if all three coordinates are changing. If the function of the motion is defined, it can be worked out from the function (ie parametric equations for r(t), [phi](t), and [theta](t))

PS: welcome to the forum! I have modified the title of this thread to be a question. Please, from now on when you start threads, make the title as a question posed. Thank you!

Title: Re: How does one calculate velocity when using spherical coordinates?
Post by: William McC on 26/09/2016 04:56:22

Quote from: kepler on 26/09/2016 02:37:28

Hi,

I have a little doubt. I have, refered to the Sun, the cartesian positions and velocities of an asteroid (in x, y and z coordinates - 6 values in 3D dimensional space). I can easely calculate the polar coordinates (longitude and latitude - along with distance). My doubt is: how do I calculate the longitude and latitude speed in degrees/radians given the cartesian values? Is it the same way? I'm sorry for this stupid doubt....

Kind regards,

Kepler

I was under the impression most asteroids travel in an elliptical orbit and their velocity is not constant at all.

Are you trying to calculate a short part of its journey? That should be fairly simple, basically the length of the curve or sequential curves that make up its path traveled over a given time.

Sincerely,

William McCormick

Title: Re: How does one calculate velocity when using spherical coordinates?
Post by: evan_au on 26/09/2016 11:27:40

Hello, Kepler.... It's been some time since you were last seen - are you a long-period comet?

If it is a known object that approaches the Earth, you can find out about it here:
http://neo.jpl.nasa.gov/orbits/

A more complete list of known objects (including ones that don't approach the Earth) are cataloged here:
http://minorplanetcenter.net/

You can use some web tools here: https://janus.astro.umd.edu/AW/awtools.html#5a

If you want software you can run yourself, try here:
http://www.projectpluto.com/find_orb.htm#Others

Title: Re: How does one calculate velocity when using spherical coordinates?
Post by: jeffreyH on 27/09/2016 11:56:11

You can download a very informative PDF covering the subject at the following url.

https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf (https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf)