# How to calculate the velocity vector components of a planet?

I'm trying to use this web site to make a DeltaV calculator but i've got stuck into calculating the velocity vector of the origin planet. Particulary i'm refering to the problem 5.6 described here where the velocity vector is given as VP = 25876.6X + 13759.5Y m/s. The problem is, how do i calculate it? I only know when i'm going to launch my spacecraft and from which planet. Of that planet i've already calculated the position vector. I haven't studied physics so if you can, keep it simple and, if you introduce new values, explain how to calculate them. Thanks!

## 2 Answers

If you're going between a planet and a moon of that planet, it's easiest to treat the planet as stationary. For planet to planet (or moon to moon) transfers within a system, if you don't need great accuracy, you can use circular orbit velocity (https://en.wikipedia.org/wiki/Circular_orbit#Velocity) as an approximation.

Complication increases rapidly beyond that. This paper is the best walk-through I've found for converting from Keplerian orbital elements to Cartesian position and velocity coordinates: https://downloads.rene-schwarz.com/download/M001-Keplerian_Orbit_Elements_to_Cartesian_State_Vectors.pdf -- it explains a great deal, but there are still some tricky bits.

• I'd like to use the math on that web site to keep on with my project. So if there is a way to break that value into x, y and z components that would be perfect. – Dottor_K Jun 2 '16 at 15:53
• I'm going to use the paper you suggested me, thanks! – Dottor_K Jun 2 '16 at 16:10
• Since you're a new user, be sure to accept the answer by clicking the grey checkmark to the left, if it answered your question. – Organic Marble Jun 2 '16 at 16:28
• thanks for the suggestion. Btw i've found out i'm an idiot. I've spent the last week writing javascript code to solve the gauss problem to find out the velocity vector of a satellite from 2 position vector and the time bewteen those, and now i'm looking all over the web to calculate the velocity vector for a planet -.- It's sad to be the kind of person not smart enough to do this kind of things, but still trying xD – Dottor_K Jun 2 '16 at 17:17
• @Dottor_K It takes time. Lots of things seem obvious once you've figured them out. Welcome to Space Exploration. – kim holder Jun 3 '16 at 15:55

To get magnitude of velocity vector use the Pythagorean theorem. $c=\sqrt{a^2 + b^2}$

In this case the speed is 29307.38 meters per second or 29.3 km/s. (sounds like earth).