<p>You must solve the <a href="http://mathworld.wolfram.com/KeplersEquation.html" rel="nofollow">Kepler's equation</a>:</p>

<p>$M = E - e \sin E$</p>

<p>(where $M$ is the <em>mean anomaly</em>, $e$ the <em>eccentricity</em> of the orbit, $E$ the <em>eccentric anomaly</em>).
As you can see, this is a <a href="http://en.wikipedia.org/wiki/Transcendental_equation" rel="nofollow">transcendental function</a>, so you will probably need to iterate through a calculator, in order to solve it.
Many of useful formulas to understand the parameters dependence are reported on the <a href="http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Formulary" rel="nofollow">Wikipedia page</a> as well. </p>

<p><a href="http://www.bogan.ca/orbits/kepler/keplerex.html" rel="nofollow">Here</a> is another page with some examples. Just use the formulas and try to play with numbers, at some point you will realize at least orders of magnitude of the binary system elements.</p>

CC BY-SA 3.0
2014-11-21T05:03:00.717Z
2015-11-30T22:22:09.850Z
2015-11-30T22:22:09.850Z
Py-ser
<p>I'm not sure how much this will help, but I can give you <a href="http://en.wikipedia.org/wiki/Orbital_elements#Orbit_prediction" rel="nofollow">this passage</a> from Wikipedia:</p>

<blockquote>
  <p>Under ideal conditions of a perfectly spherical central body, and zero perturbations, all orbital elements, with the exception of the Mean anomaly are constants, and Mean anomaly changes linearly with time[dubious – discuss], scaled by the Mean motion, $n=\sqrt{\frac{\mu } {a^3}}$. Hence if at any instant $t_0$ the orbital parameters are $[e_0,a_0,i_0,\Omega_0,\omega_0,M_0]$, then the elements at time $t_0+\delta t$ is given by $[e_0,a_0,i_0,\Omega_0,\omega_0,M_0+n\delta t]$.</p>
</blockquote>

<p>In other words, most of the orbital elements (save $M_0$) are constant under very short intervals.</p>

CC BY-SA 3.0
2014-11-21T01:42:54.890Z
2014-11-21T01:42:54.890Z
HDE 226868
<p>In a model of the solar system, given the Sun is at the point $(0, 0, 0)$, an given the six orbital elements for each object in orbit ($a$, $\epsilon$, $i$, $\Omega$, $\omega$, $M_0$), how can I calculate the relative position to the sun at a given time $t$?</p>

<orbit><orbital-elements>
How do I calculate the positions of objects in orbit?
vcapra1
# How do I calculate the positions of objects in orbit?

(Asked by: username_0 on 2014-11-21)

In a model of the solar system, given the Sun is at the point $(0, 0, 0)$, an given the six orbital elements for each object in orbit ($a$, $\epsilon$, $i$, $\Omega$, $\omega$, $M\_0$), how can I calculate the relative position to the sun at a given time $t$?

**Tags:** orbit, orbital-elements

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## 2 answers

### Answer by username_1 on 2014-11-21. Score: 3 | Accepted answer

You must solve the [Kepler's equation](http://mathworld.wolfram.com/KeplersEquation.html):

$M = E - e \sin E$

(where $M$ is the *mean anomaly*, $e$ the *eccentricity* of the orbit, $E$ the *eccentric anomaly*).
As you can see, this is a [transcendental function](http://en.wikipedia.org/wiki/Transcendental_equation), so you will probably need to iterate through a calculator, in order to solve it.
Many of useful formulas to understand the parameters dependence are reported on the [Wikipedia page](http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Formulary) as well.

[Here](http://www.bogan.ca/orbits/kepler/keplerex.html) is another page with some examples. Just use the formulas and try to play with numbers, at some point you will realize at least orders of magnitude of the binary system elements.


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### Answer by username_2 on 2014-11-21. Score: 1

I'm not sure how much this will help, but I can give you [this passage](http://en.wikipedia.org/wiki/Orbital_elements#Orbit_prediction) from Wikipedia:

> Under ideal conditions of a perfectly spherical central body, and zero perturbations, all orbital elements, with the exception of the Mean anomaly are constants, and Mean anomaly changes linearly with time[dubious – discuss], scaled by the Mean motion, $n=\sqrt{\frac{\mu } {a^3}}$. Hence if at any instant $t\_0$ the orbital parameters are $[e\_0,a\_0,i\_0,\Omega\_0,\omega\_0,M\_0]$, then the elements at time $t\_0+\delta t$ is given by $[e\_0,a\_0,i\_0,\Omega\_0,\omega\_0,M\_0+n\delta t]$.

In other words, most of the orbital elements (save $M\_0$) are constant under very short intervals.


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