<p>Just to clarify, inner planets usually refers to Mercury, Venus, Earth, Mars.    But in relation to your question, the "inner" planets are just Mercury and Venus and the outer planets are Mars and out, because the +1 / -1 formula is in relation to whether the Earth is passing the planet as it orbits the sun or being passed by the planet.   </p>

<p>Someone else can do the math if they like, the gist is explained <a href="http://astronomyonline.org/Science/SiderealSynodicPeriod.asp" rel="nofollow noreferrer">here</a>.  Because it's the motion relative to the stars in the background that you're tracking, anything that orbits closer to the sun and faster than Earth would move in a different direction and require a different formula than orbits further out and slower.</p>

<p>If your asteroid remains outside the Earth's orbit, then it would obey the outer planet formula.</p>

<p>If your asteroid is an <a href="https://en.wikipedia.org/wiki/List_of_Earth-crossing_minor_planets" rel="nofollow noreferrer">Earth crosser</a>, which isn't uncommon, then it would have a different type of orbital period that would follow neither formula, and I'm not sure what formula would apply for an earth-crossing asteroid.</p>

CC BY-SA 3.0
2017-05-17T15:05:53.450Z
Yeah, I can just see trying to calculate synodic for Halley's Comet !  I bet it can complete quite a few of its sideral orbits before showing up in exactly the same place in the Terran sky.
Carl Witthoft
CC BY-SA 3.0
2017-05-17T18:50:19.590Z
@CarlWitthoft When Halley's remains well outside the orbit of the Earth it should be mostly similar to an outer planet with a sidereal orbit similar to Uranus or Neptune.   It just gets weird when it gets close and crosses the Earth's orbit.   The apparent motion from our point of view, might be like part of a horse-shoe orbit (I would guess).    The sidereal formulas mentioned above, don't account for eccentricity, so they're just approximations.  (and sorry for the "I thinks", but I prefer to go that route when I'm not certain.)
userLTK
CC BY-SA 3.0
2017-05-17T02:53:02.807Z
2017-05-17T02:53:02.807Z
userLTK
<p>What's the orbital period of an asteroid which has synodic period of 429 days?</p>

<p>I know that the formula of orbital period for inner planets is $$P_{orb} = \frac{P_{syn}}{P_{syn} + 1}$$ and for outer planets is $$P_{orb} = \frac{P_{syn}}{P_{syn} - 1}$$ where $P_{syn}$ is the synodic period of the planet measured in years. However, I don't know whether the asteroid should be counted as an inner planet or outer planet.</p>

<asteroids>
Orbital Period of an Asteroid
MZ4Frost
# Orbital Period of an Asteroid

(Asked by: username_0 on 2017-05-16)

What's the orbital period of an asteroid which has synodic period of 429 days?

I know that the formula of orbital period for inner planets is $$P\_{orb} = \frac{P\_{syn}}{P\_{syn} + 1}$$ and for outer planets is $$P\_{orb} = \frac{P\_{syn}}{P\_{syn} - 1}$$ where $P\_{syn}$ is the synodic period of the planet measured in years. However, I don't know whether the asteroid should be counted as an inner planet or outer planet.

**Tags:** asteroids

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## 1 answers

### Answer by username_1 on 2017-05-17. Score: 1

Just to clarify, inner planets usually refers to Mercury, Venus, Earth, Mars. But in relation to your question, the "inner" planets are just Mercury and Venus and the outer planets are Mars and out, because the +1 / -1 formula is in relation to whether the Earth is passing the planet as it orbits the sun or being passed by the planet.

Someone else can do the math if they like, the gist is explained [here](http://astronomyonline.org/Science/SiderealSynodicPeriod.asp). Because it's the motion relative to the stars in the background that you're tracking, anything that orbits closer to the sun and faster than Earth would move in a different direction and require a different formula than orbits further out and slower.

If your asteroid remains outside the Earth's orbit, then it would obey the outer planet formula.

If your asteroid is an [Earth crosser](https://en.wikipedia.org/wiki/List_of_Earth-crossing_minor_planets), which isn't uncommon, then it would have a different type of orbital period that would follow neither formula, and I'm not sure what formula would apply for an earth-crossing asteroid.

> **Comments:**
> **username_2**: Yeah, I can just see trying to calculate synodic for Halley's Comet !  I bet it can complete quite a few of its sideral orbits before showing up in exactly the same place in the Terran sky.  
> **username_1**: @CarlWitthoft When Halley's remains well outside the orbit of the Earth it should be mostly similar to an outer planet with a sidereal orbit similar to Uranus or Neptune.   It just gets weird when it gets close and crosses the Earth's orbit.   The apparent motion from our point of view, might be like part of a horse-shoe orbit (I would guess).    The sidereal formulas mentioned above, don't account for eccentricity, so they're just approximations.  (and sorry for the "I thinks", but I prefer to go that route when I'm not certain.)  

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