<p>From the Keplerian-Newtonian two-body approximation (which is more than good enough for most fictional worldbuilding), eccentricity doesn't matter for orbital period. When the mass of the satellite is small enough to be ignorable, all orbits with the same semi-major axis around the same central body have the same period, regardless of eccentricity, periapsis distance, or apoapsis distance.</p>
<p>Add the periapsis distance to the apoapsis distance, and divide the resulting value by 2. That will give you the semi-major axis to plug into the orbital period formula.</p>

CC BY-SA 4.0
2023-02-27T16:32:22.337Z
Using the mass given on Wikipedia I get 451±13 days. FWIW, I wrote some code for an earlier version of this planet, but it's easy to edit it with the new eccentricity & year length. https://chat.stackexchange.com/transcript/message/63018222#63018222
PM 2Ring
CC BY-SA 4.0
2023-02-27T12:43:59.570Z
2023-02-27T19:46:40.607Z
2023-02-27T19:46:40.607Z
notovny
<p>I'm continuing my inquiry about the fictional planet I have described here: <a href="https://worldbuilding.stackexchange.com/questions/231162/length-of-seasons-on-a-planet-with-eliptical-orbit">https://worldbuilding.stackexchange.com/questions/231162/length-of-seasons-on-a-planet-with-eliptical-orbit</a>.</p>
<p>I'm now settled on the planet orbiting Delta Pavonis. According to data from Wikipedia and calculations, the habitable zone is from 0.78 to 1.56 AU.</p>
<p>My question is, what would be this planet's orbital period, keeping orbital eccentricity as high as possible while the planet stays within the habitable zone at all times?</p>
<p>I have tried calculating this using WolframAlpha, but it provides only formulae with the semi-major axis and primary and secondary mass, not eccentricity nor perihelion &amp; aphelion distances.</p>

<orbital-elements><habitable-zone>
Orbital period of a planet orbiting Delta Pavonis in habitable zone
Krišjānis Liepiņš
# Orbital period of a planet orbiting Delta Pavonis in habitable zone

(Asked by: username_0 on 2023-02-27)

I'm continuing my inquiry about the fictional planet I have described here: <https://worldbuilding.stackexchange.com/questions/231162/length-of-seasons-on-a-planet-with-eliptical-orbit>.

I'm now settled on the planet orbiting Delta Pavonis. According to data from Wikipedia and calculations, the habitable zone is from 0.78 to 1.56 AU.

My question is, what would be this planet's orbital period, keeping orbital eccentricity as high as possible while the planet stays within the habitable zone at all times?

I have tried calculating this using WolframAlpha, but it provides only formulae with the semi-major axis and primary and secondary mass, not eccentricity nor perihelion & aphelion distances.

**Tags:** orbital-elements, habitable-zone


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## 1 answers

### Answer by username_1 on 2023-02-27. Score: 7 | Accepted answer

From the Keplerian-Newtonian two-body approximation (which is more than good enough for most fictional worldbuilding), eccentricity doesn't matter for orbital period. When the mass of the satellite is small enough to be ignorable, all orbits with the same semi-major axis around the same central body have the same period, regardless of eccentricity, periapsis distance, or apoapsis distance.

Add the periapsis distance to the apoapsis distance, and divide the resulting value by 2. That will give you the semi-major axis to plug into the orbital period formula.

> **Comments:**
> **username_2**: Using the mass given on Wikipedia I get 451±13 days. FWIW, I wrote some code for an earlier version of this planet, but it's easy to edit it with the new eccentricity & year length. https://chat.stackexchange.com/transcript/message/63018222#63018222  

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