<p>Yes. They can, for instance, have circular orbits, in which case those circles would be concentric and never intersect.</p>
<p>For arbitrarily eccentric orbits there will be some maximum value of the eccentricity, that depends on the mass ratio, which will mean that one orbit can be nested inside the other.</p>

CC BY-SA 4.0
2024-10-18T12:15:57.980Z
2024-10-18T12:15:57.980Z
ProfRob
<blockquote>
<p>Two stars are orbiting each other in elliptical orbits. The primary star is 4 solar masses and the secondary star is 3 solar masses. What is the condition for their eccentricity so that the orbits of both stars don't intersect?</p>
</blockquote>
<p>I was doing homework for binary stars and this was one of the question, is it possible for a binary system to have 2 stars that their orbits don't intersect each other? If so can you guys tell me how that could happen? Or is it a mistake made by the person who gave the question?</p>

CC BY-SA 4.0
2024-10-18T12:12:05.277Z
Sure. See the 2nd diagram in my answer here: https://physics.stackexchange.com/a/558847/123208
PM 2Ring
CC BY-SA 4.0
2024-10-18T13:57:07.363Z
Maybe better tell us why would you think they had to, because it's obvious the don't...
Mithoron
CC BY-SA 4.0
2024-10-18T14:55:21.430Z
Here's an example with eccentricity 1/3 & mass ratio 1:2 where the orbits just touch. https://i.sstatic.net/4avXdzqL.png
PM 2Ring
<orbit><binary-star>
Can 2 binary stars have orbits that don't intersect each other?
Huy Tran
# Can 2 binary stars have orbits that don't intersect each other?

(Asked by: username_0 on 2024-10-18)

> Two stars are orbiting each other in elliptical orbits. The primary star is 4 solar masses and the secondary star is 3 solar masses. What is the condition for their eccentricity so that the orbits of both stars don't intersect?

I was doing homework for binary stars and this was one of the question, is it possible for a binary system to have 2 stars that their orbits don't intersect each other? If so can you guys tell me how that could happen? Or is it a mistake made by the person who gave the question?

**Tags:** orbit, binary-star
> **Comments:**
> **username_1**: Sure. See the 2nd diagram in my answer here: https://physics.stackexchange.com/a/558847/123208  
> **username_2**: Maybe better tell us why would you think they had to, because it's obvious the don't...  
> **username_1**: Here's an example with eccentricity 1/3 & mass ratio 1:2 where the orbits just touch. https://i.sstatic.net/4avXdzqL.png  

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## 1 answers

### Answer by username_3 on 2024-10-18. Score: 4

Yes. They can, for instance, have circular orbits, in which case those circles would be concentric and never intersect.

For arbitrarily eccentric orbits there will be some maximum value of the eccentricity, that depends on the mass ratio, which will mean that one orbit can be nested inside the other.


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