# Synchronous Orbits: Why Does 3:5 Jupiter/Saturn Happen?

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• rootone
In summary, planets and moons can become tidally locked due to gravitational forces. Weird phenomena like 3:5 Jupiter/Saturn orbital resonance occur because of the stable forces that result from having low integer ratios between orbital periods. This mechanism ensures that the orbits of these objects stay in resonance and do not get too close to each other. This is similar to two cars driving on a circular track, where one car will eventually catch up to the other and be forced to slow down, creating a 1:1 ratio over long periods of time. This also explains why some planets may not be in resonance if their orbits are not eccentric enough to be affected by the gravitational forces of other objects. The resonance is an average over time, not a
rootone
Why is that?
It's easy to understand how planets and moons can become tidally locked.
but why do weird things like 3:5 Jupiter/Saturn stuff happen?
Or doesn't it?

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Yes that is what I mean.
Why should they be integer values?

rootone said:
Yes that is what I mean.
Why should they be integer values?
If they were not in an integer ratio ratio of integers, the resulting configuration would not be periodic.

Edited for clarity.

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jbriggs444 said:
If they were not in an integer ratio, the resulting configuration would not be periodic.
5 revolutions by one planet and 3 revolutions by the other would bring them back to the same place.

jbriggs444
We call it resonance when the numbers are low integers.

For all we know, some planets could have resonances in the teens or twenties, but at that point, one could hardly call it resonant.

So do planets settle into approximately (low) integer resonant orbits or not?
If so, then why?

rootone said:
So do planets settle into approximately (low) integer resonant orbits or not?
If so, then why?
Because, with non-integer resonance, they keep pushing and pulling on each other. With resonant orbits, they may push and pull but the forces are stable over long periods.

rootone
DaveC426913 said:
Because, with non-integer resonance, they keep pushing and pulling on each other. With resonant orbits, they may push and pull but the forces are stable over long periods.
Aha, I think I get it. Thanks

I'm not convinced.
If gravity results in quantized orbits, isn't that something we need to know more about?

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Resonant orbits have a mechanism that ensures their periods have perfect integer ratios.
Consider the following analogy. Two cars are on a circular one-lane track. If one of the cars is driving faster than the other, it will eventually catch up to the slower car, and be forced to slow down. It it slows down and becomes the slower car, the other car will eventually catch up, etc. At any moment, their periods might not be exactly 1:1, but over long periods of time it must average 1:1.

Now let's take the case of planets. In the following animation, Neptune is held stationary, and Pluto traces a 3:2 resonant pattern librating around Neptune. For every 3 orbits of the Sun completed by Neptune, Pluto completes 2 orbits. At any given moment, however, the ratio is not exactly 3:2. Sometimes Pluto's period is slightly faster than its average value. Sometimes it is slower.

When Pluto's period is slightly faster than average, the points where its orbit intersects the orbit of Neptune advance with each orbit. But when this intersection gets too close to Neptune, Pluto is accelerated by Neptune's gravity. This causes Pluto to rise into a higher orbit with a longer period. Now orbiting the Sun with a period slightly slower than its average value, the points where Pluto's orbit intersects Neptune's orbit retreat with each orbit. Eventually, it approaches Neptune from the other direction, allowing Neptune's gravity to pull Pluto into a lower orbit with a shorter period. This repeats indefinately, ensuring that Pluto and Neptune never get too close to each other.

Notice the orbit of Uranus (green). It is tracing a 2:1 pattern, but it is not eccentric enough to be locked into resonance. Its apogee is not close enough to Neptune to allow Neptune to significantly speed it up or slow it down. So this 2:1 pattern keeps advancing in the same direction rather than librating like Pluto.

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• pluto2.gif
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rootone
Aha!,
The resonance is an average over time, not a fixed immutable ratio of orbital velocity.
Yep, that does it for me. Thanks

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## 1. What is a synchronous orbit?

A synchronous orbit is an orbit in which two celestial bodies, such as planets, have a specific ratio between their orbital periods. This causes the two bodies to align at regular intervals and have a synchronized relationship.

## 2. What is the significance of a 3:5 Jupiter/Saturn synchronous orbit?

The 3:5 Jupiter/Saturn synchronous orbit is significant because it occurs when the orbital period of Jupiter is three times that of Saturn, resulting in the two planets aligning every 20 years. This alignment is known as the Great Conjunction and has been observed since ancient times.

## 3. Why does the 3:5 Jupiter/Saturn synchronous orbit happen?

The 3:5 ratio between Jupiter and Saturn's orbital periods is a result of their gravitational interactions. As the two planets orbit the Sun, their gravitational pull affects each other's orbits, leading to this specific ratio.

## 4. How is the 3:5 Jupiter/Saturn synchronous orbit calculated?

The 3:5 Jupiter/Saturn synchronous orbit is calculated by dividing the orbital period of Jupiter by the orbital period of Saturn. In this case, the orbital period of Jupiter is approximately 11.86 Earth years, while the orbital period of Saturn is approximately 29.46 Earth years. Dividing 11.86 by 29.46 results in a ratio of 0.403, which is rounded to 3:5.

## 5. Is the 3:5 Jupiter/Saturn synchronous orbit a stable phenomenon?

Yes, the 3:5 Jupiter/Saturn synchronous orbit is a stable phenomenon. The gravitational interactions between the two planets keep them in this specific ratio, and it has been observed for centuries. However, other factors such as the gravitational pull of other planets and small variations in orbital periods may cause slight changes over time.

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