# Distance from Jupiter to minimize destructive tidal forces

There is a video from "What If" that tells about (precisely) "What if Earth was a moon of Jupiter":
What if the Earth Was a Moon of Jupiter

And, in a short story I am writing in an alternate reality I have more or less that scenario: Jupiter is located from the Sun in the Earth orbit, and Earth is a moon of Jupiter. (The video above talks about the effects of Earth as a moon of Jupiter in the current Jupiter orbit).
My question is: Supposing Jupiter is in current Earth´s orbit, and the Earth is a moon of Jupiter: At what distance should Earth be orbiting Jupiter to minmize the destructive tidal forces?

I know there have been some other similar questions in the past. For example this:
Conditions for human life in a Jupiter-like system

But in this case, I am specifically asking for a safe orbit distance (kilometers), and that datum has not been asked before (as far as I could find).

I'm struggling with a similar problem at the moment. I want to put an habitable earth-like moon around a gas giant like Jupiter. Since I studied physics I can do the celestial mechanics part (but that seems to be the easy bit).

Here is what I have so far:
Earth needs to be away farther than the so called Roche Limit which is the distance where the planet's tidal forces would just rip the moon apart. But from my calculations this should not be a problem, as the earth would orbit the gas giant at least with the distance Earth-Moon, depending on the orbit period chosen which lies outside this danger zone.

Another thing to consider: tidal locking. Very often the moons the larger planets are tidally locked. Their orbit time is equal to the rotation time. If earth would be a tidally locked moon of Jupiter I think there should be no problem with tidal forces; in fact we would not see its effects. The tidal lock means the same side of earth would face Jupiter all the time and thus no tides would move "around" on the planet like they do currently on Earth. But it gets problematic when you place other bodies beside Earth in an orbit around Jupiter. Currently, the inner moons of Jupiter (Ganymede, Europa and Io) are very tidally active because they interact with each other. I do not have a concrete solution for handling this yet.

Another remark: putting Jupiter in an earth-like orbit around the sun would most likely change Jupiter form a Gas Giant Class 1 to a Gas Giant Class 2, which would appear more white-blueish.

Hope this helps you.

• Hello Amalev. Whilst your answer is fine, somehow the phrase "I'm struggling with a similar problem at the moment" tripped an automatic referral of your answer to the low quality review queue. It might be best to avoid personal asides in future. Enjoy the site. Apr 13, 2020 at 9:50

Of the many standards we have, there is no standard for a "safe tidal force". We have then to look around for a suitable reference. You are lucky, we have one right above our heads!

The Moon is subjected to Earth tidal forces, but aside of the tidal bulge on the side facing Earth, it doesn't seem to suffer from particular damages.

I would then say, let's take it as reference: the tidal forces from Earth at Moon distance are safe. What does it mean for Jupiter?

Using Newton formula, we get that $$G_{Moon}=(G \cdot m_{E}) / r_{EM}^2$$

To have that pull with Jupiter, we would need to be at a distance $$r_J=\sqrt {G\cdot m_J / G_{Moon}}=\sqrt{r_{EM}^2 \cdot m_J/m_E}=r_{EM}\cdot \sqrt{m_J/m_E}$$.

Put in the numbers, and you get a distance of about $$7.25 \cdot 10^6$$ km from the center of Jupiter. That's 1% of the distance between Jupiter and the Sun.

• Just as a spot-check, the L1 Lagrange point between the Sun and Jupiter at 1 AU would be just under 10M km from Jupiter, so an orbit at 7.25M km should be possible. Interestingly, the Earth's orbital period around Jupiter at that distance would be ~126 days, so you'd have just under three months per year. Apr 13, 2020 at 8:44
• I think this is a good answer on the right track, but the formulas used aren't quite right. Because tidal forces have to do with gradients in the gravitational field, rather than the field itself, in general they go like $1/r^3$ rather than $1/r^2$. Also, they depend on the size of the body, although that doesn't matter here since in both cases it's just the radius of Earth. The Wikipedia article on tidal forces has a few useful formulas for this in the last section. Apr 13, 2020 at 12:35
• This is a great starting point! (and thanks for that!), however, I know that most of the intense physical "punishment" of 3 of the main Jupiter moons (Io, Europa and Ganymede) are due to the orbital resonance between themselves. And on the other hand: Callisto (at aprox. 941,000 Km from the center of Jupiter) has very little tidal heating (if any) and no geological activity at all. So I think there should be a possibility for a safe closer orbit (closer than 7.25 e6 km) for an Earth-like moon. Apr 13, 2020 at 16:34