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My settlement on Jupiter's moon Ganymede is to get a space elevator. Unfortunately, I am completely overwhelmed with the math: How long would the cable have to be to the stationary anchor point in orbit? And would this point still be within the magnetic field of Ganymede (which is favourably extended at the equatorial regions, as far as we know today)?

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You are looking for where $ \omega^2 \cdot r = GM \div r^2 $ or, more to the point, $ r = \sqrt[3]{GM \div \omega^2 }$

Ganymede has a mass (M) of $ 1.48 \times 10^{23} $ kilograms; its rotational velocity ($ \omega $) is one revolution per 7.1 days- 0.00024582 radians per second; and the gravitational constant (G) is $ 6.67 \times 10^{-11} $

That should be a "r" of 5,466 kilometers from Ganymede's core, about 2,832 kilometers from the surface.

What about a counterweight? If you have something heavy, like Apophis (300 meter diameter-- approx 98.9 million tons), the counterweight can be parked just 912 meters further down the line and you'll be good (assuming you are using untapered cable made of 7,000 kg per cubic meter steel).

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  • $\begingroup$ That would be just inside the magnetosphere of Ganymede and exactly what is needed here. $\endgroup$
    – domai2312
    May 10 at 21:15
  • $\begingroup$ Hey. I was redoing this math for a book and realized I'd forgotten to convert days to hours in the above answer. The actual geosynchronous orbit (minimum elevator length) is 45,503. But, you could put a 2,121 km space elevator starting on the ground and endong at either the Jupiter-Ganymede L1 with a counterweight hanging down Jupiter's gravity well, or on the L2 at the same length taking advantage of Ganymede's own centrifugal force around Jupiter. Sorry for the mistake. $\endgroup$ Jul 22 at 12:05
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    $\begingroup$ Still working out kinks in the math. Accordinv to this calculator, the Ganymede L1 should be at 31 thousand kilometers - orbitsimulator.com/formulas/LagrangePointFinder.html $\endgroup$ Jul 22 at 13:39
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With Ganymede having a rotation period the same as its orbit (roundly a week), and all the other moons in the system, there isn't really a stationary orbit, but there's something better: your elevator can stretch to the Ganymede/Jupiter L1 point, the quasi-stable location where Jupiter's and Ganymede's gravity fields cancel each other. Alternatively, you could go for the L2, where the addition of the two fields gives a quasi-stable region further from Jupiter with the same orbital period as Ganymede.

Your counterweight would have to go well beyond that point, of course, but once you haul your payload (ship) up to that point, you're not just in orbit, you've escaped Ganymede entirely into free orbit of the Jupiter system.

You would probably not, however, be usefully within Ganymede's magnetic protection; instead, you'd be fully exposed to Jupiter's radiation (but then you'd need shielding from that even to get to Europa and Callisto, never mind escaping the Jovian moon system).

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