Space elevator off Europa without running into a nearby moon?

Would it be possible to build a space elevator off Europa?

(The space elevator would only be for the purpose of getting items out of Europa's gravity well relative to Jupiter. At that point, the items would still be in Jupiter's gravity well.)

Length of the elevator:

My first concern was with how long the elevator would need to be. My understanding is that a space elevator on Earth would need to go past the geostationary orbit of Earth. I take it that the same would hold true of building a space elevator on any body...perhaps on Europa we could call this distance the "Europastationary orbit."

It looks like the nearest that any other moon would pass to Europa is Io at 150,000 km. So the "Europastationary orbit" would have to be considerably less than that in order to not be majorly perturbed when Io passes Europa.

To calculate the "Europastationary orbit":

Europa's orbital period around Jupiter is 3.5512 days, and it's tidally locked, so I suppose "Europastationary" orbit would have to be whatever orbit allows a body to orbit Europa every 3.5512 days as well.

The orbital period in seconds is: 3.5512 days x 24 x 3600 = 306,823.68 sec.

The mass of Europa is 4.8 x 10²² kg.

So, I think that using Kepler's Third Law, I can calculate the orbital distance needed: $$a = \sqrt[3]{GMT^2 \over 4\pi^2}$$

(where $a$ is the orbit's semimajor axis, $G$ is the gravitational constant, $M$ is the mass of the more massive body and $T$ is the orbital period)

Which reduces to the cube root of: (6.67 x 10^-11) x (4.8 x 10²²) x (9.4141 x 10¹⁰) / 39.47835 = 19,700 km.

Earth's geostationary orbit is 42,000 km and Europa, having less mass, should yield a smaller number, so maybe I calculated that correctly.

42,000 km is a lot less than 150,000km so maybe we're safe from Io.

Are there any other physical constraints what would be problematic? Or is anything about my understanding/calculations wrong?

I'm not overly concerned with how much it would cost.

posted almost 5 years ago

levininja‭

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