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Thread: Tidal effects in a large orbiting habitat

  1. #1
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    Tidal effects in a large orbiting habitat

    Here's a tricky one.
    I've conceived an idea for a large orbiting habitat, hundreds of kilometres long, extending both inwards and outwards from the centre of mass so that the extremities experience significant tidal effects. This would manifest as a small amount of apparent gravity at each end, perhaps enough to make habitation slightly more comfortable in those locations.
    Here's an image of how I imagine these structures, probably not quite to scale.
    https://orionsarm.com/im_store/macrostats%20april.png

    How would I calculate the apparent gravity at each end of such a structure? Assume each structure is 400 km long, and with a centre of mass orbiting 2000km above the Earth.

  2. #2
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    So you have an orbital period (P) for the centre of mass of such a structure, from which you can derive an angular velocity, omega=(2*pi)/P, which applies to the whole structure.
    Work out the radius of gyration (r) for each end of your structure, by adding or subtracting half its length to its orbital radius. Then, for each end of your structure, derive the gravitational acceleration from GM/r^2, and the centrifugal force from r*omega^2. The difference is your tidal gravity.

    Grant Hutchison

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    That's great; thanks!

    I figure the apparent gravity at the bottom is about 0.042g in my example, and 0.04g at the top. A bit more than the gravity on the moon Titania; a bit more than I expected. Nice.

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    It might be worth analyzing this to determine whether there is a material strong enough to not collapse on itself by its own gravity (or be pulled apart by the differential gravitation) in a 400 km long structure. You'll also have some interesting electrical effects if it is made of something conductive.
    Forming opinions as we speak

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    If the gravity is only 0.04 gees at each end I wouldn't be too worried about structural integrity. The electrical effects might even be useful, as a method of powering the habitat. I wonder about atmospheric braking though; a structure this large would slow down gradually and re-enter, unless it somehow maintained its orbit actively.

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    How about having a long tether pointing outwards with a counterweight that would pull the habitat 'upwards', counteracting the tendency for the habitat to aerobrake?

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    Quote Originally Posted by eburacum45 View Post
    If the gravity is only 0.04 gees at each end I wouldn't be too worried about structural integrity.
    Yes, the self-supporting length of steel wire at 1g is about 50km, which translates to 1250km for a structure under uniform 0.04g along its length (which your habitat isn't). So it seems you have a fair amount of structural reserve without needing any exotic materials.

    Grant Hutchison

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    Quote Originally Posted by eburacum45 View Post
    How about having a long tether pointing outwards with a counterweight that would pull the habitat 'upwards', counteracting the tendency for the habitat to aerobrake?
    I think that just delays the evil day. If your habitat is aerobraking then it's losing energy, so its orbit will decay no matter where its centre of mass is. You're going to need active manoeuvring, I think.

    Grant Hutchison

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    Quote Originally Posted by eburacum45 View Post
    How about having a long tether pointing outwards with a counterweight that would pull the habitat 'upwards', counteracting the tendency for the habitat to aerobrake?
    You might consider electrodynamic tethers, powered by reactors, perhaps, but thatís a lot of mass to lift. Though . . . for Earth 2000km would be pretty high altitude for that.

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  10. #10
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    Thanks for the suggestion!

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