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When two objects are in different orbits of the same body, no matter how close they are, the inner object will always be faster - it will move farther away from the outer one (until it gets closer again, that is).

However, when you connect the two objects mechanically, this obviously won't happen: Both now share a common center of mass and both sides of the connection are constantly under some stress (corresponding to the de- and acceleration). If the difference between velocities is too high, the link will break.

Is this a problem when constructing large orbital structures, like the ISS? Do we need to take into account these forces? Are they even measurable?

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An orbiting spacecraft of finite size experiences 'gravity gradient torques'. These torques, if left uncorrected, tend to align the long axis of the spacecraft so that it points toward the center of the earth. The ISS certainly experiences such torques due to its great size.

However, the ISS usually flies in a Torque Equilibrium Attitude which is chosen so the torques due to external effects such as gravity gradient, aerodynamics, etc, tend to balance out. This reduces the amount of effort that the attitude control system must exert.

As far as the gravity gradient torques being measurable, an instrument on the ISS can supposedly detect them, the MAMS. However, the linked web page states that it is only operated during dynamic events such as docking.

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  • $\begingroup$ Is this an unstable equilibrium - like balancing at the top of a hill? Is "What is actually stopping the ISS from aligning it's long axis towards the center of the earth?" better as a separate question, or do you think you can say something here? I'm wondering if there are actually occasional attitude adjustments to maintain this attitude, or if it happens naturally. Coffee or not, all those matrices just make me dizzy! :) $\endgroup$
    – uhoh
    Jul 14, 2016 at 1:33
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    $\begingroup$ From the 2nd link: "If left unchecked, these torques would cause the attitude of the space station to oscillate in a complex manner and the resulting motion would destroy the micro-gravity environment as well as prohibit the orbiter from docking...." $\endgroup$
    – Organic Marble
    Jul 14, 2016 at 2:21
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    $\begingroup$ ..."Ideally, the positive and negative external moments experienced by a spacecraft at the TEA would exactly cancel each other out and small cyclic control torques would be required only for precise attitude control. ... However, the atmospheric torques are proportional to the density of the atmosphere and the density varies with the orbital position, time of day, time of year, and the solar cycle. ... Therefore, there is no constant attitude that will completely balance the environmental torques and the dynamic TEA cannot be solved in closed form." $\endgroup$
    – Organic Marble
    Jul 14, 2016 at 2:22
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    $\begingroup$ pims.grc.nasa.gov/pimsdocs/public/ISS%20Handbook/… ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20100024204.pdf $\endgroup$
    – Organic Marble
    Jul 14, 2016 at 2:32
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    $\begingroup$ Please consider the context of this answer, which was addressing a particular question about forces/torques affecting the ISS. It was not intended to be a canonical discussion of gravity gradient stabilization. You asked about the undamped motion in your first comment and I replied with a quote that states that it would oscillate. It irritated me a bit to wake up and find multiple comments on the site complaining about this one answer. I think this is a good answer to the question that was asked. One should always consider context. $\endgroup$
    – Organic Marble
    Jan 22, 2019 at 13:42

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