Can a spacecraft use the planet's gravitational gradient to boost it's orbit without rockets? A spacecraft orbits a planet. It extends a mass about a horizontal direction on a long tether. At this point there is not much gravitational gradient between the craft and the ejected mass so there is not much tension in the tether. Later the gravitational gradient will tidally align this tethered two body system vertically now there is a tension in the tether due to the gradient.
To retract the ejected mass the spacecraft start pulling back the tether. Since there is a tension on the tether it will need to spend energy to do so.
The question where this energy will go? Would it boost the orbit?
 A: In terms of energy the situation I describe is very much like letting a bucket down on a rope. The gravity gradient will pull on the rope and pull the mass away and can be connected to a generator to generate some energy.
And this energy is used up when we retract the rope.
In terms of angular momentum the orbiting spacecraft has lots of angular momumentum (high radius, high speed). When the tethered mass is released on a long rope the tidal forces will align it so it will rotate once per orbit. This angular momentum must come from the orbital angular momentum, so the orbit will decay a bit as this rotational momentum is not too large compared to the orbital one.
When the cable is retracted this rotational momentum wants to be conserved, and the rotational speed increases as the cable is retracted. So this tethered system can be used to launch objects with a precise $\Delta v$. This is the operating principle of the rotating sky hooks.
If the retraction happens slowly it's possible to keep it in sync the stabilizing forces. In this case the orbital angular momentum is recovered.
