Is it possible for a spacecraft to achieve an orbit around a celestial body that has no orbital eccentricity at all? The smallest orbital eccentricity of a natural satellite is that of Triton's orbit around Neptune. Triton's orbit is almost perfectly circular despite allegedly being a captured dwarf planet. Is it possible for spacecraft to achieve an even more perfect orbit or a perfect one with no orbital eccentricity? Please don't say geostationary satellites since they don't orbit the Earth relative to its surface. I'm asking for craft that actually revolve around the Earth or another celestial body. One with little mascons, obviously since such strong mascons like on the Moon would make a perfectly circular orbit unlikely.
If you define perfection as absolutely zero eccentricity then perfection is impossible. There will always be eccentricity in an orbit, even if it is very small. Orbits vary due to:
- Spacecraft system inaccuracy: no spacecraft is perfect, no matter how accurate
- Changes in the density of the orbited planet
- Gravitational influence of other celestial bodies: my answer to this question shows that Jupiter's influence on a body in Earth orbit when the Earth and Jupiter are close together is 3.2e-7 m/second squared. That isn't much, but it will have in influence
No orbit can be perfect because the gravity of other celestial bodies will always cause a small amount of eccentricity. If you had a perfectly even sphere far away from any other celestial bodies, say halfway between galaxies, and a spacecraft with an extremely accurate guidance and control system you could get close to perfection. However, gravitational influence will always cause some minute eccentricity even if it is undetectable.
So you could get close to, but never achieve perfection.
You would need a perfect two body system, a perfect central body and a perfect spacecraft. No other planets or stars influencing the orbit.
The central body should be a sphere with constant density or at least spherical symmetry.
You need a perfect measurement of orbital parameters.
The thrusters of the spacecraft needed for circularation of the orbit should be controlled with infinite precision.
The answer depends: how accurate is the physics you consider?
Considering the symmetric system postulated in other answers/comments, one with two spherically-symmetric bodies of equal masses, orbiting their barycenter: if you use only Newtonian physics, empty the universe of all masses other than the ones you're focusing on, and make the bodies perfectly rigid (i.e., ignore the physics of non-rigid bodies to maintain their spherical symmetry), then indeed theoretically you could have perfectly circular orbits. You don't have to specify just two bodies because under these assumptions theoretically you could have three or more such objects orbiting the barycenter in circular, coplanar orbits. This geometry was discussed in a science fiction novel some decades ago — Ringworld? I don't have time to look it up.
But the foregoing assumes three things that we know not to be true in the real world. What happens when you replace these ideological models with real-world realities?
Apart from a single case, as soon as you allow other mass in the universe, "perfect" goes out the window. That single case is actually a class of cases, in which 1) all the other mass in the universe is concentrated along the line normal to the bodies' orbit plane and passing through the barycenter, and 2) those masses are either static (non-moving) or moving in such a way that the net gravitational force at the orbit of the bodies in question doesn't change. This works for Newtonian physics and special relativity, but as I said in a comment, I haven't pondered the implications of general relativity. For that matter, case 2 above is difficult to pull off, even in Newtonian physics, without resorting to electric charges to counter what gravity is trying to make them do. Hmm ... most models of the universe don't involve such geometry ... and they're based on data. So much for that single case!
If you allow non-rigid bodies (but keep Newtonian physics and an otherwise-empty universe), unless the bodies rotate at the same angular rate as they orbit (they are locked in terms of relative orientation), then tidal effects perturb the orbits. Assuming two bodies, their mutual tidal forces perturb their shapes into prolate spheroids — like rugby balls. If they rotate at the same angular rate as they orbit, then the long axes of the prolate spheroids line up with each other and there is no non-radial (from the barycenter) component of gravitational force, so a circular orbit is possible. Rotation at a rate different from synchronous with the orbit then drags the long axes of the prolate spheroids away from pointing directly toward the other prolate spheroid's center. This results in a non-radial component of force that either adds orbital energy to the other object or removes energy, depending on whether the angular rotation rate is faster or slower than the orbital rate. That makes the orbit spiral either outward or inward.
A spiraling orbit is not perfectly circular!
Once you abandon Newtonian physics and include general relativity, all possibility of a perfectly circular orbit goes out the window. Even if you have the symmetric two-body system that under Newtonian physics yields circular orbits, under general relativity the system radiates gravitational-wave energy at the expense of the system's orbital energy. The objects spiral inward.
A spiraling orbit is not perfectly circular!
The net conclusion: if you entertain a simple, ideological universe you can contrive situations that appear to give perfectly circular orbits — theoretically. As soon as you open the door to any form of real-world universe, especially real-world physics, all such possibility goes away.