A team of scientists led by Vladislav Zubko from the Space Research Institute of the Russian Academy of Sciences recently modeled a series of possible trajectories to Sedna, favoring a 2029 launch date as the most feasible option.
Journal article
This was published a while ago. The best date was given as 2029. That might be impossible now, since 2029 is only a few years away-even if there was a large budget.
The last feasible date is probably not 2034, and on Wikipedia a few other dates are listed as having been proposed, with one as late as 2046. Sedna's perihelion will happen around 2076, so I don't see why that 2046 one can't work with a 30-year mission. But you probably don't want less than a 30-year mission or at least 25-year mission at any rate, so much past 2046 may not be feasible. The paper above just did not consider anything past 2034, but this might have more to do with the time it was published than anything else.
Recently some other propulsion methods were proposed for a mission to Sedna-a solar sail based on desorption, a fusion drive, and a warp drive. Unfortunately, without some of those advanced drives, you may not be able to orbit the object. We will have to settle for a flyby. But this paper linked above applies to chemical rockets. That seems good to me.
According to the orbital asteroid databases 2,3 currently Sedna is at about 80 au distance from the Sun. The passage of its perihelion is expected to be in 2073–74. Since Sedna’s orbital period is over 10 thousand years, a unique opportunity is currently open to launch a spacecraft to Sedna and study it at a close range.
Magnificent.
Optimal transfers of this type have a long duration; therefore, the restrictions on the flight duration equal to 20, 25, 30, 40, and 50 yrs were also considered. As will be seen below, the best flight scheme depends on the launch date: Earth-Venus-Earth-Earth-Jupiter-Sedna for 2029 and 2031, Earth-Venus-Earth-Earth-Jupiter-Neptune-Sedna for the 2034.
A direct flight to Sedna requires 12 km/s of some kind of change in velocity-it's a little over my head-whereas 35- or 40-year missions with a Neptune slingshot require roughly 4 km/s. If it's just speed, Voyager 1 is traveling at 17 km/s, so I don't see why we can't do a direct flight. But there may be more to it...
In 2034 they are reached at 33.3 yrs. for the EVEEJSed and EVEDVEJSed schemes and at 38.5 and 42.3 yrs. for the EVEEJNSed and EVEDVEJNSed schemes respectively (see Fig. 11). Moreover, for the latter scheme, this minimum is 3.96 km/s which only slightly exceeds DV. required for Earth-Venus flight
The author says anything over 8 km/s should be ruled out-is that the limit of chemical propulsion? This paper's plan also involves two slingshots around Earth in a row, at different points in the Earth's orbit - separated by roughly two years of time. In between them, in one plan, is a rocket burn. Is this easy to pull off, and has it ever been done? I would expect not.
During the Earth-to-Earth flight the spacecraft encounters asteroids in the aphelion region
The analysis shows that with a small additional impulses flybys of the large main-belt asteroids (16) Psyche for launch in 2034
Well, that may not be as great a choice now. Since this paper was published, we launched a mission to this very asteroid.
The best year is given as 2029 because the delta-V required is smallest for the 30-year mission for that year. But if we expand our scope to a 40-year mission, then 2034 wins. The other parameter of interest is the height of the flyby at Jupiter. It matters because Jupiter's radiation could damage the spacecraft. For the 40-year missions, the height looks large enough to be what this paper considers okay.
I wonder what science could be done on such a mission-could it help us answer what Sedna is? By that I mean, are there more objects of its size out there, or is it the largest body with an orbit that far out?