# What's the best flightpath to get to Sedna by 2076?

Repeated Google searches over the past year, as well as recent searches of NTRS, AIAA, and arXiv, show no signs that anyone has seriously considered a mission to Sedna. I would like to propose a thought problem to further explore how one can design this mission.

Here are the elements of my Lambert’s problem:

• Launch date: January 1, 2026
• Arrival date: July 1, 2076
• Position 1: circular Earth orbit of 2000 km
• Position 2: Sedna at perihelion

For my vehicle, let’s say I have a 17U cubesat into which I’ve managed somehow to shoehorn an indium needle FEEP engine capable of a maximum thrust of 100μN, and say I have magically reduced the power/science package/structural elements so that my mass ratio is 50, and I’ve revved my Isp up to 30,000. My orbital pre-maneuver mass is 500 kg.

Any chance I could get to Sedna for a ballistic orbital capture well before perihelion, with a little gas left in the tank?

Note: besides a gestimate of feasibility, I am interested in getting an idea about the work flow of the trajectory design process, i.e., what other assumptions need to be made, how long would it take to calculate, etc.

• HopDavid's answer is a good first step, in that it shows that at least one gravity assist maneuver is required to get to Sedna by its perihelion date. No, it doesn't. Given a rocket with sufficient delta V you could send a rocket directly intersect Sedna at perihelion, no gravity assist needed. Rockets aren't restricted to Hohmann transfers only. Mar 17, 2014 at 18:28
• @DavidHammen: done. The answer to my first Sedna question proposed a big vehicle, which is why I suggested an absurdly small one for this question. Mar 17, 2014 at 18:28
• @DavidHammen: if you can propose how to get there by 2076 without a gravity assist, feel free. It doesn't seem likely to me that we could get that sort of technology up & running in time. Mar 17, 2014 at 18:32
• Getting to Sedna in 2076 using today's technology is beyond speculative. It's science fiction. A mission to Sedna will need significant developments in propulsion, power, communications, and avionics. Yes, we can still receive signals from the Voyager satellites -- at 160 bits per second. Mar 17, 2014 at 18:41
• Sedna is a captured object, according to this paper, so now a mission to Sedna should be top priority. It would be an interstellar mission to an exoplanet, even if Sedna did most of the traveling for us. Right up the alley of the stepping stone philosophy. I think a flyby mission could be greatly enhanced by putting a tiny sub-probe in orbit or even on land it. Powered on batteries for a day or so, communicating with its still nearby mothership. Hayabusa 2 uses sub-probes. JAXA and DLR lead the way. Aug 7, 2015 at 9:40

An Ion thrust probe on a direct course is a viable option for a flyby. You need a total delta-V of around 70,000kph for a direct course accelerate-coast-decelerate. A slightly better path is a single flyby non-hohman. This is because a current extant probe has sufficient delta-V to make the trip in the specified timeframe with current technology and with current fuel loads. (Noting that the probe in question would be out of fuel by the time it was out of power.)

# Data

The Dawn spacecraft has a total expected vector accumulation of 38,000 kph, or around 10.4 kps (space.com), while the voyager 2 ephemeris data (theskylive.com) shows 15.4kps solar relative velocity. A 2020-launched probe could, for a flyby, use a direct launch to get to Sedna - note that this would put perihelion at about 35 years travel time without a more efficient engine nor more relative fuel than the Dawn spacecraft. The Dawn probe, by replacing one or two instruments with additional fuel, could likely arrive direct course with fuel to decelerate, but would lack the power to make use of it.

The first order approximation is sufficient for initial mission development purposes - I'm not an engineer, and the actual calculus is not needed, since most of the trip would be coasting.

The Topaz Nuclear Reactor was theoretically capable of 5 years operation on its 12kg of fuel, in a roughly 350kg total installed mass, producing 5 kWe. This is adequate to operate the Dawn Thrusters. More recent

# Discussion

The cubesat is impractically small. It's a good size for a minimal science payload, however. Dawn has 425 kg fuel, about 90 kg of drives on a 1200 kg spacecraft; it would need at least 4 kWe to drive the ion drives at the far end.

This gives us a reasonably launchable mission profile - by using solar for the outbound, and remote starting the fission plant for the deceleration phase, we can get increased launch performance. By reducing the mission instruments, we can increase the fuel load as well.

### some really vague estimates due to lack of concrete data

We need about 450 kg of power plant, about 100 kg of drives, about 50 kg of navigational support, about 100 kg of structure. This means we can get about 600 kg of fuel, and note that I'm assuming spare fuel for a slightly more efficient nuclear reactor, and about a 6% improvement over the NStar thruster efficiency.

Mars' orbital velocity is around 23 kp/s; a martian flyby should be able to provide 5 kps or more - and redirecting for the outbound direct flight, with only a 6 month lag or so.

600 / 425 ≅ 1.41
38,000 * 1.41 ≅ 53640 kmh ∆V total fuel
53640 / 2 ≅ 26820 kmh transit velocity (halving for deceleration at end)
This is about 5577 hours per AU, or 232 days per AU, or 0.637 years per AU

we need a boost - we can get an addition 50% from a mars flyby/redirect. Which gives us about 155 days per AU, or about 0.42 years per AU.
76 * 0.42 ≅ 31.9 years. We need to double the acceleration and deceleration times

So - modified hohman to mars for redirect, and then straight out to sedna, braking on the last few years.

Dawn has 2100 days acceleration...
2100 * 1.41 ≅ 2960 days or about 8.1 years at each end
roughly 40 years travel time.

this first order approximation says we might be able to pull it off, and is close enough to make it practical for someone more skilled in calculus than I to work out the gravitational, flyby, and accelerational effects. I've also been extremely conservative by ignoring the initial earth velocity of 6.28 AU/year. Further, an additional small boost can be obtained from a lunar flyby at launch. So, being able to approximate.

The original question's probe isn't big enough for the needed current hardware; I'm working from current "off the shelf" tech, only extrapolating for a 40 year fuel supply for the nuclear reactor (at 350kg for the reactor for 5 years, and 12 kg per additional 5 years, noting that the half life for the reactor's fuel is in excess of 10^7 years... The probe, once on station, could operate with reduced fuel efficiency for several years further.

# Bottom Line

A suitable probe the size of the Dawn probe could be put on station with off the shelf components and careful engineering, plus a variation of an extant space rated power plant. The original question's probe is implausible.

# References

1. http://www.space.com/8579-nasa-spacecraft-breaks-speed-boost-record.html
2. http://theskylive.com/voyager2-tracker
3. https://en.wikipedia.org/wiki/TOPAZ_nuclear_reactor
4. www.esto.nasa.gov/conferences/nstc2007/papers/Patterson_Michael_D10P3_NSTC-07-0014.pdf
5. http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

I would swing by Jupiter, dive towards the Sun, and do a quick chemical rocket burn at perihelion. With a reasonable-sounding 2.2 km/s burn at a 0.3 AU perihelion, I can get to Sedna in 50 years. (5.5 years to get to the Sun, 44.5 years to Sedna.)

At 0.3 AU, I need to put up with eleven times the solar intensity seen at Earth. Solar Probe is being designed to tolerate greater than 600 times the intensity.

Maybe I should go closer. I can reduce the burn to 1.3 km/s with a 0.1 AU perihelion.

• So, an Oberth Kuiper maneuver, then? (xkcd.com/1244) Aug 31, 2015 at 20:58
• Yes, and it works in Kerbal Space Program. Aug 31, 2015 at 21:10
• Krafft Arnold Ehricke maneuver? Is that what you call it when it involves a solar fryby? Sep 2, 2015 at 14:11

It's possible for an object with Jupiter's L1 Jacobi constant to have a widely varying semi major axis. And something with Jupiter's L2 Jacobi constant might find it's way to Saturn's L1. Etc. But changing the semi-major axis via repeated perturbations typically takes many passages. Sedna's perihelion is about 76 AU. A Hohmann trip from 1 AU to 76 AU would take 120 years. And a trip that relies on repeated planetary perturbations for its delta V would take much longer. A 56 year trip to Sedna via ITN doesn't sound plausible to me. A mass ratio of 50 with a healthy ISP might do it (since I don't know how to model constant low thrust, I can't tell you yes or no). But I'm not sure that's what Lo et al have in mind when they talk about the ITN.

• Sounds like a good answer, but can you include the math you used to derive the 120 year Hohmann transfer? Mar 16, 2014 at 17:44
• Sure. The units I like to use are astronomical units and years. With these units you can raise semi major axis a to the 3/2 power to get period in years. For a 1 AU by 76 AU orbit, semi major axis a is 77/2 or 38.5 AU. 38.5^(3/2) is about 240. A Hohmann trip is half of the elliptical transfer orbit. 240 years/2 = 120 years. Mar 16, 2014 at 18:34

I think the best way to get to Sedna is to look to the spaceships that are now in Solar escape velocity.

### Escape Velocity

New Horizons was the first spaceship launched directly into solar escape trajectory. However, the ship used a Jupiter gravity assist. It will reach 100 AU from Sun in 32 years, but most probably it will not be functioning after 2026, when it will run out of power.

Voyager 1 & 2 used multiple gravity assists, to reach their current speed. Voyager 1 reached 100 AU from Sun around 2006, after 29 years of flying. Voyager 2 reached that distance in 2012, after 35 years from launch. Both spacecrafts are still functional, but they can hardly power-up their scientific payload.

The Pioneer spacecraft also used Jupiter and Saturn gravity assists. Both ships are supposed to be over 100 AU from Sun since 2014. However, contact has been lost before they reached this distance.

### Trajectory details

As seen above, it is possible to reach Sedna orbit in less than 30 years. Sedna will be closer in 60 years, but the difference will not be much (less then 10% from current distance). So, we could launch a probe now instead of waiting.

As New Horizons showed us, it is possible to send a spacecraft directly into solar escape velocity. However, we can use gravity assists, to reduce flight time.

Every 12 years, Jupiter is in place for a Jupiter gravity assist.

Every 29 years, Saturn is in place for a Saturn gravity assist.

Every 59 years, both Jupiter and Saturn are in place for a Double gravity assist.

A flyby mission would reach Sedna in 20 to 30 years. However, sending an orbiter or a landing probe will be very hard, if not impossible.

To send a flyby to Sedna is almost like the flyby New Horizons conducted to Pluto. We can use the same spacecraft design, only that we will need a far more efficient RTG (radioactive thermoelectric generator), so that it will keep functioning after 30 years. The probe will conduct a fast flyby, then it will spend a few years sending all data back to Earth. This kind of mission is feasible and affordable with current NASA budget.

If we send an orbiter to Sedna, we have two ways: First, we need to slow it down, to enter orbit. Second, we can send it with a very low speed, enough to enter orbit. The first method will require giant amounts of propellant and will dramatically increase ship weight at launch. One alternative is to use an ion engine, powered-up by the ship's RTG, to reduce speed in the last 10 years before encounter. However, the amount of energy still available at that time is limited. Sending a probe with little speed might be a solution, but it will reach Sedna in 100 years. At that time, its RTG would have declined energy production to a very low level and anyway there will be nobody from the building team to see the results.

Sending a lander to Sedna is even more complicated then an orbiter. However, if we conduct a fast flyby, we can use an impactor, similar to the one used by Deep Impact mission. This will at least allow us get a close picture from the surface and see at impact site sub-surface composition.

### Challenges

• The main problem with Sedna is the amount of time needed for a flyby. RTG energy decay is the main concern.
• Luminosity is lower than on Pluto, so cameras will need a longer exposure time.
• Mass and gravity of Sedna are unknown. We only approximate its diameter.
• It is not known if Sedna has moons, rings or anything in orbit around it that could harm a spacecraft.
• Communication delay is a problem. Sending a message to the ship, we will need an Earth day to get a response.
• Signal power is decreasing by the square distance. Signal power at Sedna will be 6.5 times weaker then at Pluto, meaning that a spaceship will need 6.5 times more time to download all its findings. If we needed over an year to download data from New Horizons, we will need probably 10 years for a probe that explored Sedna.
• Since we don't know major data about Sedna (mass, gravity, orbital axis, possible satellites and space debris), there is a high chance of risk. The ship will need to conduct some preliminary research before flyby, then it will need some strong trajectory correction maneuvers. At first, it will scan for possible moons or rings, to analyze the risk of a collision, then it will determine rotation axis, to see what is the best flyby path. As it gets closer, the probe will get a low-resolution image of the far side of Sedna, then it will get high-detail resolution of its encounter side. Then, as it gets behind Sedna, the probe will capture a solar eclipse, to see if there is any atmosphere. Overall, these were the steps performed also by New Horizons on Pluto.

### Conclusion

A similar mission to New Horizons, but with a more powerful RTG, eventually with the help of Jupiter and Saturn flybys, could get to Sedna in 20 to 30 years.

• When I said that a flyby to Sedna is affordable within NASA budget, I had in mind that it is possible with current founds, not that they have in plan sending a probe to Sedna. We know how much time it took to send a probe to Pluto and how many missions they cancelled, including Pluto Express and Voyager 3. Jul 28, 2016 at 11:01

Sedna Sample Return

Even if this is not feasible with current technology, it is a very interesting subject. Is it possible to send a Sedna Sample Return mission?

To get an answer, we must look to space missions that have already been launched.

Vehicle design: The spaceship must contain an orbiter and a lander. The lander will reach the surface of Sedna, will take a sample and will return. It must have enough propellant to land and to return. The orbiter must be used as a communication relay to Earth and must have enough propellant to return to Earth. The orbiter must also have an RTG, strong enough to function up to 100 years.

For this, we should look at ESA's Rosetta and Philae spacecrafts. Sedna has a low gravity, but probably no atmosphere. So, we need propellant both at landing and at launch, but not in too large an amount. We don't know Sedna's escape velocity, but Pluto's is 1.2, 10 times smaller then Earth's. Philae had 100 kg. Our lander will have probably 250 kg, with all its fuel tanks full of hydrazine.

The orbiter will have to survey and map Sedna, then it will deploy the lander, then it will wait, then capture the lander and return home. Rosetta had 1500 to 2000 kg, but New Horizons only 500 kg. We will need the lightest spaceship, to preserve hydrazine.

The lander can be battery powered. The orbiter will need an RTG. Plutonium used in an RTG has a half lifetime of over 80 years, but the thermocouples don't live that long. Basically, the energy produced by an RTG decreases by half in about 25 years. The mission will take probably 100 years, so energy production will decrease to less then 10%. This means that, without at least 100 kg of plutonium, a sample return mission is impossible. It could be possible to use a backup empty RTG, to reinsert plutonium in it. The probe, with lander and without its fuel, must not weight more then 1000 kg.

The vehicle will include a lander, an orbiter, but also a huge amount of fuel needed to decrease ship velocity, and also fuel needed to send the probe back to Earth. We might have to send into space a total of 5000 kg.

Launch. The only way to send into space such a large spaceship is with the use of some of the largest existing rockets. An Atlas V would hardly be enough.

Trajectory. Sending the probe directly into solar escape velocity is out of question. We have to use the advantages of Jupiter and possible Saturn flybys. If possible, a Mars or Earth flyby are also useful. This will also result in a longer time to reach Sedna. It will take at best 40 years.

Sedna Approach Phase. The probe will approach Sedna with high speed, probably 15 km/s. At that speed, it is impossible to be captured into orbit. We have to decrease speed somehow. Using conventional chemical engines is out of the question, because of the huge amount of fuel needed. The only solution will be a ion engine. As Dawn have shown us, with 400 kg of xenon, it managed to produce a total thrust close to 10 km/s. So, it is possible, if the RTG produces enough energy, to decrease speed from 15 km/s to 1 km/s in 12 years.

Bonus Ship. One extra mission that can benefit from a Sedna encounter is a fast flyby. We can add a 3rd spacecraft, with its own RTG and suite of science instruments, that will detach from the main ship before slowing down. The bonus ship will continue to move with the same speed and will soon reach the interstellar environment. Its mass can be of 300 kg, not much compared to the 5000 kg already needed.

Sedna Orbit Phase. Once in orbit, the probe will first enter a high-altitude orbit, to search for moons and characterize Sedna system. Just as Dawn did at Vesta and later at Ceres, our probe will enter closer orbits, mapping the dwarf planet and in the final phase, looking for a place for the lander. Finally, it will deploy the lander who will have a few days to touchdown, to explore the surface, to drill, to take samples and to return. To return to the orbiter, the lander will need to perform high-accuracy maneuvers. The orbit phase will probably take 5 years to complete.

At the end of this phase, the spacecraft will need to detach all unnecessary weight. This might include much of its scientific payload, empty propellant tanks, the lander (except for the tank containing samples) and used RTG.

It is also possible to make the whole spaceship land on Sedna, without the need of a special lander. However, this will result in more fuel needed.

Return phase. Sedna has a low gravity. As shown above, the escape velocity for Pluto is a bit above 1 km/s. For Sedna, it is probably 0.7. The orbital speed is only 1.07 km/s. so, a spaceship will only need a 2 km/s thrust to detach Sedna's surface and to get to a 0 km/s speed relative to the Sun. At that point, solar gravity will do all the work and will take the ship on a trajectory towards the Sun. The resulting orbit will not be a straight line, but something looking more like the path of a long-term comet.

As the probe approaches, its speed will increase gradually. It will move very slowly up to the orbit of Neptune. To speed-up the process, almost all the remaining xenon should be used by the ion engines to increase speed. If not, it could take 400 years to reach Earth. Nobody wishes to wait that long. So, we must accelerate the ship to at least 10 km/s.

As the probe passes the orbit of Neptune, its speed increases fast. At Earth's orbit, the spaceship can move with 30 km/s faster then Earth. It can become impossible to land on Earth with such a huge speed. To slow down, the best option is to use a Jupiter flyby, and possibly other flybys.

Earth Landing. The final phase of the mission is an Earth landing. At that time, after almost 100 years, the RTG will produce only a very small amount of power. Many devices will not be working. Maybe, it will be a good idea to have onboard a small solar panel, to provide the power needed for the final phase of the mission. The spacecraft will conduct its final trajectory correction maneuvers, then it will detach the tank containing samples from Sedna. Only the samples will return, softly landing with the help of a parachute. The spacecraft will enter a solar orbit or will burn in the atmosphere.

Mission Conclusion: After 100 years of travel and with great costs, the mission will return to Earth a sample from Sedna. Probably there will be samples from the surface, materials drilled from a few meters deep and an atmospheric sample (if Sedna has any). Also, the probe can bring dust samples acquired along the journey.

There is one major problem about this mission. On Sedna, many solid rocks can be in fact gasses on Earth. We know from Pluto, that its crust is made almost entirely of substances that on Earth should be gasses or liquids. Rocks brought from Sedna should melt or even evaporate. In the lab, scientists will have big problems analyzing the samples. The long needed time and degradation of the samples, together with high mission costs, are the reasons why a sample return mission to Sedna is unfeasible.

P.S.: No spacecraft has flown for that long and nobody has ever designed complex electronic devices able to operate for 100 years. A mission to Sedna requires that all devices will still be functioning after many years. Also, for the return phase, we must make sure that navigation computers, engines, the RTG and reaction wheels are working well until the end of the mission. A sample return mission will be at high risk because we have not enough time to test all systems and sub-systems.

In addition, there are many unknown things. Nobody knows what the mass and gravity of Sedna is. We must design the ship to the highest estimated mass, to make sure we have enough propellant. And, as we don't know the exact mass, there is no way to know how much fuel will remain for the return phase. If we have more fuel available for the return phase, we can get our samples faster, but we will have to re-calculate the return route and Jupiter flyby to decrease speed.

Also, since we don't know the mass, we don't know how to enter orbit. All these not known parameters means that many parts of the mission will have to be calculated fast and only when the ship will get to a certain point. There will not be much time for estimations and backup plans. Powerful computers on Earth should decide what to do within hours.

Communication delay is big, because of distance. There will not be much time for analyzing problems. It can be a very good thing to program the ship to automatically find the best trajectory.