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Answers to the Astronomy SE question Can New Horizons probe turn back and start orbiting Pluto are of course no, it would have to have been a different mission with a lot more fuel and a bigger launch vehicle.

Question(s):

  1. Roughly how much more of a flying fuel tank would New Horizons have to have been (i.e. how many more kg of fuel) in order to slow down and match Pluto's orbit rather than fly past it. note: The new mission design can be very different, the launch vehicle can be very different, but add only fuel to the spacecraft and add no more than roughly a decade to the arrival time at pluto.
  2. If the what looks like it's an Atlas 551 were swapped out for a hypothetical Atlas HLV or whatever else earthlings could have put together for a juicy contract at the time, could it have even done the job?

Atlas rocket family from http://www.b14643.de/Spacerockets_2/United_States_3/Atlas_V/Versions/AtlasV.htm

Source

I'm asking that we keep the payload and instrumentation of New Horizons the same, and just make the fuel tank's kilogramage bigger for a back of the spherical cow's envelope estimate.


The Atlas V rocket used to launch the New Horizons spacecraft.

Source

The Atlas V rocket used to launch the New Horizons spacecraft.

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    $\begingroup$ Same flight plan, or is a Hohmann, or even a Bi-elliptic course on the table? $\endgroup$
    – notovny
    Jun 26 at 4:04
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    $\begingroup$ @notovny Good point! The flight plan is up to you, task is to get it there. You can add some years and some reasonable amount of flybys, up to adding another decade or so to the arrival time if necessary. Same payload, bigger tank, new mission design, new launch vehicle. $\endgroup$
    – uhoh
    Jun 26 at 4:07
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    $\begingroup$ highly relevant Requirements to orbit Pluto $\endgroup$ Jun 27 at 15:50
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    $\begingroup$ @BrendanLuke15 I think you can add a short "supplementary answer" here, pointing to those answers and sourcing from references therein; the "adding another decade or so" is the real challenge! $\endgroup$
    – uhoh
    Jun 28 at 2:15
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New Horizons had a launch mass of 478 kg, of which 77 kg was propellant, but only around 47.5 kg of that was for course changes, with the rest reserved for attitude control. New Horizons was launched at a speed of 16.26 km/s, which put it on a solar system escape trajectory. It then also received a speed boost from the Jupiter flyby.

Fuel requirements

New Horizon's propellant budget gave it a delta-V capability of "over 290 m/s". Its hydrazine propellant has an ISP (efficiency) of around 220 seconds. For going into orbit you would typically use a hohmann transfer instead of an escape trajectory that NH uses. That means the spacecraft would launch a bit slower so that it would come to an almost dead stop when arriving near Pluto. Pluto itself however is traveling in its orbit around the Sun, and to match its speed in order to orbit it, you need a delta-V of around 3000 m/s, so around ten times as much as NH had. Note also that a hohmann transfer to Pluto takes 45 years instead of the almost 10 years that New Horizons took.

The amount of fuel needed scales exponentially with your required delta-V. Using the same fuel, NH would need 1300 kg of it to get into Pluto orbit. Maybe a bit less if it uses a Charon gravity assist, but Pluto and Charon are not very large so they won't gravity-assist you much. But for an orbit insertion mission a probe would typically not use hydrazine monopropellant, but a more efficient bipropellant. Galileo and Cassini used MMH-NTO bipropellant for their main thrusters. Cassini had an ISP of 312 seconds, and using that, NH would need 'only' around 720 kg of fuel to do the orbit insertion. Note that I am ignoring the extra mass from the larger fuel tanks and heavier thruster.

Instead of a hohmann transfer NH could also have taken a bi-elliptic transfer. Those take a lot longer, I haven't done the caluclation but probably we are talking about much more than a century here. According to this graph a bi-elliptic transfer could reduce the needed delta-V by up to about 7.5% when the time you take approaches infinity. (note: r₂/r₁ for Earth to Pluto is about 30.) This would reduce the required fuel from 720 to 640 kg.

Could it have been done?

The Atlas V 551 was the second most powerful launch vehicle that existed at the time. The only more capable one was the Delta IV Heavy. Of course if the contract was juicy enough someone could have just have designed a new super heavy lift rocket, or just resurrect the Saturn V. Creating bigger rockets is relatively straightforward. So with enough money an orbital New Horizons mission was certainly possible. However Nasa is on a budget, and that wouldn't have happened just for a Pluto probe.

The Delta IV is a bit less than twice as powerful as the Atlas in what it can lift. Howver I don't know how to make the exact calculations on what it could have launched toward Pluto, as there are a number of complicating factors. New Horizons was launched at a speed of 16.26 km/s, but then it received a speed boost from Jupiter of around 4 km/s. Since Jupiter is already quite a way out there, that 4 km/s translates into (I think) a bit less of additional speed if the launch vehicle would have needed to supply the speed. So for a hohmann transfer which requires about 16 km/s the launch velocity with a Jupiter assist would have to be a bit more than 12 km/s. Secondly, the launch used an additional Star 48B as a third stage, to give NH more speed over what the Atlas could deliver by itself. The Star 48B weighs 2137 kg.

The NH would weigh some 2.5 times more with the fuel for a hohmann transfer trajectory, excluding the additional mass for the probe itself to accomodate the additional fuel. The Delta is only less than twice as powerful as the Atlas, but maybe the lower speed required for a hohmann transfer is just enough to make it possible. Or maybe not. I'm not sure.

interplanetary transport network

There are other ways to get to Pluto, known as the interplanetary transport network. That means that you repeatedly fly by other planets in order to get multiple gravity assists. In principle it is possible to get anywhere in the solar system with minimal fuel requirements. You only need to get to the Earth-Moon L1 lagrange point and from there you can use gravity assists. The only problem is that this is much slower than even the bi-elliptic transfer. So how much time do you have?

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Oh, you are limiting the additional time to take to 'another decade or so'. That precludes even a simple hohmann transfer, and would require accellerating to an escape trajectory and then breaking at Pluto. That would clearly be impossible with the rockets available at that time, and probably also with the rockets that exist now (The only new more powerful rocket is the Falcon Heavy, but it isn't so good at bringing small things to a very high speed.) You'll need to wait for SpaceX's Starship or for someone to build a space grade nuclear reactor to power an ion drive.

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    $\begingroup$ A nice answer thank you! Yes that was good spotting the "adding another decade or so to the arrival time" comment; I should have immediately moved that back into the question itself, and I'll do so now. Good catch! A quick question; "The NH would weigh some 2.5 times more with the fuel for a Hohmann transfer trajectory, the additional mass for the probe itself to accommodate the additional fuel." Can you add a little bit showing how that was obtained? I don't necessarily doubt the number but it's important for answers to support assertions, including quantitative ones. Thanks! $\endgroup$
    – uhoh
    Jun 26 at 13:54
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    $\begingroup$ @uhoh I got the numbers from this online calculator: strout.net/info/science/delta-v $\endgroup$
    – JanKanis
    Jun 26 at 15:14
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    $\begingroup$ I took the needed delta-V from this diagram on Wikipedia. The 3000 is roughly to a low Pluto orbit. For an barely bound elliptic orbit only 2700 m/s is needed according to the diagram. I'm not sure what part of Pluto's orbit these numbers apply to. $\endgroup$
    – JanKanis
    Jun 28 at 7:22
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    $\begingroup$ Note also that your subtraction applies to entering the same orbit as Pluto around the Sun while in deep space. Doing a burn while close to a planet is more efficient, so takes less delta-V. I'm not sure how much of a difference this makes for a small body like Pluto. See Oberth effect. $\endgroup$
    – JanKanis
    Jun 28 at 7:25
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    $\begingroup$ For the calculation I used a dry mass of 430 kg (including hydrazine for attitude control) and an ISP of 312 seconds (assuming bipropellant). A total mass of 1150 kg then gives a delta-V of 3009.9 m/s. For the monopropellant calculation I used an ISP of 220 seconds. A total mass of 1730 kg gives a delta-V of 3003.39 m/s. $\endgroup$
    – JanKanis
    Jun 28 at 7:35
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The answer to question 1 will come from the chosen trajectory's arrival $V_\inf$ (hyperbolic excess velocity). The answer to question 2 will come from the chosen trajectory's launch $C3$ (characteristic energy). The two are coupled to an individual trajectory dependent on dates and routes (which planets to flyby). Luckily, I have (student) experience in interplanetary trajectory searches.

I chose to maintain the (as flown) mission architecture of a Jupiter gravity assist to try to leverage a lower launch $C3$ (compared to Pluto direct) and a stronger gravity assist at Jupiter. It is also easier to compare with the as flown New Horizons primary mission.

Search Constraint Dates:

  • Launch Dates: 2003 - end 2006
  • JGA Dates: 2003 - end 2010
  • Pluto Arrival Dates: 2008 - End 2030*
  • state vector data from JPL Horizons (5 day step size)

*The New Horizons mission design supported arriving at Pluto as late as 2020 in a Pluto direct trajectory (New Horizons Mission Design, Guo et al.)

I used a heavily modified version (mainly the Lambert solver) of this MATLAB file exchange package$^1$ to create the porkchop plots for each leg of the trajectory (Earth-Jupiter, Jupiter-Pluto). Here is the initial leg (launch $C3$) with the New Horizons actual annotated: Earth to Jupiter porkchop

The trick comes in finding suitable Jupiter to Pluto trajectories that match the hyperbolic excess velocity, $V_\inf$, approaching and leaving Jupiter, enabling a 'free' flyby/gravity assist. I usually consider a difference of less than 100 m/s to be sufficiently close.

The Pluto arrival hyperbolic excess velocity strongly favours a slower route from Jupiter to Pluto (again, New Horizons actual annotated). Slower is the name of the game here:

Jupiter to Pluto arrival porkchop

A secondary, not immediately evident constraint is how close you are willing to get to Jupiter and its strong radiation during the gravity assist. New Horizons passed at a close approach of about 33 $R_J$, Jovian radii (TRAJECTORY MONITORING AND CONTROL OF THE NEW HORIZONS PLUTO FLYBY, Guo et al.). I have no good knowledge on what is a reasonable close approach distance for a spacecraft flying by Jupiter (in the scope of radiation damage) so for now I will leave this constraint wide open (just don't have the close approach inside of Jupiter).

With these constraints, and a launch $C3$ less than 150 km$ ^2$/s$ ^2$, there are 32,075 viable trajectories, shown here in this nifty plot of the key values we care about: Trajectories Map

The red markers show the region of most efficient trajectories (low $C3$ and $V_\inf$). The most efficient trajectory is:

Launch: Jupiter Flyby: Pluto Arrival: $C3$: $V_\inf$ @ Pluto: Jupiter Close Approach:
12-Nov-2003 22-Oct-2005 31-Dec-2020 91.9 km$ ^2$/s$ ^2$ 3.72 km/s 24 $R_J$

It looks like this (with New Horizons actual, left, for comparison): New Horizons actual Proposed trajectory

Observations:

  • This trajectory arrives at Pluto on the last day of the time constraint (slower is the name of the game)
  • The trajectory remains gravitationally bound to the Sun throughout the entire trajectory (S.M.A. E-J: 3.7 au, S.M.A. J-P: 30.3 au)

Answers:

I am going to ignore Charon in the orbital insertion calculations. I am also going to assume a 'dry mass' (including attitude control propellant) of 500 kg for our New (and improved) Horizons probe to accommodate the increase in propellants. $I_{sp}$ of 220 s as discussed in JanKunis' answer.

  1. Pluto Orbit Insertion (instantaneous burn at periapsis assumed):
Periapsis Distance: Velocity @ Periapsis: Capture Velocity @ Periapsis ($C3$=0): Circular Orbit Velocity:
1500 km (~300 km above surface) 3.872 km/s 1.078 km/s 762 m/s
Capture dV: Circular Orbit dV: Capture Initial Mass: Circular Orbit Initial Mass:
2793 m/s 3109 m/s 1824 kg 2112 kg

73% & 76% propellant by mass, respectively.

  1. Launch Vehicles:

I used a previously developed algorithm of mine to determine how much mass a given launch vehicle + STAR48B combination can throw to a specified $C3$. Basic performance is taken from NASA Launch Services Program Launch Vehicle Performance Website and Northrop Grumman Propulsion Products Catalog. If a reference altitude is assumed you can get velocity from $C3$ and Star48B + spacecraft $\Delta V$ from the public specifications. Get a final velocity and then recompute the $C3$.

The Delta IV Heavy is no longer listed on the NASA Launch Services Program Launch Vehicle Performance Website (it was in April 2020), but I have a a curve fit of the data saved from some old school projects :). I realize that the proposed launch is ~1 year prior to the Delta IV Heavy's maiden flight but the contract could be very juicy to make this possible. I included other launch vehicles for comparison:

For a $C3$ of 91.9 km$ ^2$/s$ ^2$:

Delta IV Heavy: Atlas V 551: Atlas V 401: Falcon Heavy (Expandable): Falcon Heavy (Recoverable):
2215 kg 1381 kg 704 kg 2847 kg 1249 kg

A slim margin for sure, but definitely plausible.

1: Bogdan Danciu (2021). Interplanetary Mission Design (https://www.mathworks.com/matlabcentral/fileexchange/66192-interplanetary-mission-design), MATLAB Central File Exchange. Retrieved June 27, 2021.

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    $\begingroup$ Holy granola this is great! We can certainly figure out some crazy/clever way to add a Juno radiation vault that can be at least partially ejected if necessary after the flyby and before more propellant is needed. It might not need to be 200 kg if it's just for one perijove and not an extended series of orbits if that's what it takes to make the mission work. $\endgroup$
    – uhoh
    Jun 29 at 0:41

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