What an interesting object Methone is. Discovered by the Cassini imaging team in 2004 along with the nearby Pallene, this moon of Saturn is a scant 1.6 kilometers in radius, orbiting between Mimas and Enceladus. In fact, Methone, Pallene and another moon called Anthe all orbit at similar distances from Saturn and are dynamically jostled by Mimas. What stands out about Methone is first of all its shape and, perhaps even more strikingly, the smoothness of its surface. We’d like to know what produces this kind of object and would also like to retrieve imagery of both Pallene and Anthe. If something this strange has equally odd companions, is there something about its relationship with both nearby moons and Saturn’s rings that can produce this kind of surface?
Image: It’s difficult not to think of an egg when looking at Saturn’s moon Methone, seen here during a Cassini flyby of the small moon. The relatively smooth surface adds to the effect created by the oblong shape. NASA/JPL-Caltech/Space Science Institute.
Our path to interstellar missions will see us ramp up the velocities of our probes to objects in our own system, made more accessible by shorter mission times, sail technologies and miniaturization. There is no shortage of targets between high-interest moons like Europa, Titan and Enceladus and Kuiper Belt Objects like Arrokoth. For that matter, the interstellar interloper ‘Oumuamua may yet be within range of faster missions (and in fact we’ll be examining ‘Oumuamua prospects in at least one upcoming article). But the point is that intermediate steps to interstellar will enhance exploration of objects we’ve already visited and take us to numerous others.
One way to proceed is discussed by Greg Matloff and Les Johnson in a recent paper for the Journal of the British Interplanetary Society that grew out of a presentation at the 6th International Space Sailing Symposium this summer. Here the idea is to adjust the parameters of a solar sail so that a balance is achieved between the gravitational force of the Sun and the solar photon radiation impinging upon it. The parameters are clear enough: We need a sail of a specific thickness (areal density), and tightly constrained figures for its reflectance and absorbance. We want to cancel out the gravitational acceleration imposed by the Sun through the propulsive effects of solar photons, allowing us to effectively ‘hover’ in place.
Hovering isn’t traveling, but bear with me. We’ve looked at this kind of sail configuration before and discussed its development in the hands of Robert Forward. It was Forward who dubbed the configuration a ‘statite,’ implying that when the force on the sail from solar radiation exactly balances the gravitational force acting upon it, the spacecraft is effectively in what the paper calls a ‘force-free environment.’
This gets interesting in terms of fast probes because while the statite is normally considered to remain stationary (and it will do so when the sail is stationary relative to the Sun during sail deployment), something else happens when the craft is orbiting the Sun when the sail is deployed. The sail now moves in a straight line at its orbital velocity at the time of deployment. The authors style this ‘rectilinear sun-diving.’ As Matloff noted in an email the other day:
“To do this operationally, it is necessary to maintain the sail normal to the Sun – broadside facing the Sun – during the acceleration process. The sail moves off at its velocity relative to the Sun at sail deployment because radiation pressure force on the sail balances solar gravitational attraction. This is a consequence of Newton’s First Law.”
Using this method we can fling the sail and payload outward. What is known as the sail’s lightness factor is the ratio of solar radiation forces divided by the solar gravitational force, and in the case of the rectilinear trajectory described above, the lightness factor is 1. So consider a sail being deployed from a circular orbit of the Sun at 1 AU. The statite, free of other forces, now moves out on a rectilinear trajectory at 30 kilometers per second, which is the Earth’s orbital velocity. The number is noteworthy because it practically doubles the interstellar velocity of Voyager 1. Matloff and Johnson point out that at this velocity, the Sun’s gravitational focus at 550 AU is reachable in 87 years.
Moving at the same pace gets us to Saturn (and the interesting Methone) in 1.5 years. I’m going to run through the other two scenarios the scientists consider to show the range of possibilities. Assume an orbit that is not circular but rather one having a perihelion of 0.7 AU and aphelion at 1 AU. Deploying the sail at perihelion allows the spacecraft to reach 38 kilometers per second, getting to the inner gravitational focus in about 66 years. Finally, with an aphelion at 1 AU and perihelion at 0.3, our craft achieves a velocity after sail deployment of 66 km/sec, reaching the focus in 38 years.
As regards to ‘Oumuamua, the third scenario, with sail deployment at perihelion some 0.3 AU out from the Sun, achieves enough interstellar cruise velocity to catch the object roughly around 2045, when it will be some 220 AU from the Sun. To these times, of course, must be added the time needed to move the sail from aphelion to the sail deployment point at perihelion, but the numbers are still quite satisfactory.
This is especially true given that we are talking about relatively near-term technologies that are under active development. Matloff and Johnson calculate using an areal mass thickness of 1.46 X 10-3kg/m2 for the proposed missions. They show current state of the art solar sail film as 1.54 X 10-3kg/m2 (this does not include deployment mechanisms, structure, etc). The point is clear, however: Achieving 30 km/sec or more offers us fast passage to targets within the outer Solar System as we analyze options for missions beyond it, using technologies that are not far removed from present capability.
The authors note that we can’t assume a constant value for solar radiation; the solar constant actually varies by about 0.1% in response to the Sun’s activity cycle. Hence the need to explore options like adjusting the curvature of the sail or using reflective vanes for fine-tuning. Controlling the sail will obviously be critical. The paper continues:
Control of the sail depends upon the ability of the system to dynamically adjust the center of mass (CM) versus the center of (photon) pressure (CP). Any misalignment of the CM versus the CP will induce torques in the sail system that have to be actively managed lest the offset result in an eventual loss of control. The sail will encounter micrometeorites and interplanetary dust during flight that will create small holes in the fabric, changing its reflectivity asymmetrically and inducing unwanted torques. Depending upon how the sail is packaged and deployed, there may also be fold lines, wrinkles, and small tears that occur with similar end results.
Hence the need for a momentum management system, which could involve possibilities like reflective control devices for roll or diffractive sail materials that manipulate the exit direction of incoming photons as needed to counter these effects. The authors point out that the solar sail propulsion systems for this kind of mission are at TRL-6 despite recent failures such as the loss of the Near-Earth Asteroid Scout Cubesat mission, which carried an 86 square meter solar sail that was lost after launch in late November 2022. With solar sails under active development, however, the prospect for exploring rectilinear sundiver missions in the near term seems quite plausible.
The paper is Matloff & Johnson, “Breakthrough Sun Diving: The Rectilinear Option,” Journal of the British Interplanetary Society Vol. 76 (2023), 283-287.
I am not clear what the advantage is. The concept is just to use a sail to cancel out the gravitational attraction of the body it orbits, in this case, the sun. Doing this just means that any orbit, elliptical or circular, will result in a velocity equal to the orbital velocity at deployment.
I assume that as both gravitational attraction and the pressure of sunlight are both subject to an r-squared effect, no adjustment to the sail is needed.
But why make a sail so finely balanced, other than as a proof of concept? Solar sails below the needed thrust can still acquire a high velocity. Sails able to exceed the thrust can accelerate and reach an even higher velocity.
Is the advantage that the trajectory is linear so that the trajectory is simple and can be pointed at the target?
The presentation Breakthrough Sun Diving:
The Rectilinear Option isn’t that enlightening. I assume the BIS Journal article is more explanatory.
What happens when this CME hits the sail? See video at 10 seconds.
The X2.8 flare generated a halo CME mainly directed westward, with a possibility of a glancing impact on Dec 17th.
https://twitter.com/i/status/1735558528637526298
https://youtu.be/Pej5nhmoAsw
Dear Alex,
You are of course correct. An operational mission might use a sail that is slower or faster than the rectilinear trajectory. Our point, and that of at least one paper that we reference, is that rather simple rectilinear calculations indicate how close we are to the ability to conduct fast missions to the outer solar system or near interstellar space using solar photon sails.
Regards, Greg
So, theoretically, if there was a sail material (aerographite?) that could survive the heating at the perihelion of the Parker Solar Probe, and have the needed areal density (including payload), the sail could achieve a velocity of about 190 km/s. That would get the sail to the start of the solar gravitational lens at 550 AU in less than 14 years. That would be not just spectacular, but also make the mission time very viable.
Such a sail would reach the Kuiper Belt in a little over 18 months, and pass Voyager 2 within 4 years. Make them small and cheap enough and they could be launched in swarms to explore the ISM in all directions around the solar system.
Assuming the sail could definitely start at Mercury’s orbit (~0.4 AU), giving a velocity of 47 km/s, and perhaps get to the 0.049 AU of the PSP, the most important question is how far away are we from being able to manufacture sails with the requisite density (.00146 kg/m^2 [1.46 g/m^2])? I assume Les Johnson is the expert here, as his sail roadmap extends to sails made of graphene that are nowhere near being constructible, even in space.
The CD article about the aerographite sails Interstellar Sails: A New Analysis of Aerographite suggests a very high performance, but with an areal density of 1E-6 kg/m^2, 3 orders of magnitude lower than needed for this exercise. How achievable might this be, including a simple instrument?
While the orbit of Saturn is a nice distance (even though there is no monolith on Iapetus, and Methone is probably not a lurker), it can be reached within reasonable mission times with conventional propulsion. However, IMO, it would be a game-changer to reach deep into the Kuiper belt and map the local ISM with many inexpensive probes.
But baby steps before running.
It would be very challenging to integrate a useful payload into such a lightweight package. But…
Imagine sending a series of such sails on that trajectory, capable of little more than doing course corrections. And then have them impacting a pusher plate on the actual probe!
It would be a very macroscopic “mass beam” propulsion system.
I’ve long thought that this was a more practical use for the Starshot proposal, too.
This way the ultra high performance sail doesn’t need to be very much more than just a sail, and the probe itself can be more conventional in construction, and not nearly as mass constrained.
I agree that using these sails with some sort of course adjustments might be very suited to such propulsion as the linear trajectory makes this a lot easier.
Where I think the idea is difficult is that all the sails must travel at the same velocity, traveling in a stream to hit the main ship. But each momentum transfer increases the ship’s velocity up to the sail velocities. Thus the acceleration is reduced as the impact rate declines and the velocity difference declines as the ship and sail velocities converge.
What might be a reasonable final ship velocity if the distance to the ship was set at a maximum, e.g. A AU, and the sails have to be separated by B km, with the baseline ship mass of C kg, and the sail mass of D kg, and the deployment at E AU from the sun (or F km/s). I assume some sort of exponential decline in acceleration until the ship velocity = sail velocity.
It should make for a fairly simple computation. The delta_V cost of placing the sails in an orbit to propel the main ship needs to be taken into account too, although that might be minimal if the deployment was at 1 AU.
Another issue is that the ship itself would start in an elliptical orbit and effectively spiral outwards. Therefore the sails taking a linear trajectory need to be timed so that their linear trajectory intersects the ship after it has been accelerated after N sails in the stream before the nth sail has deployed. That is potentially a lot of computation which must be accurate enough to allow for fairly minimal course adjustments. Lastly, the sails would become part of the ship’s mass, so unless the ship’s final velocity was much less than the sails, then we have something akin to the rocket equation but with the exhaust velocity also decreasing, so the average velocity differential might be the exhaust velocity.
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e.g. [Assuming calculation approach is correct. Use rocket equation adjusted for average relative impact velocity => Ve, and where aggregate sail masses = propellant mass.]
V_sail = 30 km/s
delta_V_ship = 3 km/s
Ave “exhaust velocity” = (30 + (30-3))/2 = 28.5
M0/M1 = 1.11 (aggregate sail masses ~= 1/9th ship mass)
V_sail = 30 km/s
delta_V_ship = 15 km/s
Ave “exhaust velocity” = (30 + (30-15))/2 = 22.5
M0/M1 = 1.94 (aggregate sail masses ~= ship mass)
V_sail = 30 km/s
delta_V_ship = 30 km/s
Ave “exhaust velocity” = (30 + (30-30))/2 = 15
M0/M1 = 7.39 (aggregate sail masses ~= 6.4x ship mass – and much larger than the 1.7x of propellant to rocket mass for the rocket equation with constant constant Ve)
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OTOH, the same approach might be useful for asteroid deflection as each sail would not seriously disrupt rubble-pile asteroids.
The previous calculation assumed that the sails added their mass to the ship as it was accelerated, thus mimicking the rocket equation but with variable Ve (“exhaust velocity”). What if I assume that the sail provides a perfectly elastic momentum transfer, thus ending up with the velocity of the ship before impact as the ship departs with an incrementally increased velocity?
Then there is a simple momentum transfer, where the final ship’s de;ta_V is the sum of the sail masses x relative_velocity, In aggregate, the velocities of the sail average out as before.
M_ship * delta_V = m_sails * Ve
For M_ship = 1, m_sails = delta_V/Ve
For ship delta_V of 30,
m_sails = 30/15 = 2
Much less than the prior version, but still greater than the rocket equation that would require 1.7x the ship’s empty mass of propellant.
What both these approaches show is that the use of linear trajectory statite sails can only push a ship to the velocity of the sail, unlike the rocket equation that allows the final velocity to exceed the exhaust velocity.
To get high delta_V for the ship, the sails must be deployed in orbits with velocities at least as high as the designed ship delta_V. This requires the orbits to approach closer to the sun, and therefore tolerate the increased heating.
IMO, the use of macroscopic matter to accelerate a ship is better done with beamed sails which can be given very high velocities (e.g. Breakthrough Starshot velocities of fractions of c) that can efficiently accelerate a larger ship with very little averaged impact velocity decline over the accelerating period, making the performance more like that of an ion engine – small propellant mass with very high exhaust velocity.
Using the above approach, we can determine the delta_V for any ship assuming the sail velocity (Vs), and the same breakeven mass ratio of propellant to empty weight for an equivalent rocket [1.718].
For any Vs, if 1.718 x the mass of the ship is hit by sails to impart momentum and increase the ship’s velocity, the delta_V of the ship will be 0.924xVe. This is less than the 1.0 Ve for a rocket and is also a limit for using sails to accelerate a ship using the linear trajectory statite sails. This implies that to push any ship to escape velocity from our sun, the statite sails must be deployed from an orbit inside the ship to compensate for the maximum velocity the ship can achieve.
Therefore if the sails are launched from Earth orbit, with a linear velocity of 29.8 km/s, then the ship can only gain 27.5 km/s from the sails’ momentum, assuming it was at rest or a very low orbital velocity in the outer solar system.
If the ship was also in Earth’s orbit, there would be no velocity gain as the sails and the ship would have the same velocity. The ship must therefore already be in the outer solar system to gain useful velocity.
Alternatively, the sails could be deployed much closer to the sun. As the escape velocity from the sun at 1AU is around 43 km/s This means the sails must be in an orbit that provides the needed 43 km/s. If the mass required is 1.72x the ship mass, then this orbit needs to have a velocity of about 46.5 km/s. That would require deploying the sails near the orbit of Mercury (~= 48 km/s), or fewer sails inside Mercury’s orbit with higher velocities.
Assuming that the construction of the sails is inexpensive and that the navigation to the inner system is simple so that a stream of sails can fall into the required perihelion, set their deployment time and position to create the needed linear intercept trajectory, and with perhaps some course correction capability, this might indeed be a possible way to launch a larger ship into the outer solar system with the needed escape velocity to enter interstellar space. As the sails need be no more than very low mass, needed for the required low areal density, and probably onboard computation and navigation capability, this is very much in the design direction of Breakthrough Starshot sails, albeit with different heat and acceleration requirements. As these sails need no laser propulsion, they can be released in huge swarms to make their way into the inner system, then deploy in a stream that accelerates the ship until it reaches escape velocity. This is a complex logistical problem, but it does offer the scope of huge manufacturing economies of scale and relatively inexpensive deployment, whether from low-cost launchers to LEO, or space manufacture.
One final thought. If teh sails simply transfer their momentum, they can then fall back towards the sun, redeploy, and be aligned for a renewed deployment to transfer momentum back to teh ship again. This recycling of the sails reduces the needed sail mass considerably. It reminds me of the fanciful ideas of recycling rocket exhaust in some early, pre-space-age spaceship concepts, or even the Russian funicular concept for a space elevator.
This doesn’t solve the very high velocities needed for interstellar travel, and it is even more complex than the idea of a small swarm of probes that can combine to make a larger craft, but I think the recycling of sails to accelerate a ship is a novel concept. How workable it is, even using non-statite sails, I have no idea.
You’d probably want to start out with the solar driven sails during initial acceleration, and transition to Starshot, with it’s higher energy cost, as that started to be ineffective. This works out because early in the flight the angle between your Starshot laser array and the path of the probe would vary radically over the Earth’s orbit, a factor that would decline once the probe was several AU out, while the path of sails accelerated by the Sun could be individually tailored to the trajectory of the probe and remain constantly aligned.
Use of the Starshot array this way really suggests that it shouldn’t be on the Earth’s surface, or at least not anywhere near the equator; You’d want close to a 100% availability if the sails were being used to propel something else. If the array were situated at the South pole, it would be available about 100% of the time for missions approximately aligned with the Earth’s axis, and you’d have less concern about effects on satellites, either accidental or intended.
I don’t think an elastic transfer is necessarily feasible, (Possibly it could be approximated at high enough relative velocities that the sails were vaporized by the impact.) but there’s no reason the sails have to be retained after the impact.
Starshot lasers seem to be targeting the sails quite close to Earth, within cislunar space. IDK what the effective useful range of the phased laser arrays is, but it may be much less than a few AU, although I could be very wrong about this.
My view on much of this is economic, “good enough” technology, coupled with miniaturization and software. Space advocacy people generally assume that very large projects can be done (like Apollo) by anticipating a growing economy that will make these projects affordable. Beamed power is very expensive, and therefore needs a DoD level of funding justified by some means. Lubin pitched his lasers for planetary defense, but I would bet the military has different uses in mind (think of the X-ray laser satellites being proposed during Reagan’s term in office.). But if the economy doesn’t grow, then these projects will likely be delayed, possibly indefinitely. We are seeing that now with the NASA science missions.
Solar sailing is attractive because of what could be low costs, married with good performance. To keep the areal density low when considering the payload, miniaturization of the payload is very important. CubeSats are low-cost and relatively lightweight. Starshot carries this to extremes with both small sails and tiny payloads – mostly microelectronics and some sensors. There is plenty of room between CubeSats and Starshot levels of miniaturization to aim for, and we know that microelectronics continues to evolve, as will the sophistication of the software that is possible.
Solar sail performance regarding velocity depends on how close the sail can approach the sun (sundiver maneuver) and areal density. Velocities of 100+ km/s have been suggested, far faster than any other near-future propulsion system, and possibly with low cost too. Economies of scale could make solar sails very attractive for low-cost exploration and monitoring of our solar system as far out as the ISM. Sophisticated software that allows the sails to be autonomous would reduce mission control costs. With mass-produced, small sails with off-the-shelf payloads, and low-cost access to space, these sails could become ubiquitous, as common as the comsat swarms being placed in orbit today. They cannot replace everything, but they may just make some types of missions easy and very affordable, with redundancy reducing the need for as close to operating perfection as desired.
If only these were so inexpensive that one could buy “packs of 10” with specific sensors and comms, subscribe to a monitoring service for the data, instantiate the mission goals on the sails’ computers, have them released with a low-cost launch option, all for less than a graduate student’s annual salary.
With statite sails, if the goal is to deploy them with a predetermined velocity and linear trajectory, I think that they would be designed with materials that were lower areal density than needed, and then electronically tailored to be statites by dynamically modifying the sail reflectivity, perhaps like JAXA’s IKAROS. Monitoring of the solar output would be needed to adjust reflectivity during the flight, and course corrections, if needed, would use symmetric and asymmetric reflectivity changes, all under control by the onboard computers, rather like “fire and forget” munitions.
As Douglas Adams said: “Space is big. Really big…” I wonder how many millions/trillions of these sails could operate all over the system doing the routine work of data collection, much like our ground-based and satellite instruments do of our planet. At least some fraction might look out for lurkers, artifacts, and biosignatures including space-borne spores.
Rather than naming this object Methone, an alternate could have been “Roc” of the Sinbad stories or else its egg. And had Arthur C. Clarke ever known…
Still, looking up the Wikipedia description of this “natural” moon, the details have an oddly familiar but distorted depiction for anyone involved in the design and characterization of an artificial satellite. Starting with Methone’s depiction here is how.
Abbreviating somewhat Wikipedia observes:
0 Methone’s smooth ellipsoidal form suggests that it developed an equipotential surface, and this may be composed largely of an icy fluff, perhaps mobile enough to explain the moonlet’s lack of craters. This material property causes Methone to take the shape of a triaxial ellipsoid, in which all 3 of its principal axes are of different lengths. These differences reflect the balance between tidal forces exerted by Saturn and centrifugal forces from the moonlet’s own rotation, as well as the moonlet’s own force of gravity.
0 Methone’s longest axis points towards Saturn, and is 1.6x longer than its polar axis. This elongation is caused by tidal forces, whereas the elongation of its intermediate-length axis (1.07x the length of the polar axis) is caused by the centrifugal force of Methone’s rotation (I presume around Saturn).
0Methone’s low-density regolith may respond to impacts in a way that smooths its surface more rapidly than on rigid moonlets such as Janus or Epimetheus. Movement of the regolith may also be facilitated by more “exotic” processes such as electrostatic effects.
Assuming that Methone is in hydrostatic equilibrium, i.e. that its elongated shape simply reflects the balance between the tidal force exerted by Saturn and Methone’s gravity, its density can be estimated: 0.31+0.05 −0.03 g/cm3, among the lowest density values obtained or inferred for a Solar System body.
=
Thus, perhaps Methone is a loosely packed glob of ice, shaped by orbital dynamics. But several of the properties mentioned should be candidates for additional asides…
On the other hand, were we to engage in an “artificial” satellite design exercise starting with assigning mechanisms and instrument packages to positions on a skeletal truss, the engineering representation for dynamics and control would be a three axis inertial tensor, the proportions of its principal axes defining a similar smooth egg. Not defined by external forces but by the distributions of internal concentrations of mass.
While one’s eye might see a hatbox, the tensor representation would portray an egg, perhaps with the principal axes tilted due to the distribution of the hardware inside. Moreover, if there were an attempt to keep the satellite aligned with its geometrical coordinates, there would be a gravitational torque that would attempt to realign it, make it tumble or rock with a pendular swing about the radial axis of the body it orbited.
If Methone originated as a cooling “glob”, then perhaps it rectified that problem from the start with its long axis aligned toward Saturn. And correspondingly, when projects such as stabilizing the Extetrnal Tank in low Earth Orbit were proposed, the longitudinal axis of that object was so aligned as well. The ET is somewhat symmetric about its X or cylindrical axis, but a number of fitting on one side for oxygen feed lines give it three differing principal inertias somewhat like Methone.
While Methone has a distinctly different profile than any known natural satellite, it probably resembles artificial satellites in one respect. Should it be subject to perturbation such as an impact, it just might start to tumble. IIRC, at least one of Saturn’s satellites has been detected to rotate “chaotically”, but I have less idea of what its surface features or inertial tensor might be.
Odd how Methone seems to have avoided that.
Hyperion is the Saturnian moon subject to chaotic tumbling. Methone seems too uniform to be a chaotic tumbler.
If Methone were spherical, I don’t think we would notice much difference.
But if Methone were struck by something and not shattered, it could experience pendular motions and, I would dare to say, possibly flip about erratically until the motions were damped out. To be sure, linear analysis of a uniform density object with the geometry described could give an answer. But stable or not, it will remain an intriguing object worth further examination.
The statute might double as reflector or space solar power.
Place statites where they can hand-off power.
Maybe bouncing light between two sails?