Speaker 1: Welcome to Bedtime Astronomy. Explore the wonders of the cosmos
Speaker 1: with our soothing Bedtime Astronomie podcast. Each episode offers a
Speaker 1: gentle journey through the stars, planets, and beyond, perfect for
Speaker 1: unwinding after a long day. Let's travel through the mysteries
Speaker 1: of the universe as you drift off into a peaceful
Speaker 1: slumber under the night sky.
Speaker 2: You know, it's so easy when you step outside on
Speaker 2: a clear night and look up. It is incredibly easy
Speaker 2: to fall into this psychological trap of thinking about space
Speaker 2: as just this this quiet, echoing void.
Speaker 3: Right, Yeah, Like it's just endless emptiness exactly.
Speaker 2: Just a massive expanse with a few major planets scattered
Speaker 2: around in the dark. But I mean, if you actually
Speaker 2: zoom in on our immediate cosmic neighborhood, the physical reality is,
Speaker 2: oh no, it's entirely different. It's crowded, it is bustling
Speaker 2: right now as we speak. There are there are tens
Speaker 2: of thousands of Near Earth objects. Neo's just tumbling through
Speaker 2: the dark right in our backyard.
Speaker 3: Yeah, and we're talking about miniature worlds here. Some are
Speaker 3: the size of a city block, others are the size
Speaker 3: of a mountain.
Speaker 2: Right, And these aren't just you know, scientific curiosities for
Speaker 2: us to map and then forget about for you listening.
Speaker 2: Think of these as the most easily accessible resource caches
Speaker 2: in the entire Solar system.
Speaker 3: Absolutely heavy metals, rare earth.
Speaker 2: Elements, volatile compounds, water, ice, for institu resource utilization. They're
Speaker 2: practically right next door astronomically speaking. But the catch, and
Speaker 2: it's a huge catch to actually reaching them is massive.
Speaker 2: It really is, because figuring out the astrodynamics, like how
Speaker 2: to mathematically plot path drive up to one of these
Speaker 2: rocks and actually park next to it is a notoriously
Speaker 2: mind bendingly difficult problem.
Speaker 3: Okay, let's unpack this.
Speaker 2: Yeah, it remains one of the supreme challenges in aerospace
Speaker 2: engineering because the assumption by a lot of people is
Speaker 2: often that well, since space is a vacuum devoid of
Speaker 2: atmospheric friction, you simply aim your thrust vector at the
Speaker 2: target rendezvous coordinates and just let momentum do the rest.
Speaker 3: Just point and shoot right like a bullet exactly.
Speaker 2: But the reality of astrodynamics is governed by this chaotic
Speaker 2: web of n body gravitational interactions. Every planetary mass, every moon,
Speaker 2: the Sun, itself. They are all constantly warping the space
Speaker 2: time around them.
Speaker 3: You're all pulling at once, right, They're exerting these dynamic
Speaker 3: gravitational pulls. So calculating a viable fuel efficient path through
Speaker 3: that that constantly shifting gravitational topography has historically been one
Speaker 3: of the tightest bottlenecks in mission planning.
Speaker 2: It sounds like a nightmare.
Speaker 3: You are essentially trying to thread a needle, right, but
Speaker 3: the needle is moving at tens of thousands of miles
Speaker 3: an hour, and the thread is constantly being pulled by
Speaker 3: invisible magnets from every direction.
Speaker 2: Man. That is a great visual which makes the recent
Speaker 2: work coming out of Khalifa University so incredibly compelling. Alisandra
Speaker 2: Biolci and his co authors, they put this out on
Speaker 2: our sleeve. They've effectively rewritten the fundamental mathematical road maps
Speaker 2: we use to navigate deep space.
Speaker 3: It's a massive deal.
Speaker 2: And just to be clear, this isn't some minor optimization
Speaker 2: of existing software. They haven't just like tweaked a fuel
Speaker 2: mixture or shaved a few kilograms off a chassis.
Speaker 3: No, not at all.
Speaker 2: They are proposing a wholesale paradigm shift in the underlying
Speaker 2: mathematics of trajectory generation. By integrating modern continuous thrust propulsion
Speaker 2: models with highly complex dynamical systems theory, they've unlocked, get this,
Speaker 2: over two million new incredibly low energy, highly viable routes
Speaker 2: to these asteroids. Yeah.
Speaker 3: The magnitude of finding two million viable trajectories, I mean,
Speaker 3: it really cannot be overstated. It's staggering because for decades,
Speaker 3: orbital mechanics has been heavily constrained by a very rigid
Speaker 3: set of mathematical assumptions. And you know, those assumptions were
Speaker 3: brilliant for the Apollo era, right, they got us to
Speaker 3: the Moon exactly, and they successfully navigated the voyager probes
Speaker 3: entirely out of the Solar system, but they were inextricably
Speaker 3: tied to the hardware and the computational limitations of the
Speaker 3: mid twentieth century.
Speaker 2: So it changed.
Speaker 3: Well, what Bilchi's team recognized is that our modern hardware,
Speaker 3: specifically our propulsion technology, has vastly outpaced those legacy trajectory algorithms.
Speaker 3: We have basically been trying to fly twenty first century
Speaker 3: ion engines using math that was designed for chemical rockets.
Speaker 2: That sounds like running a modern video game on a
Speaker 2: computer from the nineteen nineties.
Speaker 3: It's exactly like that. And by abandoning those legacy constraints
Speaker 3: and developing a less computationally prohibitive way to model multi
Speaker 3: body gravity, they've drastically reduced the launch escape energy required
Speaker 3: to get these missions off the ground.
Speaker 2: Okay, so to really understand why this new math is
Speaker 2: so groundbreaking, we first have to understand the flawed kind
Speaker 2: of brute force way we've been exploring space for decades, right.
Speaker 3: Yeah, the legacy constraints, right.
Speaker 2: So the contrast is where the genius of this new
Speaker 2: approach really shines. Let's talk about the patched conics method,
Speaker 2: because for a long time this was the absolute gold
Speaker 2: standard for NASA mission planners.
Speaker 3: He was the only way to do it really right.
Speaker 2: And the mathematical foundation of this patched conics method relies
Speaker 2: heavily on something called the two body problem. It simplifies
Speaker 2: that crazy magnetic thread chaos you mentioned earlier by stripping
Speaker 2: the universe down to just two interacting masses at any
Speaker 2: given time. Usually that's just the Sun and the spacecraft, right.
Speaker 3: And it's an incredibly clever workaround for the lack of
Speaker 3: raw supercomputing power back in the day. In the two
Speaker 3: body problem, you actually have an analytical solution.
Speaker 2: Meaning you can solve it cleanly on paper.
Speaker 3: Exactly thanks to Johannes Kepler and Isaac Newton. If you
Speaker 3: only have two bodies, you can perfectly predict their positions
Speaker 3: at any point in the future using relatively simple algebraic equations.
Speaker 3: The orbit will always be a perfect conics section, a
Speaker 3: circle and ellipse, a parabola, or a.
Speaker 2: Hyperbola, hence the name patched conics. Right.
Speaker 3: But the moment you introduce a third body, say you
Speaker 3: have the Earth, the Sun, and a spacecraft all interacting,
Speaker 3: that neat analytical solution just vanishes. You enter the realm
Speaker 3: of chaos.
Speaker 2: Theory, like on repoint great Proof back in the late
Speaker 2: nineteenth century.
Speaker 3: Right, Yes, you can no longer solve it with a
Speaker 3: neat equation. You have to use numerical integration. You have
Speaker 3: to calculate the forces step by step, microsecond by microsecond,
Speaker 3: which is computationally exhausting.
Speaker 2: Wait, so to avoid that computational nightmare for decades the
Speaker 2: space exploration the map basically pretended Jupiter, Mars, and even
Speaker 2: Earth didn't exist once we launched. Essentially, yes, That sounds crazy.
Speaker 2: That sounds like planning a cross country road trip by
Speaker 2: drawing a perfectly straight line on a map and just
Speaker 2: assuming there are no mountains in the way.
Speaker 3: It's a great analogy, but there's a good reason for it,
Speaker 3: computational pragmatism. Calculating multiple gravities at once requires a massive
Speaker 3: amount of computational power, So they effectively sliced the Solar
Speaker 3: System up into isolated spheres.
Speaker 2: Of influence, well place spheres right.
Speaker 3: Exactly when a probe launches, the math considers only the
Speaker 3: Earth and the spacecraft. The Sun is ignored, Jupiter is ignored.
Speaker 3: There Once the probe crosses an invisible mathematical boundary the
Speaker 3: edge of Earth's sphere of influence, the software essentially drops
Speaker 3: Earth from the equation entirely and switches to a Sun
Speaker 3: spacecraft two body problem.
Speaker 2: So it treats the complex overlapping gravity wells of the
Speaker 2: entire Solar System as just a series of isolated sterile bubbles.
Speaker 3: That is the absolute essence of it. You solve the
Speaker 3: geocentric hyperbola for the escape, you solve the heliocentric ellipse
Speaker 3: for the cruise phase, and you solve the target centric
Speaker 3: hyperbola for the arrival. Then you mathematically, quite literally, patch
Speaker 3: these conic sections together at the boundaries.
Speaker 2: That's wild. It's basically a mathematical fiction.
Speaker 3: It is a brilliant mathematical fiction. But the friction between
Speaker 3: that fiction and the actual physical reality of the Solar system, well,
Speaker 3: that has to be paid for, and it is paid
Speaker 3: for in fuel.
Speaker 2: Because Earth doesn't actually stop pulling on the spacecraft just
Speaker 2: because crossed some imaginary mathematical line.
Speaker 3: Exactly, The actual trajectory drifts from the patched conic mathematical prediction.
Speaker 3: So to fix that drift you have to perform mid
Speaker 3: course correction burns. You spend delta V meaning fuel to
Speaker 3: force the reality to match your simplified math man.
Speaker 2: And that reliance on delta V that perfectly aligns with
Speaker 2: the hardware of that era, doesn't it the chemical.
Speaker 3: Rocket, oh, perfectly. The patched conics method fundamentally assumes impulsive maneuvers.
Speaker 2: Meaning explosive right. It assumes that all velocity changes happen instantaneously,
Speaker 2: which from a mathematical perspective, makes total sense. If you
Speaker 2: are firing a massive chemical engine, you ignite hydrolocks or
Speaker 2: hypergolic propellants. Dump massive thermal energy at the nozzle and
Speaker 2: generate thousands of kilinusians of thrust in just a matter
Speaker 2: of minutes.
Speaker 3: Right, The velocity vector changes so rapidly that for the
Speaker 3: sake of the orbital integration math, you can treat the
Speaker 3: burn time as effectively zero.
Speaker 2: It's an instant note on the path exactly.
Speaker 3: The math and the hardware were perfectly symbiotic, but there's
Speaker 3: a massive penalty. The Silkovski rocket equation dictates that if
Speaker 3: you want to perform these massive impulsive plane changes or
Speaker 3: orbital insertions, you need a tremendous amount.
Speaker 2: Of chemical propellant, and propellant is heavy, very.
Speaker 3: Heavy, and that propellant adds mass to the spacecraft, which
Speaker 3: requires an even larger rocket to lift out of Earth's
Speaker 3: gravity well, which requires even more propellant. It's the tilent
Speaker 3: of mass fraction.
Speaker 2: So we were optimizing missions purely to minimize flight time
Speaker 2: and limit the number of those impulsive burns, because every
Speaker 2: single burn required dragging tons of all chemicals into deep
Speaker 2: space exactly.
Speaker 3: Chemical rockets are the hair in space travel, fast, explosive,
Speaker 3: but they really limit your long term options. The patched
Speaker 3: conix method was designed explicitly to string together these explosive
Speaker 3: instantaneous nodes.
Speaker 2: But the Brude force math that worked for explosive rockets,
Speaker 2: it just doesn't compute for the new hardware we have Now.
Speaker 2: Mulsion paradigm has completely shifted.
Speaker 3: It has We are increasingly moving away from chemical propulsion
Speaker 3: for deep space transit.
Speaker 2: Right We're moving in favor of solar electric propulsion or SEP,
Speaker 2: things like gridded ion thrusters, hall effect thrusters, and SEP
Speaker 2: operates on a completely different physical principle.
Speaker 3: Totally different.
Speaker 2: Instead of chemical combustion, we are using solar arrays to
Speaker 2: generate electricity, using that power to ionize an inert gas
Speaker 2: like xenon, and then accelerating those ions out the back
Speaker 2: through a high voltage grid. And the specific impulse the
Speaker 2: efficiency of the engine is an order of magnitude higher
Speaker 2: than the best chemical rockets.
Speaker 3: The efficiency is just staggering. A really good chemical engine
Speaker 3: might give you a specific impulse of say four hundred
Speaker 3: and fifty seconds. A modern ion thruster can easily push
Speaker 3: three thousand to four thousand seconds. Wow, you are getting
Speaker 3: vastly more delta V per kilogram of propellant. But the
Speaker 3: tradeoff is the raw thrust. The mass of those xenon
Speaker 3: ions is so incredibly low that the actual physical force
Speaker 3: imparted on the spacecraft at any even moment is minuscule.
Speaker 2: Now minuscule, we're talking.
Speaker 3: Well, if you activated a standard five kilo ion thruster
Speaker 3: right here on Earth, the thrust it produces wouldn't even
Speaker 3: be enough to counteract the friction of a rolling coin.
Speaker 3: It is roughly equivalent to the downward gravitational force of
Speaker 3: a single piece of tinder paper resting in the palm
Speaker 3: of your hand.
Speaker 2: Wait, okay, here's where it gets really interesting. Let's pause
Speaker 2: on that, because the disconnect between the visual of like
Speaker 2: a towering Saturn V launch and the reality of deep
Speaker 2: space propulsion is vast. You're telling me I could push
Speaker 2: a multi ton spaceship with the force of a sticky
Speaker 2: note and eventually outraise a chemical rocket.
Speaker 3: Yes, because it's continuous. But if you only have that
Speaker 3: tiny fraction of a newton of thrust, you can't perform
Speaker 3: an impulsive maneuver, right.
Speaker 2: You can't just fire the engine for three minutes to
Speaker 2: enter an orbit like in the movies.
Speaker 3: No, you have to run that ion thruster continuously for
Speaker 3: thousands of hours. You're accumulating that tiny acceleration week after week,
Speaker 3: month after month. It is the tortoise of space travel.
Speaker 2: So how does the old math handle that?
Speaker 3: It doesn't. NASA's old code literally couldn't understand or map
Speaker 3: routes for slow burn technologies. Like step in a chemical trajectory,
Speaker 3: you have long periods of ballistic cursting where Kepler's laws
Speaker 3: apply perfectly, punctuated by brief burns. But within sep engine
Speaker 3: firing constantly, the spacecraft never actually settles into a clean
Speaker 3: cauplearian orbit.
Speaker 2: Because the orbital energy is constantly changing.
Speaker 3: Exactly this semi major axis is constantly expanding or contracting.
Speaker 3: The patched conics method completely collapses when you try to
Speaker 3: feed it a continuous thrust profile, because it relies on
Speaker 3: the assumption of instantaneous state changes. You can no longer
Speaker 3: patch simple curves together. You have to integrate the trajectory
Speaker 3: over massive time scales.
Speaker 2: And if your engine is only pushing with the force
Speaker 2: of a piece of paper, you are completely at the
Speaker 2: mercy of the surrounding gravitational environment, aren't you.
Speaker 3: Absolutely you can't ignore the Earth and the mood anymore.
Speaker 2: It makes me think a chemical rocket is like a speedboat.
Speaker 2: Right you point it, hit the throttle, and you can
Speaker 2: largely ignore the ocean currents because you're just blasting over them.
Speaker 2: But a set powered spacecraft is more like a sailboat.
Speaker 3: That is a perfect way to look at it.
Speaker 2: If you try to fight a strong gravitational tide with
Speaker 2: an engine that week, you will simply be overpowered and
Speaker 2: dragged way off course. You have to learn how to
Speaker 2: read the currents and sail.
Speaker 3: With them, and the necessity of reading those currents is
Speaker 3: exactly what forced Biulci's team to abandon the two body
Speaker 3: patched conics approximation in the vicinity of Earth. If your
Speaker 3: thrust is that low, the gravitational perturbations of the Moon
Speaker 3: in the Sun are no longer rounding errors you can
Speaker 3: just correct later with a fuel burn.
Speaker 2: They're dominant forces that dictate your trajectory.
Speaker 3: Exactly to accurately model how an SCEP spacecraft navigates the
Speaker 3: Earth Moon Sun environment, you have to upgrade the mathematics.
Speaker 3: You have to use what's called the circular restricted three
Speaker 3: body problem or CR three BP, and the CR three.
Speaker 2: BP introduces that gravitational tug of war instead of isolating
Speaker 2: the Earth and ignoring the Sun. The math explicitly models
Speaker 2: the spacecraft moving through the combined gravitational topography of both
Speaker 2: massive bodies simultaneously.
Speaker 3: Right, and the physical topology of space changes completely under
Speaker 3: the CR three BP well. In a two body system,
Speaker 3: the gravity well is just a simple symmetrical funnel leading
Speaker 3: straight down to the central mass. But when you have
Speaker 3: two massive bodies orbiting their berry center, like the Earth
Speaker 3: and the Sun, their intercepting gravitational fields create a highly
Speaker 3: complex potential energy surface like it's lumpy, very lumpy. The
Speaker 3: centrifugal force of the rotating reference frame combined with the
Speaker 3: gravitational pull of the two primary bodies, creates specific regions
Speaker 3: where the forces perfectly cancel each other out, and these
Speaker 3: are the lagrange.
Speaker 2: Points right L one through L five. We frequently hear
Speaker 2: about those like the James Web Space Telescope parking out
Speaker 2: at L two or the solar observatories at L one.
Speaker 2: They are essentially points of equilibrium.
Speaker 3: Exactly if you navigate a spacecraft to a lagrange point,
Speaker 3: it takes a virtually non existent amount of station keeping
Speaker 3: delta V to maintain that position. It's a gravitational balancing act.
Speaker 2: So they serve as the perfect staging nodes.
Speaker 3: They do, but the lagraage points themselves are just the
Speaker 3: anchors for something much more profound in dynamical systems theory.
Speaker 3: The mathematics of the CR THREEVP reveals that these equilibrium
Speaker 3: points are actually connected by invariant manifolds.
Speaker 2: Invariant manifolds, what exactly does that look like?
Speaker 3: Well, to visualize this, you have to look at phase space,
Speaker 3: which maps not just the position of the spacecraft in
Speaker 3: three dimensions, but it's velocity in three dimensions as well.
Speaker 3: So within that six dimensional fase space, stable and unstable
Speaker 3: manifolds emerge from the lagrange points. They form these topological
Speaker 3: tubes that sneak their way through the Solar system.
Speaker 2: Okay, so these are the invisible highways. Yes.
Speaker 3: What's fascinating here is that space is not empty. It
Speaker 3: is a topological landscape of peaks and valleys of gravity.
Speaker 2: So instead of using a speedboat to blast across the water,
Speaker 2: we are suddenly reading the ocean currents. We're parking our
Speaker 2: raft and a the lagrange point and then catching a
Speaker 2: riptide the invariant manifold to drift exactly where we need
Speaker 2: to go for basically free.
Speaker 3: Exactly, you expend a tiny bit of fuel to get
Speaker 3: into the manifold tube, and the natural gravitational gradient does
Speaker 3: all the heavy lifting, carrying you millions of kilometers into
Speaker 3: deep space. By mapping the CR THREEVP, we aren't fighting
Speaker 3: nature with rocket fuel anymore. We are literally surfing the
Speaker 3: Solar System's natural gravity waves.
Speaker 2: That is just so elegant.
Speaker 3: It is by coupling the continuous, highly efficient thrust of
Speaker 3: INCEP engine with the zero cost transit of an invariant manifold,
Speaker 3: bi Alce's team solved the massive fuel constraints that played
Speaker 3: all those early asteroid missions. You just use a little
Speaker 3: ion engine to gently steer between manifolds rather than fighting
Speaker 3: gravity to create your own path.
Speaker 2: Okay, but navigating the complex currents near Earth is brilliant.
Speaker 2: But earlier you mentioned that integrating the CR THREEVP introduces
Speaker 2: a computational nightmare. If the three body math is highly
Speaker 2: chaotic and incredibly sensitive to initial conditions. You know the
Speaker 2: classic butterfly effect where a microscopic rounding error on day
Speaker 2: one compounds into a million kilometer or miss by year three.
Speaker 2: How do they actually run a simulation for a multi
Speaker 2: year asteroid rendezvous without the computers just melting down.
Speaker 3: It's a very real problem. The chaotic nature of the
Speaker 3: CR three BP means that long duration numerical integration is
Speaker 3: intrinsically unstable. There are these things called Lyapunov exponents, which
Speaker 3: basically measure how quickly two slightly different trajectories diverge in
Speaker 3: a chaotic system, and they guarantee that computing a continuous,
Speaker 3: unbroken path from Earth to a deep space NEO and
Speaker 3: back is mathematically intractable.
Speaker 2: The optimization algorithms will simply fail to converge on a.
Speaker 3: Solution every time. So to solve this, the researchers had
Speaker 3: to decouple the trajectory. They employ a modular architecture Frankenstein trajectory. Yeah,
Speaker 3: Frankenstein trajectory. They break the mission into segments. They use
Speaker 3: the complex CR three VP math while the spacecraft is
Speaker 3: navigating the Earth's sun lagrange, utilizing those invariant manifolds to
Speaker 3: escape the Earth's gravity well efficiently. But once the spacecraft
Speaker 3: travels far enough into deep space where the Earth's gravitational
Speaker 3: influence drops below a significant perturbation threshold, the software intentionally
Speaker 3: drops the three body dynamics.
Speaker 2: Oh, it reverts to the traditional two body heliocentric.
Speaker 3: Model exactly because at a certain distance, the complex dynamical
Speaker 3: topography smooths out, the Sun becomes the overwhelmingly dominant force,
Speaker 3: and trying to model the Earth's distant microscopic pull is
Speaker 3: just a waste of computational resources that only introduces integration errors.
Speaker 2: That makes total sense, But the.
Speaker 3: Real breakthrough in the decoupling is how they handle the
Speaker 3: return trip. They don't run a forward integration from launch
Speaker 3: to return as one long math problem. They calculate the
Speaker 3: outbound leg from Earth to the asteroid, then completely independently,
Speaker 3: they calculate the inbound leg from the asteroid back to Earth.
Speaker 2: Wait. Wait, so we're effectively running two completely different software
Speaker 2: program and just duct taping the results together when we
Speaker 2: reach the asteroid. Why does separating the trip home from
Speaker 2: the trip there matters so much?
Speaker 3: Because of that computational chaos we talked about. If you
Speaker 3: calculate a round trip as one continuous equation, a tiny
Speaker 3: variable change on day one completely ruins the math for
Speaker 3: year three. By cutting the trip in half and stitching
Speaker 3: it together at the destination, you save massive amounts of
Speaker 3: computational power.
Speaker 2: But if you calculate the outbound trip and the inbound
Speaker 2: trip as two completely isolated mathematical events, how do you
Speaker 2: reconcile them at the asteroid? The spacecraft is physically one
Speaker 2: continuous object. You can't just arrive at an asteroid with
Speaker 2: one velocity and instantly swap to a different coordinate system
Speaker 2: and a different velocity for the trip home without violating
Speaker 2: the laws of physics.
Speaker 3: Right, there has to be a physical bridge, and that
Speaker 3: bridge is established through highly advanced boundary value optimization.
Speaker 2: How does that work well?
Speaker 3: When the outbound trajectory arrives at the near Earth object,
Speaker 3: it has a specific state vector, a precise position, velocity, mass,
Speaker 3: and time epoch. Now, the independently calculated return trajectory requires
Speaker 3: a very specific starting state vector to successfully ride the
Speaker 3: manifolds back to Earth. The gap between those two state
Speaker 3: vectors that is the optimization problem I see. The algorithm
Speaker 3: uses nonlinear programming to iteratively adjust the launch parameters, the
Speaker 3: manifold insertion points, and the SEP thrust profiles until the
Speaker 3: state vector at the end of the outbound leg perfectly
Speaker 3: matches the state vector required for the inbound leg.
Speaker 2: So they're effectively working the problem from both ends toward
Speaker 2: the middle, just tweaking the variables on both sides until
Speaker 2: the math perfectly aligns at the asteroid, allowing for a
Speaker 2: seamless transition.
Speaker 3: Duct tape, high tech mathematical duct tape. Yes, they enforce
Speaker 3: continuity constraints. They ensure that mass, time, position, and velocity
Speaker 3: match perfectly at the boundary, and by doing this they
Speaker 3: completely bypass the chaotic instability of a single continuous integration.
Speaker 2: Okay, so the researchers built this brilliant, computationally efficient, slow
Speaker 2: burn friendly gravity surfing mathematical model. What happened when they
Speaker 2: actually turned it on?
Speaker 3: The simulation results were just they were staggering. This mathematical
Speaker 3: architecture is so computationally efficient that they were able to
Speaker 3: run simulations on eighty different Near Earth objects, testing the
Speaker 3: entire parameter space of departure dates, in flight times.
Speaker 2: Eighty actual asteroids with relatively flat, low eccentricity orbits. And
Speaker 2: what did the model spid out?
Speaker 3: Over two million distinct viable round trip trajectories.
Speaker 2: Two million.
Speaker 3: Yes, and they didn't just generate these in a vacuum.
Speaker 3: They benchmarked them against NASA's Near Earth object human spaceflight
Speaker 3: accessible targets study.
Speaker 2: The NAHATS database NAHATSS represents the pinnacle of legacy trajectory
Speaker 2: design right utilizing standard impulsive maneuvers and traditional mathematical models exactly.
Speaker 3: And when they compared the new hybrid continuous thrust CR
Speaker 3: three BP trajectories against the nahat's ATA base, the required
Speaker 3: delta V for the missions was somewhat comparable. But the
Speaker 3: critical metric that plummeted, the one that really matters, was
Speaker 3: the launch escape energy, which is widely known in orbital
Speaker 3: mechanics as C three.
Speaker 2: Okay, break C three down for us because that sounds important.
Speaker 3: C three is arguably the single most restrictive metric in
Speaker 3: mission architecture. It represents the square of the hyperbolic excess velocity.
Speaker 2: So what does this all mean for you the listener.
Speaker 2: Let's translate this into plane English.
Speaker 3: Well, when a launch vehicle lifts a payload off the pad,
Speaker 3: it has to overcome the immense gravitational potential energy of
Speaker 3: the Earth. To send a probe into deep space, you
Speaker 3: don't just need to reach orbital velocity, you need to
Speaker 3: exceed Earth's escape velocity, the energy required to leave the
Speaker 3: Earth's sphere of influence with a specific remaining velocity. That
Speaker 3: residual speed is your hyperbolic excess velocity is quantified as
Speaker 3: C three and C three scales exponentially with the required velocity.
Speaker 2: So if your trajectory algorithm dictates that you need a
Speaker 2: massive initial kick to brute force your way onto an
Speaker 2: inter planetary transfer orbit, your C three requirements skyrockets.
Speaker 3: Yes and high. C three dictates a massive heavy lift rocket.
Speaker 3: If you need a C three of say thirty square
Speaker 3: kilometers per second squared, you might need a Falcon Heavy
Speaker 3: or an SLS just to throw a modest probe into.
Speaker 2: Deep space, and those cost hundreds of millions of dollars.
Speaker 2: But by utilizing the invariant manifolds of the Earth some
Speaker 2: of the garnge points, the new trajectories effectively siphon energy
Speaker 2: from the dynamical system itself.
Speaker 3: Precisely, the spacecraft isn't relying entirely on the launch vehicle
Speaker 3: to provide the kinetic energy required to reach deep space.
Speaker 3: It's riding the gravitational gradients. Consequently, the C three requirement
Speaker 3: drops precipitously, so.
Speaker 2: Lower launch escape energy means you need way less rocket
Speaker 2: power to get off Earth, which translates to a massively
Speaker 2: cheap e mission. A mission that previously required a dedicated
Speaker 2: heavy lift rocket could potentially hitch a ride on a
Speaker 2: medium lift vehicle or even launch as a secondary payload.
Speaker 2: It opens the door for a gold rush of cheap probes.
Speaker 3: If we connect this to the bigger picture. The fact
Speaker 3: that they found two million viable paths for just eighty
Speaker 3: asteroids proves that the Solar System is infinitely more accessible
Speaker 3: than our old brute force math led us to believe
Speaker 3: the economics of asteroid exploration fundamentally shift. It opens the
Speaker 3: inner Solar system to university research teams, private resource prospecting companies.
Speaker 2: Smaller national space agencies, anyone, really, But two million trajectories
Speaker 2: is an abstract number. Let's look at how this new
Speaker 2: math handles specific real world rocks floating out there right now.
Speaker 2: Because the true test of an algorithm isn't just lowering
Speaker 2: the C three for easy, simple targets. It's handling the
Speaker 2: chaotic outliers.
Speaker 3: Oh absolutely, and the researchers highlighted two specific case studies
Speaker 3: that really push the boundaries of orbital mechanics. The first
Speaker 3: one is asteroid nineteen ninety one veg.
Speaker 2: What makes nineteen ninety one veg so special.
Speaker 3: It's a fascinating dynamical object. Its orbit is so similar
Speaker 3: to Earth's that it routinely enters our immediate neighborhood, and
Speaker 3: occasionally it even gets temporarily captured by Earth's gravity as
Speaker 3: a q as I satellite or a mini moon. Oh cool, right,
Speaker 3: But because its sonotic period, the time it takes to
Speaker 3: return to the same position relative to Earth is so complex.
Speaker 3: Plotting a rendezvous requires incredible precision. The legacy approach would
Speaker 3: typically struggle with all the overlapping perturbations, but.
Speaker 2: The hybrid algorithm plotted an alternate GIT transfer. It did.
Speaker 2: It mapped a path where the spacecraft launches from Earth,
Speaker 2: navigates to the L one lagrange point directly between the
Speaker 2: Earth and the Sun, and just parks. It waits for
Speaker 2: the precise epic when nineteen ninety one VG drifts through
Speaker 2: the localized phase space, initiates the rendezvous, and then, rather
Speaker 2: than fighting its way back to L one, it departs
Speaker 2: via a completely different manifold.
Speaker 3: Exactly, it utilizes a heteroclinic connection. It transfers from the
Speaker 3: stable manifold associated with the L one region directly into
Speaker 3: the orbital regime of the asteroid, and then for the
Speaker 3: return it couples onto a manifold that winds toward the
Speaker 3: L two lagrange point, which is located on the far
Speaker 3: side of the Earth opposite the Sun.
Speaker 2: I love this. It's like sneaking out the front door,
Speaker 2: visiting a mini moon, and then sneaking back into the
Speaker 2: back door. It turns orbital mechanics into a beautifully choreographed dance.
Speaker 3: It really does. The spacecraft effectively uses the gravitational currents
Speaker 3: to sweep across the Earth's orbital path, intercept the target,
Speaker 3: and ride the wake back to the other side of
Speaker 3: the planet, and the delta vie required for the actual
Speaker 3: transit is negligible because the manifolds are doing all the work.
Speaker 2: It transforms trajectory design from a root force artillery problem
Speaker 2: into something closer to fluid dynamics, but nineteen ninety one veg.
Speaker 2: While dynamically tricky, still exists relatively close to the ecliptic plane.
Speaker 2: The ultimate stress test for any trajectory algorithm is a
Speaker 2: highly inclined, highly eccentric.
Speaker 3: Orbit, which is why their second case study focused on Apofus.
Speaker 2: Apofus, the famous one.
Speaker 3: Yeah Apofus is notorious in the astrodynamics community. Its eccentricity
Speaker 3: means its velocity fluctuates wildly as it moves from periapsis
Speaker 3: to apoapsis, making phasing a rendezvous in incredibly difficult. But
Speaker 3: the true penalty comes from its orbital inclination right.
Speaker 2: Apofus does not orbit on the same flat, two dimensional
Speaker 2: plane as the Earth. Its orbit is tilted highly.
Speaker 3: Tilted, and inclination changes are the most punishing maneuvers in
Speaker 3: all of spaceflight.
Speaker 2: If a spacecraft is cruising along the ecliptic plane and
Speaker 2: it needs to pitch up to intercept a target like
Speaker 2: a poffas it isn't just a matter of steering, is it.
Speaker 3: No? Vector mathematics dictates that you effectively have to cancel
Speaker 3: out a massive portion of your existing velocity vector in
Speaker 3: the horizontal plane and reaccelerate in the vertical plane. It
Speaker 3: is catastrophically expensive in terms of delta V.
Speaker 2: And performing a deep space inclination change using only a
Speaker 2: low thrust step engine. I mean that's often mission ending right.
Speaker 3: Usually yes, the engine simply cannot impart enough force quickly
Speaker 3: enough to crank the orbital plane before the spacecraft overshoots
Speaker 3: the intercept window in a legacy two body framework, a
Speaker 3: pofics requires massive chemical burns.
Speaker 2: So how did the algorithm handle it beautifully?
Speaker 3: Bi Olce's algorithm leverages the CRS three dynamics to bypass
Speaker 3: the plane change entirely.
Speaker 2: Wow.
Speaker 3: By utilizing the complex three dimensionaltography of the invariant manifolds
Speaker 3: near Earth, the spacecraft can essentially use the Earth's gravity
Speaker 3: to crank its inclination naturally as it escapes the local system.
Speaker 3: The manifold itself is heavily inclined, providing the necessary out
Speaker 3: of plane velocity without expending onboard propellant.
Speaker 2: That is incredible. The algorithm doesn't fight the geometry of
Speaker 2: the Solar system. It uses the geometry to solve the
Speaker 2: physical constraints of the engine. It proves its robustness. It
Speaker 2: doesn't just work in easy, flat conditions. It works in
Speaker 2: the messy reality of space exactly, which brings us to
Speaker 2: the final critical phase of the architecture. Because we've figured
Speaker 2: out how to launch cheaply, coast on gravity highways, and
Speaker 2: visit tricky asteroids. But the most dangerous part of any
Speaker 2: space mission is the very last step coming home. Whether
Speaker 2: you are returning a sample of rare earth metals from
Speaker 2: an asteroid or bringing a crew home. The deep space
Speaker 2: transit is only prologued to the thermal nightmare of hitting
Speaker 2: the Earth's atmosphere.
Speaker 3: Yeah, the atmospheric interfhase is the most unforgiving regime of
Speaker 3: any mission. When a spacecraft returns from deep space, it
Speaker 3: typically arrives with immense hyperbolic excess velocity. It slams into
Speaker 3: the upper thermosphere at eleven or twelve kilometers per second.
Speaker 2: And all that kinetic energy of the spacecraft is instantly
Speaker 2: converted into thermal energy through shock layer compression. The temperature
Speaker 2: at the stagnation point on the heat shield scales with
Speaker 2: the cube of the velocity.
Speaker 3: The cube of the velocity, meaning a small increase in
Speaker 3: a rival speed results in a massive exponential increase in
Speaker 3: the heat generated.
Speaker 2: Right, So, a capsule hitting the atmosphere at twelve kilometers
Speaker 2: per second requires a significantly thicker, heavier, and more complex
Speaker 2: ablative thermal protection system than a capsule arriving at say
Speaker 2: eight kilometers.
Speaker 3: Per second, and mass is exactly what we are always
Speaker 3: trying to eliminate. Every kilogram of phenolic confused carbonublader on
Speaker 3: the heat shield is a kilogram of scientific payload or
Speaker 3: asteroid regolith that you cannot bring back.
Speaker 2: Traditional legacy trajectories optimized purely for transit time often resulted
Speaker 2: in those brutal high energy direct entries.
Speaker 3: Didn't they they did, But the manifold return trajectories generated
Speaker 3: by this new algorithm fundamentally alter the arrival dynamics because
Speaker 3: the spacecraft isn't dropping straight down the gravity.
Speaker 2: Well, it is riding the stable manifold back toward the
Speaker 2: Earth Moon system. The top logical tube of the manifold
Speaker 2: forces the spacecraft to take a winding, circuitous route, bleeding
Speaker 2: off kinetic energy and gradually matching its velocity vector with
Speaker 2: the Earth before it ever touches the atmosphere exactly.
Speaker 3: The relative velocity at atmospheric entry drops significantly. The spacecraft
Speaker 3: eases into the gravity well rather than plunging into it,
Speaker 3: and this translates directly to reduced peak heating rates and
Speaker 3: lower total heat loads.
Speaker 2: So hitting Earth's atmosphere at a slower speed means the
Speaker 2: spacecraft requires significantly less heat shielding. It's ironic we spent
Speaker 2: decades obsessed with going fast, but the real secret to
Speaker 2: unlocking the solar system was learning it goes slow.
Speaker 3: That's entirely it. It's a massive win win. The thermal
Speaker 3: protection system can be drastically lighter, further improving the mass
Speaker 3: fraction of the entire architecture. Furthermore, the lower structural loads
Speaker 3: broaden the entry corridor, increasing the margin of safety for
Speaker 3: the vehicle.
Speaker 2: The compounding efficiencies are just extraordinary to think about. You
Speaker 2: reduce the C three at launch, meaning you use a smaller,
Speaker 2: cheaper rocket. You use solar electric propulsion, replacing tons of
Speaker 2: chemical propellant with a few tanks of xenon gas. You
Speaker 2: navigate the chaotic Earth sun regime using zero cost invariant manifolds.
Speaker 3: You seamlessly stitch the coordinate systems together in deep space
Speaker 3: to bypass supercomputer constraints.
Speaker 2: Yes, you utilize the three dimensional geometry of the manifolds
Speaker 2: to intercept highly incline eccentric targets like Apophice without suicidal
Speaker 2: plane change burns. And finally, you bleed off the velocity
Speaker 2: naturally on the return, shedding hundreds of kilograms of heavy
Speaker 2: thermal shielding.
Speaker 3: It is a complete architectural overhaul of how humanity interfaces
Speaker 3: with the inner Solar System. It forces a complete reevaluation
Speaker 3: of what we consider physically possible. For the better part
Speaker 3: of a century, the aerospace community has assumed that the
Speaker 3: primary barriers to deep space industrialization and exploration were materials, science,
Speaker 3: and propulsion. We assumed we needed to forge lighter alloys,
Speaker 3: engineer denser chemical propellants, or develop nuclear thermal rockets to
Speaker 3: make the asteroid belt economically viable.
Speaker 2: We viewed the Solar system as an antagonist to be
Speaker 2: overcome with raw explosive power. Stepping away from the brute
Speaker 2: force of chemical rockets and simplistic two body math and
Speaker 2: embracing the elegant, computationally clever gravity surfing reality of three
Speaker 2: body math and solar electric propulsion. It changes everything.
Speaker 3: It really does because the physics of the Solar System
Speaker 3: weren't the actual barrier. The barrier was the mathematical lens
Speaker 3: through which we were viewing the problem. The legacy equations
Speaker 3: built for an era of slide rules and early mainframes
Speaker 3: created artificial walls in orbital phase space. The energy wasn't lacking,
Speaker 3: it was hidden within the chaotic dynamics of the three
Speaker 3: body problem, waiting for algorithms sophisticated enough to map it.
Speaker 3: The Ology's work proves that the most profound advancements often
Speaker 3: don't come from applying more brute force, but from increasing
Speaker 3: the computational elegance of the models we use to interpret nature.
Speaker 3: It leaves us with a lingering concept to mull Over.
Speaker 3: We often think the greatest barrier to space exploration is physical,
Speaker 3: building bigger rockets or stronger materials. But as this research shows,
Speaker 3: the most profound barrier wasn't physical at all. It was
Speaker 3: our imagination and our mathematics. What other impossible boundaries in
Speaker 3: your life or in our world are actually just waiting
Speaker 3: for a slightly better algorithm.
Speaker 2: A brilliant conceptual framing the universe often yields not to
Speaker 2: the loudest explosion, but to the most precise calculation. The
Speaker 2: invisible highways of the Solar system are mapped in waiting.
Speaker 2: Keep questioning the models, keep looking up at the bustling
Speaker 2: cosmic neighborhood right in our backyard, and we will talk
Speaker 2: to you next time.