Why does it take so long to get to Mercury?(esa.int)
esa.int
Why does it take so long to get to Mercury?
https://www.esa.int/Science_Exploration/Space_Science/BepiColombo/Why_does_it_take_so_long_to_get_to_Mercury
122 comments
In "Blue Mars" they build a city on tracks on Mercury, always staying at the terminator as the planet slowly rotates under it.
Hopefully on the dusk terminator and not the dawn terminator? If a mechanical problem slows you down would we rather see it start getting colder, or hotter as we work on correcting it?
The city is pushed by the natural expansion of the tracks due to heat.
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The journey to Mercury is even more impressive in his earlier book "The Memory Of Whiteness" where you also get fascinating meditations on the intersections of physics, metatheater, and music theory.
What's solar rapture? Sounds like a Scientology ritual.
I'm so curious what the navigation department for a place like NASA/JPL consists of. Each probe/satellites mission is so custom, do they have a software suite that they've refined over the last 50 years, is it a couple physics professors etc, are there two teams working independently to make sure no one messes up?
They use GMAT, the General Mission Analysis Tool
https://opensource.gsfc.nasa.gov/projects/GMAT/index.php
I should have expected it to be matlab...
Where do you see it being MATLAB? It just says that has a MATLAB compatible syntax. This is the SF page, with some screenshot: https://sourceforge.net/projects/gmat/
Yes! This was a surprise to me to learn as well. I mean, it was in a different context (how to get to the sun), but the same issue applies, of having to shed a ton of angular momentum/orbital energy.
(If you're curious about the opposite direction, of objects with the least angular momentum, that would be either bosons, or Texas's four-day-long "rotating" power outages.)
(If you're curious about the opposite direction, of objects with the least angular momentum, that would be either bosons, or Texas's four-day-long "rotating" power outages.)
I wonder how hard it would be to build a big shock absorber and fire it directly at Mercury. Maybe delicate electronics and sensors could survive the impact if the force is spread out over a long enough time.
This reminds me of a fun brain teaser:
Of all the planets, which is Earth closest to on average?
Of all the planets, which is Earth closest to on average?
CGP Grey did a video on this. Mercury is the mostest-closest for all the planets.
Ahem. Unclear if this is intentional or an artefact of their blog software, but I couldn’t help but notice that the phrase “vacuum of space” in the article has an extraneous . It is quite visible to the naked eye.
Shurely shome mishtake?
Shurely shome mishtake?
Delta-v
Only on HN can a correct comment be 'disagreed' with silently to oblivion. :)
When you just say "delta-v", it means nothing to anyone who doesn't already know what that means, and it provides no additional value to those who do, so the comment has no purpose. At least a complete sentence like, "This illustrates why it's difficult to overcome the large delta-v between Earth and Mercury," would say the same thing in a way that could actually be useful to someone. Even better if it defined delta-v as well.
Right because HN is a tutorial? Nobody here can understand much without detailed explanations.
The purpose is, so folks can look up delta-v and start to understand. It's not necessary to recapitulate everything on the web in a post. For instance I google 'orbital mechanics delta v' and the whole story is right there for the taking.
The purpose is, so folks can look up delta-v and start to understand. It's not necessary to recapitulate everything on the web in a post. For instance I google 'orbital mechanics delta v' and the whole story is right there for the taking.
It’s a decent explanation for a phenomena that is not intuitively obvious just by looking at a diagram of the solar system. I wonder just how much fuel is needed to go directly without gravitational slingshots.
The delta-V is around 16km/s.
For high-efficiency chemical propulsion (e.g. hydrogen - which, note, non-storable!) that's about 3.5-4x the exhaust velocity, meaning around 98-99% of your spacecraft's mass needs to be fuel.
For electric propulsion (which has issues because of low thrust and electrical power requirements), it's only about 0.5-1x the exhaust velocity, so only maybe 50-70% of spacecraft mass needs to be fuel.
In any case, it's a LOT.
For high-efficiency chemical propulsion (e.g. hydrogen - which, note, non-storable!) that's about 3.5-4x the exhaust velocity, meaning around 98-99% of your spacecraft's mass needs to be fuel.
For electric propulsion (which has issues because of low thrust and electrical power requirements), it's only about 0.5-1x the exhaust velocity, so only maybe 50-70% of spacecraft mass needs to be fuel.
In any case, it's a LOT.
Ah thanks, Project Orion makes a lot more sense in that context!
Yeah, people tend to pretty easily understand how the rocket equation is exponential in the required ∆V, but the way it's inversely exponential in exhaust velocity is less well understood.
Good specific impulse plus good thrust is a combo that requires nuclear-explosion-scale energy, ie Project Orion or Nuclear Salt Water Rockets (an option that is, shockingly, even more insane than Orion).
Good specific impulse plus good thrust is a combo that requires nuclear-explosion-scale energy, ie Project Orion or Nuclear Salt Water Rockets (an option that is, shockingly, even more insane than Orion).
The short version: it takes much more fuel to fly directly from the earth into the sun than it does to escape the solar system. Because of this you need to use longer and slower methods.
The problem is not flying into the Sun, it's slowing down to get in an orbit around Mercury.
It's both. The sun is actually pretty expensive to hit from Earth... Earth's orbital velocity around the sun is about 29.78 km/s. Even to fall into the sun, you need to kill most of that (not quite zero is needed, of course, as the sun has a wide radius... But closer to zero than simple Earth escape velocity).
The Parker Solar Probe, for example, pulled the trick off of getting a high-eccentricity orbit around the sun by slingshotting Venus seven times (the transfer orbit from Earth to Venus is about 3 km/s delta-v).
There's a pretty good overview of the math at the Space stackexchange: https://space.stackexchange.com/questions/38612/how-much-les...
The Parker Solar Probe, for example, pulled the trick off of getting a high-eccentricity orbit around the sun by slingshotting Venus seven times (the transfer orbit from Earth to Venus is about 3 km/s delta-v).
There's a pretty good overview of the math at the Space stackexchange: https://space.stackexchange.com/questions/38612/how-much-les...
https://www.reddit.com/r/space/comments/1ktjfi/deltav_map_of... is another way of looking at the problem. Once you're in Earth orbit, you need 2.4+.68+.14+.68+1.73 = 5.63 km/s to get to the moon. But you need 2.4+.68+.09+.28+2.06+6.31+1.22+3.06= 16.1 km/s to get to Mercury.
So if you don't use gravitational slingshots (which can be modeled as ramming your spaceship into a planet's gravitational field and bouncing off in the other direction), then you need ~3x the delta-v to get to Mercury compared to the moon. And getting to the Moon required one of the most powerful rockets in human history.
In theory, you could just use a rocket that's 3x as powerful as the Saturn V to get enough fuel into orbit to get to Mercury via a direct route. But this runs into engineering issues with creating a rocket that big. Alternatively, you could develop a way to refuel rockets in orbit and then launch 3x Saturn Vs with one space probe and 2 fuel tanks. This is the plan for SpaceX where they will launch a Starship with humans/robots and a Starship with fuel to get enough fuel into orbit for a trip to various parts of the Solar System.
[edited to fix units]
So if you don't use gravitational slingshots (which can be modeled as ramming your spaceship into a planet's gravitational field and bouncing off in the other direction), then you need ~3x the delta-v to get to Mercury compared to the moon. And getting to the Moon required one of the most powerful rockets in human history.
In theory, you could just use a rocket that's 3x as powerful as the Saturn V to get enough fuel into orbit to get to Mercury via a direct route. But this runs into engineering issues with creating a rocket that big. Alternatively, you could develop a way to refuel rockets in orbit and then launch 3x Saturn Vs with one space probe and 2 fuel tanks. This is the plan for SpaceX where they will launch a Starship with humans/robots and a Starship with fuel to get enough fuel into orbit for a trip to various parts of the Solar System.
[edited to fix units]
Please fix your units :)
You don't need 16.1 m/sec to get to mercury, there's a 'k' missing. To put it another way: that's off by about a factor of 1000.
You don't need 16.1 m/sec to get to mercury, there's a 'k' missing. To put it another way: that's off by about a factor of 1000.
How long until we can strap a massive laser to the moon and use it to push ships around the solar system?
Any old time. Powering and maintaining it would be a chore, and since it's on a rotating body it wouldn't always be pointing the direction we wanted it to, but solve those problems and we're great.
Also somewhat fun is the idea of "solar sailing." Both the particulate solar wind and the raw solar radiation have momentum, and by redirecting either one you can get a push. Since increasing / decreasing the "height" of your orbit is actually a function of causing acceleration in the direction of orbit (or opposite that direction), we should be able to change the shape of a vessel's orbit by deflecting outward-streaming sunlight and particles so they're facing along the orbital path (i.e. a 90-degree turn, with a 45-degree-angle mirror). You'd need a lot of surface area for a reasonable amount of delta-V in a human timeframe, but nothing we know of makes this approach impossible. JAXA demonstrated it can work (https://en.wikipedia.org/wiki/IKAROS); the Planetary Society has been looking into it (https://www.planetary.org/sci-tech/lightsail).
Also somewhat fun is the idea of "solar sailing." Both the particulate solar wind and the raw solar radiation have momentum, and by redirecting either one you can get a push. Since increasing / decreasing the "height" of your orbit is actually a function of causing acceleration in the direction of orbit (or opposite that direction), we should be able to change the shape of a vessel's orbit by deflecting outward-streaming sunlight and particles so they're facing along the orbital path (i.e. a 90-degree turn, with a 45-degree-angle mirror). You'd need a lot of surface area for a reasonable amount of delta-V in a human timeframe, but nothing we know of makes this approach impossible. JAXA demonstrated it can work (https://en.wikipedia.org/wiki/IKAROS); the Planetary Society has been looking into it (https://www.planetary.org/sci-tech/lightsail).
Millenia, if ever?
On the side facing the earth probably never as it will become trivial to threaten earth with a giant laser on the moon. Same objection with kinetic launchers (aka flinger, mass drivers) on the moon. On the side facing away, maybe but you lose half the utility.
I don't fully understand that chart, but it seems like it's showing that it's harder to get to smaller planets than larger ones - i.e. takes more effort (fuel) to get into a smaller planet's gravitational pull, but you get a lot less benefit since the gravitational pull is less. Is that a reasonable assessment?
https://en.wikipedia.org/wiki/Orbital_mechanics explains the mathematics behind the delta-v calculations quite well.
It's actually the other way around. If takes more effort to lower yourself into a large gravity well than a small one.
Traveling anywhere outside of Earth's gravity means you are always going to fall into a well, so the smaller the better. The problem with Mercury is to get there you have to fall into the Sun's gravity well.
The sun has the biggest gravity well around, and Mercury is deep down inside of it. If Mercury was bigger it would actually be even harder to get there, since you'd then also have to fall down it's large well too.
Traveling anywhere outside of Earth's gravity means you are always going to fall into a well, so the smaller the better. The problem with Mercury is to get there you have to fall into the Sun's gravity well.
The sun has the biggest gravity well around, and Mercury is deep down inside of it. If Mercury was bigger it would actually be even harder to get there, since you'd then also have to fall down it's large well too.
Right on. Someone has mentioned aerobraking somewhere above, but for those with fewer hours spent in Kerbal, this may be of interest ;)
A delta-v map will usually include atmosphere as a separate route from the raw energy requirements of entering and exiting gravity wells. Some of the counterintuitive aspects of these flight plans involve “very nice, ok! But how do you plan to slow down when you get there?”
On arrival to the moon or mercury (or Minimus) you have to be able to stop under your own power, which you have necessarily brought in your tanks. And therefore mass.
Too bad the resonant microwave propulsion thing was more likely a poorly designed experiment (acceleration without propellant). But… it violated our understanding of physics, so we’re stuck with bringing our gas everywhere.
A delta-v map will usually include atmosphere as a separate route from the raw energy requirements of entering and exiting gravity wells. Some of the counterintuitive aspects of these flight plans involve “very nice, ok! But how do you plan to slow down when you get there?”
On arrival to the moon or mercury (or Minimus) you have to be able to stop under your own power, which you have necessarily brought in your tanks. And therefore mass.
Too bad the resonant microwave propulsion thing was more likely a poorly designed experiment (acceleration without propellant). But… it violated our understanding of physics, so we’re stuck with bringing our gas everywhere.
> we’re stuck with bringing our gas everywhere.
Bringing your own gas is fine. The real problem with space travel is you need to bring your own roads. Because what you're short of isn't energy, it's something to push against.
Bringing your own gas is fine. The real problem with space travel is you need to bring your own roads. Because what you're short of isn't energy, it's something to push against.
Good point!
Hey, this is just a share to see if anyone shares my interest. In my spare time, I have been kind of been making a videogame based on this question. (I’ve worked on sims professionally, but it is not most of my career.)
A “floating origin” and using alt dynamics is nothing new, but I’m a bit obsessed with weird sim physics in games. I had been playing around with a kinetic quadracopter dogfighting concept in godot engine for about a year.
Then the “tic-tac UFO” videos resurfaced, and I’ve been having a lot of fun imagining “how those physics would work” if reality happened to be as interesting as what Commander Fravor says he saw.
I doubt the UAP news is what anyone thinks it’s about, but I’ve made little simulations involving everything from spacetime warping to matrix-style “if you fly close to c.”
Sadly, it’s not a very rewarding game concept beyond “woah neat!” Gets me back to why I started programming, though.
Hey, this is just a share to see if anyone shares my interest. In my spare time, I have been kind of been making a videogame based on this question. (I’ve worked on sims professionally, but it is not most of my career.)
A “floating origin” and using alt dynamics is nothing new, but I’m a bit obsessed with weird sim physics in games. I had been playing around with a kinetic quadracopter dogfighting concept in godot engine for about a year.
Then the “tic-tac UFO” videos resurfaced, and I’ve been having a lot of fun imagining “how those physics would work” if reality happened to be as interesting as what Commander Fravor says he saw.
I doubt the UAP news is what anyone thinks it’s about, but I’ve made little simulations involving everything from spacetime warping to matrix-style “if you fly close to c.”
Sadly, it’s not a very rewarding game concept beyond “woah neat!” Gets me back to why I started programming, though.
The physics would be a mechanism, but to be a game, there needs to be some sort of conflict or problem to solve.
I think you should keep exploring it. Maybe this is how folks get an intuition for orbital mechanics.
I think you should keep exploring it. Maybe this is how folks get an intuition for orbital mechanics.
Ah, got it - thanks.
[edit: typo was corrected, nevermind]
5.63 m/2 vs 16.1 m/s ?
Neither 5.63 meters divided by 2, nor 16.1 meters per second can be right, from context.
5.63 m/2 vs 16.1 m/s ?
Neither 5.63 meters divided by 2, nor 16.1 meters per second can be right, from context.
One might employ a solar sail/parachute. When you get near Mercury, you’d have more than 4 times the force on the sail too.
How would the sun push a solar sail towards the sun?
You sail at night. It's not rocket science.
Obviously it is sail science and therefore boat stuff. This should be a joint NASA + NOAA mission.
"For outward bound trajectories, the sail force vector is oriented forward of the Sun line, which increases orbital energy and angular momentum, resulting in the craft moving farther from the Sun. For inward trajectories, the sail force vector is oriented behind the Sun line, which decreases orbital energy and angular momentum, resulting in the craft moving in toward the Sun. It is worth noting that only the Sun's gravity pulls the craft toward the Sun—there is no analog to a sailboat's tacking to windward. To change orbital inclination, the force vector is turned out of the plane of the velocity vector."
https://en.wikipedia.org/wiki/Solar_sail
https://en.wikipedia.org/wiki/Solar_sail
Orbital manuevers are kinda counter-intuitive in that you when you want to get closer/farther from whatever you're orbiting you actually want to change the speed at which you're orbiting. So in the case of solar sails, you would tack in a retrograde direction.
In space you practically never ever want to accelerate radially away or towards whatever you're orbiting. Counterintuitively, on average that doesn't get your closer to or farther from the primary, it only serves to change the eccentricity of your orbit (raising the apoapsis and lowering the periapsis or vice versa).
What you want to do is accelerate either parallel or antiparallel to your orbital velocity (ie. tangent to the orbit). With a solar sail you do this simply by orienting the sail at a roughly 45° angle relative to the sun, allowing you to either accelerate or decelerate depending on which way you reflect the photons (the resulting force will be normal to the sail so in practice solar sailing is more complicated than that, but you get the point).
What you want to do is accelerate either parallel or antiparallel to your orbital velocity (ie. tangent to the orbit). With a solar sail you do this simply by orienting the sail at a roughly 45° angle relative to the sun, allowing you to either accelerate or decelerate depending on which way you reflect the photons (the resulting force will be normal to the sail so in practice solar sailing is more complicated than that, but you get the point).
If only our solar sailing boats could have a keel.
But to tack you need a centerboard or keel in the water to push against. I can't think of a way to do this in space.
On Earth you need a keel to oppose the force on the sail, which has a component in the direction of the wind. In orbit, the equivalent radial force is mostly perpendicular to the direction of motion, and so does very little work. Radial forces in orbit are much less efficient at changing orbital parameters than the equivalent axial (prograde/retrograde) acceleration. Moreover, if your orbit is roughly circular the applied force mostly averages out over each orbit.
That's a really good point. Here's what I was able to find about the matter from a brief search.
https://space.stackexchange.com/questions/370/can-you-tack-a...
https://space.stackexchange.com/questions/370/can-you-tack-a...
Tacking not only uses a keel, it also uses the shape of a sail and Bernoulli's principle [0] to get the perpendicular and forward force.
I'm not versed in solar-particle-physics, but I doubt the Bernoulli's principle applies to solar particles.
[0] https://en.wikipedia.org/wiki/Bernoulli%27s_principle
I'm not versed in solar-particle-physics, but I doubt the Bernoulli's principle applies to solar particles.
[0] https://en.wikipedia.org/wiki/Bernoulli%27s_principle
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> then you need ~3x the delta-v to get to Mercury compared to the moon. [..]
> In theory, you could just use a rocket that's 3x as powerful as the Saturn V to get enough fuel into orbit to get to Mercury via a direct route
I'm a bit confused. I have a vague memory that due to the Tsiolkovsky rocket equation the amount of fuel needed to reach a delta-v grow exponentially. How is it possible that you need a 3x bigger rocket to reach 3x the delta-v?
I'm a bit confused. I have a vague memory that due to the Tsiolkovsky rocket equation the amount of fuel needed to reach a delta-v grow exponentially. How is it possible that you need a 3x bigger rocket to reach 3x the delta-v?
I'm fuzzing the math a bit, but assume you have a Saturn V style rocket that can get 100 tons into orbit. And that consists of 50 tons of spaceship and 50 tons of fuel. Then you get something like V_e * ln((50+50)/50) = .69 * V_e of delta-v. But if you had two more rockets that launched an additional 2 * 100 tons of fuel into orbit, you get V_e * ln((250+50)/50) = 1.79 * V_e. This gives you 2.5x the delta-v. Decrease the propellant mass fraction and this value goes up.
The numbers are completely made up and based on my time playing KSP (https://xkcd.com/1356/) rather than real rockets so change the numbers as you see fit. But my core point is that orbital refueling greatly extends the usable delta-v of a rocket once it's prepared in orbit since it's easier to build 3x of a normal rocket than a rocket with 3x the payload.
The numbers are completely made up and based on my time playing KSP (https://xkcd.com/1356/) rather than real rockets so change the numbers as you see fit. But my core point is that orbital refueling greatly extends the usable delta-v of a rocket once it's prepared in orbit since it's easier to build 3x of a normal rocket than a rocket with 3x the payload.
………
> When you escape earth orbit you have to exceed its orbital velocity around the sun.
This doesn't sound right. Orbital and escape velocities for the earth should depend only on the mass of the earth.
This doesn't sound right. Orbital and escape velocities for the earth should depend only on the mass of the earth.
You can escape earth's orbit going barely faster, or barely slower than earth relative to the sun, depending on where you're going. This stuff can be confusing, because you're mixing two different reference frames (earth and the sun).
This analysis falls short if you apply three body orbital mechanics. Going barely faster or slower than the Earth in close proximity to Earth will slowly cause Earth's gravity to pull the spacecraft back in. This can mean all sorts of funny shaped trajectories (horseshoe asteroids etc).
You need about 11-12 km/s to relative to the Earth to escape Earth's gravitational pull from LEO (only a bit more than it takes to reach the moon). Earth itself is orbiting the sun at about 30 km/s. To not get re-captured, the spacecraft needs to be far enough in distance or the difference in velocity needs to be large enough. How much is "enough" depends on the time scale, but for spacecraft we're talking several km/s.
You need about 11-12 km/s to relative to the Earth to escape Earth's gravitational pull from LEO (only a bit more than it takes to reach the moon). Earth itself is orbiting the sun at about 30 km/s. To not get re-captured, the spacecraft needs to be far enough in distance or the difference in velocity needs to be large enough. How much is "enough" depends on the time scale, but for spacecraft we're talking several km/s.
That sounds like you're assuming you're standing still beforehand. Sure, the effect afterwards might look like you're going around the sun faster/slower than Earth but you started deep in Earth's gravitational well.
One big factor that the Tsiolkovsky rocket equation fails to account for is the square–cube law. When you scale up a rocket, the mass of the structure of the rocket tends to grow more slowly than the mass of the fuel it contains, which more or less cancels out the log term in the rocket equation. Note that this does not necessarily hold true for extremely small or extremely large rockets.
But even if the mass of the rocket structure was zero, you still need fuel to move the fuel right?
Huh, LEO really is just about halfway to almost anywhere if you are willing to aerobrake, other than Mercury.
I wonder why the chart doesn't consider the possibility to aerobreak into the sun.
I wonder why the chart doesn't consider the possibility to aerobreak into the sun.
A lot more delta-v to get a transfer to the sun, then you have to deal with the thermal problems which are pretty difficult to overcome. If you're close enough to the sun to be in its atmosphere, it's going to be pretty hot.
Now where's the version of the map that accounts for lithobreaking[1] as well as aerobraking? :)
[1] I feel that lithobreaking is slightly more correct than lithobraking.
[1] I feel that lithobreaking is slightly more correct than lithobraking.
Here's another angle: Look at the orbital velocities. Mercury's is 48 km/s, Earth's is 30, and an object at infinity would be zero. Kinetic energy is proportional to velocity squared. Square those orbital velocities, and you see it takes more kinetic energy to change from Earth's orbit to Mercury's than to go from Earth's orbit to escaping the solar system.
> 16.1 km/s to get to Mercury
That's if you want to slingshot yourself to Mercury with no fuel though, right?
If you have fuel then you can keep going to Mercury at a steady 0.1 km/s by constantly firing rockets to maintain that speed, and get there eventually.
You don't need escape velocity to leave the Earth either; you only need escape velocity if you want to maintain orbit without constantly firing rockets.
That's if you want to slingshot yourself to Mercury with no fuel though, right?
If you have fuel then you can keep going to Mercury at a steady 0.1 km/s by constantly firing rockets to maintain that speed, and get there eventually.
You don't need escape velocity to leave the Earth either; you only need escape velocity if you want to maintain orbit without constantly firing rockets.
These are delta-v numbers. How much do you need to change your velocity by to get there, basically.
I think your comment misunderstands inertia and orbital dynamics, but it's hard to follow what you propose doing differently than your basic earth escape + transfer.
I think your comment misunderstands inertia and orbital dynamics, but it's hard to follow what you propose doing differently than your basic earth escape + transfer.
You can burn your rocket engine in short powerful burst or in long gentle burst, but delta-v calculation still applies.
https://en.wikipedia.org/wiki/Delta-v
https://en.wikipedia.org/wiki/Delta-v
That "27" in front of Venus has to be a typo, right?
Nope; Venus has a very thick atmosphere and thus a rocket ride off the surface would require a prodigious amount of energy.
Hm. The creator did label it "delta-v", but apparently they did mean "energy required by a simple rocket" instead.
No, they mean Δv. When launching from atmosphere the losses of doing so are included in the calculation. The losses from gravity drag are also included but that’s a different topic. The numbers on the map are a low guideline and are nearly ideal vehicles. Depending on the drag coefficient of the vehicle and such, actual results will be worse. Often significantly. Saturn V punched its way to orbit and wasn’t exactly svelte.
I understand the confusion, though, because Δv in a space dynamics context is different than in a physics one. It is not a direct measure of added velocity as you’d expect from kinematics, but instead required impulse per unit of mass in order to achieve the desired outcome, which is ever so slightly different and considers additional impactful variables. Remember, the question being answered is really about fuel, so how much impulse you lose to any number of factors goes into your Δv budget as if you needed the extra anyway.
I’m assuming LEO is 9.4 on the map (won’t load for me for some reason), and if it is, that’s the best number for space people. Physics would instead tell you that it can be done in 8. Different questions.
I understand the confusion, though, because Δv in a space dynamics context is different than in a physics one. It is not a direct measure of added velocity as you’d expect from kinematics, but instead required impulse per unit of mass in order to achieve the desired outcome, which is ever so slightly different and considers additional impactful variables. Remember, the question being answered is really about fuel, so how much impulse you lose to any number of factors goes into your Δv budget as if you needed the extra anyway.
I’m assuming LEO is 9.4 on the map (won’t load for me for some reason), and if it is, that’s the best number for space people. Physics would instead tell you that it can be done in 8. Different questions.
Orbital refueling is probably the most practical answer in the short run.
If you had a thousand (or million) satellites doing this, could you actually measurably modify the orbits of planets? Mercury is small enough that presumably 1000 satellites each doing 9 gravity assists could change it in some way?
Of course by slowing down the speed of the Mercury it would affect is ability to be stable and it might end up be sucked into the Sun :-(
Because comets and asteroids have been zooming around for billions of years, it's clear that the effect would be negligible.
Not negligible at all. Comets and asteroids do not target to move a planet in some other direction, but a swarm of satellites can do it in a coordinated way. Of course you will need millions of satellites performing such dives over million of years.
But if your goal is to move the planet farther from the sun because it becomes more luminous and threatens to scorch the earth and you need to move away to cancel it, it is probably doable.
But if your goal is to move the planet farther from the sun because it becomes more luminous and threatens to scorch the earth and you need to move away to cancel it, it is probably doable.
Let's take Voyager as an example. It weighs under 1000kg. 1 million Voyagers then weighs 1x10*9 kg.
A 1km radius rock asteroid, which is nowhere close to the maximum, weighs an order of magnitude more than this.
A 1km radius rock asteroid, which is nowhere close to the maximum, weighs an order of magnitude more than this.
Solar sails give you essentially free power to fly around the solar system. So it is just a matter of time. With millions of years (and sun burning out is not exactly a fast process), this is quite doable.
This is literally impossible to tell without more information.
According to Wikipedia Mercury weighs about 3.285 × 10^23 kg, about 10^20 times more than most satellites. You'd need much more than 1000 satellites (or have much heavier satellites) to significantly impact the orbit. OTOH, if you'd have sensitive enough instruments you could measure the effect of even a single gravity assist.
According to Wikipedia Mercury weighs about 3.285 × 10^23 kg, about 10^20 times more than most satellites. You'd need much more than 1000 satellites (or have much heavier satellites) to significantly impact the orbit. OTOH, if you'd have sensitive enough instruments you could measure the effect of even a single gravity assist.
Cycling a large asteroid between Earth and Jupiter could be used to slowly shift the orbit of Earth, most of the energy coming from Jupiter. Astronomical engineering: a strategy for modifying planetary orbits [https://arxiv.org/abs/astro-ph/0102126]
Yes, you can do this with Mercury. Mercury's orbit is chaotic, so even modifications in its position on the order of millimeters can build up to produce completely different long-term dynamics. In particular, there's a few percent probability that Mercury will get ejected from the Solar System before the Sun dies. [1] It's also possible that Mercury will collide with Venus.
[1]: https://www.nature.com/articles/nature08096
[1]: https://www.nature.com/articles/nature08096
Isn't space exploration then a bit like playing with fire? Like, we could mess up some delicate balance by attempting too many fly-bys
Chaotic systems like mercury orbiting the sun have zone of stability where all the potential orbits lay. The energy from a space probe doing a flyby won't impart enough energy to pop it out of that zone. I'm not going to do the math but probably other planets have a larger effect on Mercuries orbit than a space probe does.
No. Everything gets hit by big rocks all the time and are subject to all sorts of perturbations which dwarf anything a little spacecraft can do to a planet.
There's kind of an XKCD What If for this, though with Jupiter: https://what-if.xkcd.com/146/
Summary is no for Jupiter, even the entire planet Earth wouldn't affect it that much. Mercury is much smaller though, so it might be possible to make a significant change, though you're probably still talking about sending a significant fraction of the mass of the whole planet Earth.
You might be able to alter the orbit like that without destroying the Earth if you figure out how to gather a ton of mass already in space, asteroids or something maybe. But now you've got to figure out how to redirect their orbit into the exactly right one without throwing most of their mass around, and do it with a reasonably-sized mission from Earth.
Summary is no for Jupiter, even the entire planet Earth wouldn't affect it that much. Mercury is much smaller though, so it might be possible to make a significant change, though you're probably still talking about sending a significant fraction of the mass of the whole planet Earth.
You might be able to alter the orbit like that without destroying the Earth if you figure out how to gather a ton of mass already in space, asteroids or something maybe. But now you've got to figure out how to redirect their orbit into the exactly right one without throwing most of their mass around, and do it with a reasonably-sized mission from Earth.
Mercury's mass is 3.285 × 10^23 kg, so if we assume each satellite is 328.5 kg and there are 1,000 of them, then that's 1/10^18 of Mercury's mass.
So, if each satellite changes speed by 10 km/s, then Mercury's orbital speed will change by 10^-14 m/s, or about 0.03mm/century.
Doesn't seem like we'll notice it.
So, if each satellite changes speed by 10 km/s, then Mercury's orbital speed will change by 10^-14 m/s, or about 0.03mm/century.
Doesn't seem like we'll notice it.
"There is an art to flying, or rather a knack. The knack lies in learning how to throw yourself at the ground and miss. ... Clearly, it is this second part, the missing, that presents the difficulties."
-- The Guide
Turns out that missing the Sun is much much easier.
-- The Guide
Turns out that missing the Sun is much much easier.
This is super cool. I recommend reading the article and then watching the animation. I'm no physicist, but it looks like the fundamental idea is to use elliptical orbits to slip in front of a planet along it's orbital track, and have the planet's gravity slow the probe, and then get out of the way fast as the planet passes. It's kind of the opposite of a cyclist drafting.
Apparent size of the sun from the planets http://www.astronoo.com/en/children/sun-apparent-size.html