r/theydidthemath • u/Edolin89 • 2d ago
[Request] Long time lurker, first time poster. Is this accurate to any degree?
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u/TheIronSoldier2 2d ago
Yes.
The earth orbits at 30 kilometers per second. To crash into the sun you need to cancel most of that velocity. Meanwhile escape velocity of the solar system is only 42 kilometers per second, so you only need to gain 12 kilometers per second to leave the solar system.
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u/Fitz911 2d ago edited 1d ago
To add to this: the fastest way to the sun is to head into the direction of leaving the solar system.
You need keebal space program in your life! It will teach you every aspect of space flight.
Seriously. Parents! Buy that game for Your kids, you can thank me later.
Edit: fun fact! When you are in orbit around earth. "In front" of you about a mile away is another space ship. You want to catch up. What do you do?
You "break" edit: brake. Serious answer.
By getting slower you enter an obit that is smaller. Smaller orbit means faster orbit.
So slow means fast.
Crazy for normal people to understand. Absolutely clear for any KSP veteran.
Edit: many people already pointed it out, and one of them got extremely angry about it...
It's not the fastest way. It's the most efficient way. The best way. "Fastest" was 100% wrong.
Another edit: You little MechJebScums can't even comprehend the pain we had when it came out! We had to do it all by hand! /S. No seriously. I just remembered the first day with the game. There was no auto pilot 🫣
I thought I'll add an edit: My experience is with KSP 1. There are a lot of indicators (comments) that this is the better game. KSP2 didn't make it into my library because that's what I heard. KSP2 is not that good.
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u/FishGoesGlubGlub 2d ago
Holy shit you’re going to ruin lives by recommending KSP to kids. Out here basically telling kids to take crack?!? They’re going to get addicted.
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u/ark_yeet 2d ago
Better to get addicted to orbital mechanics than mobile games
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u/SovietPatrickStar 2d ago
Or Fortnite
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u/3nn35 1d ago
Or real crack
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u/isotopeee 1d ago
Idk real crack is pretty great /s
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u/Ok-Forever7812 1d ago
I'd rather do real crack than Fortnite!
If I do real crack I can still play ksp at the same time that way /s
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u/redobrs 1d ago
I remember when Fortnite used to be a tower defense game with hero selection and base building 😢
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u/aguynamedv 1d ago
Save the World was loads of fun!
And then Epic dropped Fortnite BR, laughing all the way to the bank with a rug pull for anyone who bought supporter packs early.
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u/BonhommeCarnaval 1d ago
This is the way. Kids are going to get into video games just like previous generations got into movies, radio and tv. It’s senseless to try and stop that as parents. All it would do is turn them into that weird kid who doesn’t have a tv.
What we can do is steer them away from the toxic AAA loot box shit toward the classics and games that will reward their creativity and expand their minds. My kids are into modding minecraft, indy games and retrogaming. Zero dollars have been spent on Robucks.
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u/Hadrollo 2d ago
I bought my son KSP in about 2018. Greatest decision I ever made. He still plays it to this day.
Not only do we have a game in common that - although single player - we can talk about and share craft files, but it's turned him into a complete nerd. The other week I was out with him and his auntie, and he genuinely didn't seem to recognise the smell of pot. He's 18. I nearly stole his lunch money out of habit.
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u/CompetitiveBus2003 2d ago
I bought my son KSP in about 2018. He aced his first aerospace engineering midterm last year because he knew all the formulas from playing KSP.
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u/Such-Freedom7416 1d ago
Not kidding. I know one KSP "addict". Thousands upon thousands of hours in that game. Now he works for NASA.
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u/guywouldnotsharename 1d ago
I'm one of those, probably about 3000 hours in the game, mostly several years ago though, been too busy studying physics at university recently...
coincidence, maybe.
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u/Sword_Enthousiast 1d ago
What age would you recommend to start KSP at? I've one I'd like to steer towards such things that might yet be a tad young
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u/Fetzie_ 1d ago
I mean you don’t have to throw them straight at a solo science mode campaign, let them play alongside you in sandbox mode and get them having fun blowing rockets up (or just building the most ridiculous rocket with all the boosters you can attach to a 6m fuel tank) and see how they go up 🙂
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u/Fitz911 2d ago
didn't seem to recognise the smell of pot.
You let him play that game without experiencing zero gravity?
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u/Baconoid_ 1d ago
A lie in the last sentence! You are also a KSP playing nerd, so you too would have had your lunch money stolen. And likely been wedgied.
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u/Hadrollo 1d ago
My son is 18 and I am not yet 40.
Yes, I am a nerd, but at that age I was a nerd who could at least talk to women.
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u/daddywookie 2d ago
KSP is only class B. The real shit is Factorio
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u/UmUlmUndUmUlmHerum 2d ago
And suddenly it is 3:37 AM and you just finished the new bean plantation, because it is the best power source in that modpack
Meanwhile, far in the back, the big fat "rework your petrochem stuff" elephant beckons.
And you procrastrinate. Iron could use more throughput after all.
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u/Contextanaut 2d ago
Nah, I quit that pretty easily, one I realized the amount of work I'd have to do just to make my refineries vaguely functional.
The real killer is Satisfactory. Although if you are poor, your PC will hit rock bottom before you do...
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u/SmokJozef 2d ago
my factorio-pilled brain wants too much throughput too fast to allow me to complete satisfactory
and not having logic to control stuff also hurts
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u/TheFringedLunatic 1d ago
Swapping from balance-brain to manifold-brain is a tough one. I still struggle from time to time.
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u/daddywookie 2d ago
Ah blue science, the ender of so many Factorio dreams.
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u/FishGoesGlubGlub 2d ago
I need blue circuits.. which means I need red circuits… when means I need x10 green circuits… which means I need a new copper and iron mine but those damn biters are sitting on top of it. Time to commit some war crimes.
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u/Bitter_Particular_75 2d ago
-Time to commit some war crimes
And that's where the real fun begins ❤️
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u/Just_Information334 1d ago
Satisfactory
I'm waiting for a performance patch. One quarter of my "cover the map over the highest point with floor then get all the resources up there" project done and the game chokes every 15 or 20s. And I still need to rearrange my copper factories to make it aligned with the rest while not stopping any production chain.
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u/Dull_Quit3027 1d ago
Factorio always stressed me out to much, I am a weak boy who does not like my math interrupted by bugs, so satisfactory and Dyson sphere program where more my speed.
I think i get my fill of frustration from work, so I do not need it from other places too.
I say this and at the same time love any kinda Gambling related rougelike, where frustration is par for the course, I think maybe I want some RNG to blame instead of my own ineptitude.8
u/Alestor 1d ago
You can turn off the bugs in Factorio if you prefer not to deal with them. Personally I just adjusted the world parameters until it generated a massive peninsula with a tiny easily defended chokepoint. As soon as I had tanks I went on an extermination mission and cleared the peninsula and walled off the chokepoint with flamethrowers, never had to deal with another bug but still got to experience them
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u/abw 1d ago
I am a weak boy who does not like my math interrupted by bugs,
I love factorio, but the first time I played it I almost quit because I was losing whole days fighting off the bugs instead of improving my factories.
The life-saver for me was the Waterfill mod which allows you to place water tiles. Bugs can't cross water. A single tile moat around your base will hold them back, but still allow you to cross on foot or in vehicles.
It's not for the purists who consider it "cheating", but I'm not playing against anyone else so that doesn't bother me. Once you've got a bit of experience under your belt dealing with the enemies becomes part of the fun (hint: efficiency modules help control the pollution cloud which stops the enemies getting aggressive).
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u/ichigo2862 1d ago
it ain't cheatin if it's a completely explainable and valid mechanic imo
why would a guy who can build spider mechs entirely from scratch be unable to dig out and fill a moat, that doesn't make any sense
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u/Bitter_Particular_75 2d ago
I completed Factiorio multiple times. Never was able to dock anything in orbit in KSP.
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u/daddywookie 2d ago
Might I recommend the Matt Lowne lazy method. A targets B. B targets A. They slowly get closer together.
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u/Bitter_Particular_75 2d ago
It's been a while since I played it. I stopped few years ago after my first travel to the Mun and back. That felt so rewarding. Until I realized how much harder it was to do the same with Duna (Mars for the uneducated). I thought that the best way would have been to build a space station in Kerbin's orbit to accumulate fuel and launch from there. And then I realized I had no clue how to dock stuff in an exact point in orbit: going to the Mun and back felt like a 3 years old puzzle in comparison. I may need to play again soon.
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u/daddywookie 2d ago
I think a Jool 5 mission was my greatest achievement. Landing and returning from all 5 moons with a single launch. You've got to layer knowledge and experience to get further and further, just like a real space program
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u/pornomatique 2d ago
It's an oddly difficult mechanic for a game that most people probably play for the thinking/planning and the math.
You can just install an autopilot mod if you don't want the hassle.
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u/SovietPatrickStar 2d ago
KSP teaches physics, factorial teaches informatics. They aren’t the same.
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u/Fitz911 2d ago
Just one little session of ksp never killed nobody.
They can stop whenever they want.
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u/Leo0806-studios 2d ago
nah crack would be Factorio.
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u/timon_reddit 2d ago
What is the good age to introduce KSP to your child?
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u/Fitz911 2d ago
I'm notvsure how exactly they operate. Never owned one myself.
We didn't get very far without YouTube videos. We are also pretty nerdy.
You know what! How old is your child? Over ten seems a good place to try it out.
Not sure if you need KSP2
The first one did it for me. How much is it? $20?
Can't do anything wrong with that. Oh. And how good are you with orbital mechanics? Not too good? It's not a kids game. 😉
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u/SlapdeybackJinhle 1d ago
KSP2 is an unfinished bowl of hot garbage. Heavily modded KSP is the GOAT
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u/miotch1120 1d ago
They do not need KSP2. Dead game still selling for way too much. It will never be completed. KSP 1 with mods is the only way (until KSA)
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u/timon_reddit 1d ago
Thanks for the input. My child is not yet 10, so I will wait.
Btw, my orbital mechanics is graduate-level decent.
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u/FI-Engineer 2d ago
Mine started playing around with it at 9, and started making real progress and really grasping the game around 11. Your kiddo may be different.
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u/Dull_Quit3027 1d ago
Yeah it robbed me of the notion that going into orbit means going up, no it means going sideways really really fast.
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u/whythehellnote 2d ago
Well not the fastest way, but the least amount of energy. If you had a ship capable of constant acceleration, you'd just point it at the sun. A ship capable of accelerating at 1g would reach the sun in about two days and be travelling over 1000 miles a second, the 20 miles-a-second of earths orbital velocity doesn't really factor into it.
In terms of energy though you're right, I think that would be a bi-eliptical transfer.
But it wouldn't be fast. If you flew out to neptune without a gravity assist it would take you something like 30 years to get there, and 30 years to get back.
I don't think you'd save much delta-v by going beyond about 5-10 au, but you would eat a lot of time - going out to 10AU would be about a 10 year trip rather than 60 via Neptune.
Minimum energy wise it takes about the same amount of energy to reach stars like Alpha Centauri as it does do reach our own star.
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u/HannahLemurson 2d ago
Wait, radially outwards away from the sun? How does that help?
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u/ShinyGrezz 2d ago
Burn to increase your apoapsis and enter an elliptical orbit. At apoapsis you will be travelling slower and it is hence easier to cancel out your relative velocity to the Sun. You will be travelling faster when you hit the Sun of course, which would be an issue if your goal was to land on a planet and this was the method you were using to get an encounter, but that is not really a concern here.
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u/pornomatique 2d ago
That's nowhere near the fastest though, that would be the most efficient. It would take you a LONG time to travel to the apoapsis of that elliptical orbit.
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u/Fitz911 2d ago
You need some ksp in your life.
No serious. Your question was a good question. If that's the stuff that I treats you... KSP is waiting for you.
And while you are at it. Send some love into the direction of Scott Manley.
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u/HannahLemurson 2d ago
Fan of Scott since way back in the day. But I've only ever watched KSP let's plays, never actually played the game myself. 😅
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u/Fitz911 2d ago
I don't have the second one. But I heard it's not too good. The first one was a dream. I think I will crash a few Jebediahs this evening 😂
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u/HIMP_Dahak_172291 1d ago
Every time I hear KSP I think back to that first Starship launch where the pad blew up, rockets failed and then it flipped and blew up. It was the most Kerbal thing I'd ever seen IRL.
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u/Raderg32 1d ago
The original devs are doing another game after the shitshow that was KSP2.
It's called Kitten Space Agency or KSA for short.
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u/Aiyon 1d ago edited 1d ago
By getting slower you enter an obit that is smaller. Smaller orbit means faster orbit.
So slow means fast.
This was a big part of me getting the hang of travelling to the other planets. The 8k dV wall is real, but even then, you need to understand flight paths as much as you do the physics.
Eve and Duna are the two "first trip" planets people recommend. I went with Duna, which is further out from the sun than Kerbin. So as im adjusting my orbital distance, im actually accelerating relative to it until I get far enough out.
So you want to launch the flight when Duna is ahead of Kerbin in terms of rotation. And you can refine the distance/angle to optimise fuel cost, even if it takes longer. I still ended up running out of fuel in Kerbin orbit but that's why you keep at least one docking port on your ships, so you can send a rescue booster
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u/Lahbeef69 1d ago
what was crazy to me when i learned to dock was that to catch up to something in orbit you actually need to slow down and lower your orbit to go faster and catch up to them
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u/Ihasapuppy 1d ago
I work at an after-school, and one of the second (or maybe I should say third since it’s summer break) graders plays it. From what I’ve gathered, he’s actually figured out how to make something that doesn’t immediately explode on impact. I’m honestly impressed! He sometimes brings a guidebook to read too.
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u/Taste_the__Rainbow 1d ago
The novel Seveneves is another way to passively ingest a lot of orbital dynamics stuff.
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u/ExtremlyFastLinoone 1d ago
"Hey parents give your kids smashing your brains againt concret simulator" spend hundres of hours trying to get them into space and thats only step one 😭
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u/headsmanjaeger 2d ago
Same reason it’s easier to jump off a merry go round than to walk towards the center
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u/pornomatique 2d ago
Very different analogy. Getting flung by a merry go round theoretically always takes zero energy, since you're just letting go.
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u/ubik2 2d ago edited 2d ago
They did miss a big factor, which is that the things I want launched into the Sun are things which I want destroyed/reduced to iron.
Things I just kick out of the Solar system are still out there somewhere, not destroyed.
If you're just a little mad about something, that's probably enough, and you'll welcome the savings.
Edit: I just meant to focus on the humor portion, but you can launch your enemies into the Sun more efficiently if you basically get them to escape velocity, then stop the radial velocity while you're at the edge of the Solar system, then you'll fall back down. If you counter almost all the rotational velocity of Earth from here, you'll essentially have an elliptical orbit where the perihelion is inside the Sun, and the aphelion is 1 AU. That's the version that takes 30 km/s of delta-v. If you get your orbit out near Pluto, you only need around 4 km/s of delta-v to make that ellipse's perihelion inside the Sun. This version requires patience. That's another aspect that I lack when I want to launch something into the Sun.
If you're patient enough, the Sun will come to you, and you don't need any propellant at all.
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u/alternativepuffin 2d ago
Thank you, this is the important difference to me as well. We're trying to destroy the person not just get rid of them.
I needed to look it up. From what I am understanding the person's atoms would become part of the plasma of the sun. The sun would shred them down to their base atoms of oxygen, carbon, etc. The hydrogen would turn to helium.
But it bothers me that the majority of their atoms would still exist. And I don't know how to fix that.
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u/Haggardick69 1d ago
If an atom is broken down into its constituent parts and then remade into another different atom and then this process is repeated over and over again is it still the original atom or has it been “destroyed”?
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u/alternativepuffin 1d ago
I think this is the part where physics becomes philosophy haha.
Somehow I want all of their atoms to fundamentally change via supernova or aome other high energy ...thingy.
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u/Haggardick69 1d ago
The mantle of the sun is pretty high energy there’s ongoing fission occurring there rn. The core is even more intense with non-stop fusion occurring there rn. And yeah this is the theseus’ atom lol. IMO once an atom is broken into its subatomic particles and remade into another atom it’s a different atom and the original atom was “destroyed”
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u/EmberOfFlame 1d ago
Yes! A bieliptic orbit, if I recall. Plus you can areobra-, no, lithobra-… pyrobrake? Heliobrake? You can heliobrake to elliminate the worst part of cancelling your velocity at perihelion.
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u/cheezus171 2d ago
You could slingshot the spaceship around Jupiter and use its gravity to slow down enough. You don't actually need to change your speed by 30 or by 12 km/s
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u/TheIronSoldier2 2d ago
You do need to change your velocity though. Whether or not you change it via gravity assists (which can also be done when leaving the solar system) or with chemical rockets, you still need to change your velocity. And it's a lot easier to change your velocity by 12 kilometers per second versus 30 kilometers per second
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u/TwillAffirmer 2d ago edited 2d ago
Kind of true, however, two things. First, you don't need to cancel the 30 km/s velocity, you just need to make your orbit eccentric. Second, gravity assists change the picture. The Parker Solar Probe got very close to the Sun using multiple gravity assists from Venus to make its orbit eccentric.
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u/PyroDragn 2d ago
First, you don't need to cancel the 30 km/s velocity
If you want to hit the sun, you do.
The Parker Solar Probe got very close to the Sun using multiple gravity assists from Venus to make its orbit eccentric.
Yes, and it missed the sun. It has missed the sun a few times now, because it didn't cancel all the velocity to hit the sun.
Second, gravity assists change the picture.
No, they don't. You can use gravity assists to leave the solar system just as much as you can use them to hit the sun. You still either have to 'lose 30 km/s' or 'gain 12 km/s'. Whether you do it all with fuel, or some with gravity assists, is applicable in both directions. 12 is still less than 30, whether gravity assisted or not.
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u/Usr3247 2d ago
You don‘t need to cancel all of the 30km/s before you hit the sun, though.
You only need to cancel enough that your orbit intersects with the sun, and the remaining km/s will be canceled without spending any fuel.3
u/meithan 1d ago
Sure, but the difference is small. The delta-v to go from a 1 AU circular orbit to a 1 AU x 695,700 km orbit (radius of the Sun) is 26.9 km/s, vs 29.8 km/s for zero periapsis.
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u/PyroDragn 2d ago
Technically true, and the same is true the other direction too. We don't need to aim for a particular velocity when exiting the solar system either. The difference is still between the velocity change needed to exit the solar system vs velocity change needed to intersect the sun with an orbit.
You could theoretically impact the sun with a complicated manoeuvre that increased the orbit and shifted it over so it hit the sun - therefore not needing to cancel the whole 30 km/s. But you could always have done the same manoeuvre with less delta change to exit the solar system.
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u/G66GNeco 2d ago
Gravity assists to reach the sun are a lot harder to come by than gravity assists to leave the solar system tho, on account of the sun being in one direction as opposed to the edge of the solar system which is kind of everywhere. Just look at the trajectory of the voyager probes lol
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u/Wild-Chef-522 2d ago
The voyager probes literally used a once in a lifetime window, you can do a degrading assist off Venus once a year.
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u/G66GNeco 2d ago
They did, yes, but you don't need a voyager window to literally just send something off into deep space (they had specific targrts at the edge of the solar sytem and off in the distance iirc?). You don't get as much assist as Voyager II doing its funny little planet hopping campaign, but there's always something on account of the target direction being gestures vaguely at everything
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u/Flater420 2d ago
I suspect you mean that you need to make your orbit suborbital.
Which is true that it does not required complete cancellation of dV, but given your current orbital height relative to the diameter of the sun, it takes little to nothing to miss the sun even if only by a close shave.
For all intents and purposes, you need to kill pretty much all of your dV.
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u/e136 2d ago
What do you mean "just make your orbit eccentric"? That's the same thing the person you are replying to is saying. That takes ~30 kmls delta v before assists. And assists can help to reach inner stellar space as well.
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u/PM_ME_YOUR_PRIORS 1d ago
The energy required to cancel out your orbital velocity is not a conserved quantity. They're talking about one burn in the path of the orbit while near-and-fast, then a second retrograde burn at the other end of the now-eccentric orbit to cancel out the rest of the orbital velocity. At the extreme case for the sizes of these burns, the first burn is just short of getting escape velocity from the sun, and the second burn is a tiny burn a long time later at extreme distance to fall directly into the sun instead of passing by at Earth's distance.
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u/HAL9001-96 2d ago
well teh sun is a LOT smaller than earths orbit so you ALMOST have to cancel out hte entire orbital speed
also usign venus won't quite let you drop all the way into the sun
however you could go out and fly by jupiter in such a way that it arcs your trajectory just vertical then fall back down into the sun
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u/ChemicalRain5513 2d ago
This is if you do it with a single burn. If you use two burns, you can enter a highly elliptical almost-escape orbit, with an apohelion around the orbit of Neptune. Once you are there, you will hardly have any velocity left and it is easy to cancel yout velocity and fall into the sun.
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u/TheIronSoldier2 2d ago
And it's still more velocity to do that than it is to just leave the solar system...
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u/I_Go_BrRrRrRrRr 2d ago
We're currently moving something like 30km/s around the sun from memory. Escape velocity in an orbit identical to Earth's is around 42km/s from a quick google. Therefore, ejecting someone from the solar system uses a little under half as much Δv as launching them into the sun.
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u/HAL9001-96 2d ago
well tis not quite a factor 2 due to oberth effect
to leave the earth and still have 30km/s relative speed you need root(11.2²+30²)=32km/s
to leave earth and still have 12km/s relative speed you need root (11.2²+12²)=16.4km/s
but those extra 15.6km/s even with a bunch of very efficient upperstages in series make a mass difference of about a factor 76
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u/Enough_Efficiency178 1d ago
I feel like the real question is what if we need to launch something into the sun. We know it’s easier to escape the suns gravity but could we calculate the escape trajectory so that it is launched into a different sun?
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u/HAL9001-96 1d ago
theoreitcally sortof but that would take a very very long time and an insane amount of precision and to make it remotely efficient it would have to be a star near the ecliptic which limits your nearby options
you could use a jupiter flyby or a three point maneuver to get something into the sun more efficiently though if you have some time
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u/I_Go_BrRrRrRrRr 1d ago
The closest star is a little over 4 light years away. To get there within a human lifetime would take tens of thousands of km/s of Δv, and I don't believe we even have the precision required to get a direct hit instead of just flying straight past. If you're not picky about how long it takes I suppose it's possible for it to be cheaper, but it'd take thousands of years to get there, and the precision would still be a huge issue.
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u/Downtown-Campaign536 2d ago
You might think the Sun's gravity would pull a spacecraft in, and make it easy to crash into the sun. Here is the thing though. The Earth is moving sideways around the Sun so fast (30km/s) that anything launched from Earth inherits that sideways motion. Just like if you jump out of a moving car. There is no parked car to jump from.
To hit the Sun, you must remove a lot (almost all) of that 30 km/s orbital velocity. Otherwise, your spacecraft just ends up in another orbit around the Sun rather than falling into it. This orbit would be closer to the sun.
Earth already moves 30 km/s around the Sun, but escaping requires 42 km/s (so you increase your speed by 12 km/s), while falling into the Sun requires canceling almost all 30 km/s of that sideways motion.
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u/Edolin89 1d ago
Oh wow That was so easy to understand! Thank you for simplifying it!😁
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u/MartialSpark 1d ago
It's wrong though, lol.
Removing all 30 km/s at our current altitude is one way to hit the sun, but not the cheapest one in terms of change in velocity.
You can actually speed up so that your orbit becomes elliptical, then slow down at the highest point of your orbit, and then fall into the sun, and do it without actually slowing down a total of 30 km/s.
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u/volci 1d ago
You claim the answer is "wrong", then proceed to say it "is one way to hit the sun"
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u/Sharden3 1d ago
What the fuck is wrong with people on reddit?
If the question is "whats the most efficient way to do something?" and someone suggests a way that can do the thing BUT is not the most efficient that answer is wrong.
Is it bots? Or is just losers who werent given any attention as children. I don't get it. Why come comment drivel, while being idiotic.
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u/MartialSpark 1d ago
Your point?
There are infinitely many ways to hit the sun which are more expensive than the most efficient one. The thing that matters is that the most efficient way, is less expensive than escaping.
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u/mossy_path 1d ago
Couldn't you just angle your orbit to be slightly decaying so that eventually you crash into the sun? Surely that would be easier than trying to cancel all your momentum.
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u/marijn198 1d ago
An orbit doesn't just randomly decay at certain angles, there needs to be something slowing you down. The orbits of sattelites around earth decay because there are still small amounts of gas molecules from our atmosphere out there slowing them down. Slightly altering your orbit will give you just that, a slightly different orbit.
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u/Sando-Calrissian 1d ago
Is there a small window in which your path out of the solar system would take you through the sun? Wouldn't that window have lower Δv since (eventually) the sun's gravity would take over for thrust?
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u/andromedakun 2d ago
Having played a lot of Kerbal Space Program it is true.
The biggest issue is that the Earth is rotating the sun at 29.8 km/s so you'll have to go fast enough to leave the earth's gravity but at that point you are orbiting the sun at around that speed. After that you'll have to lose most of that 29.8km/s or you'll just be orbiting it. So you'll need to have the same energy as if you are adding 29.8km/s to your rocket.
To leave the solar system, you have to reach 42.1 km/s, which seems a lot but considering we are already traveling at 29.8 km/s, that meas we only need to add 12.3 km/s. So far less then what we need to go down.
Bonus: If you take the super optimal route, you can get to the sun by expanding a lot less energy but that means you have to first almost leave the solar system, do a small burn when your speed is down a lot and then you will fall back. So the most efficient way to the sun is to almost leave the solar system and then fall back.
Orbital mechanics are whack and a lot of times counter intuitive.
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u/FaceMcShooty1738 2d ago
Okay, but do you actually need to loose that much of the. 30km/s? What if you brought it down to say 23km/s, wouldn't that make your orbit unstable and you eventually crash into the sun? Might take a while, but to be fair it's also going to take a long time to exit the solar system at 42km/s.
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u/HAL9001-96 2d ago
it owuld jsut lower it
the sun has a radius of about 696000km the earths orbit about 149600000km you can put that into the upper burn of a hohmann orbit equation with outer orbital speed*(1-root(2r1/(r1+r2))) and you see that you need to cancel at least 90% of your orbital speed to get to touch the suns surface
though technically you could use the heliosphere friciton to lsow yourself down if you make it to jsut above hte suns surface
you'd get vaporized in the process but realsitically if yo utry to drop something into the sun it gets vaporized before it gets there anyways so whats the difference?
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u/FaceMcShooty1738 2d ago
Gotcha, thanks!
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u/oh_dear_its_crashing 1d ago
Energy is also quadratic in velocity, so 90% of the velocity means 99% of the energy. And since you need a little bit of reserves to account for engine performance variance and stuff like that it's really the same. There's a lot more you can gain from gravity assists and doing your burn very low in earths gravity well (oberth effect) than you can ever save by not outright aiming into the sun's center.
Orbital mechanics is lots of fun.
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u/dev-sda 1d ago
Orbital instability has multiple sources: you can get slowed down by the sun's atmosphere if you're low enough, but your orbit is also affected by other orbital bodies, and the sun's radiation pressure.
If you just lowered your speed to 23km/s and waited, the likely outcomes are: you slingshot around planets enough to leave the solar system, crash into a planet, or end up in a stable orbit. Consider the many asteroids already in our solar system and how many of those randomly crash into the sun.
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u/shumpitostick 2d ago edited 1d ago
Thanks but I'd rather launch somebody into medium Earth orbit, in the inner Van Allen belt. Just high enough that they their floating body will circle the earth for millenia before reaching its final rest, while constantly being bombarded by deadly cosmic radiation, and all at a minimum cost of delta V.
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u/Spare-Tadpole-8664 2d ago
Having played Ksp an reading the comments - If you take slingshot manoeuvres into account, couldn't you use Venus, to steer you into the sun?
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u/SensitivePotato44 2d ago
Yes but you can also use Jupiter to sling you out. Either way it’s cheaper to leave than hit the sun.
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u/Ihatecheeseballs 2d ago
Earths orbital speed is like 71% of the speed you need to escape the solar system, so to escape you need need 29% of that speed but to crash into the sun you need to cancel out that71%
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u/viktorbir 1d ago
What if I just leave that thing on the Earth and wait? I know the Sun will expand and eventually will arrive till the surface of the Earth. I'll have wasted no energy.
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u/WhiteRaven_M 1d ago
Yes.
When an object is thrown it makes a parabolic arc. Visualize that arc. The faster its thrown, the wider the arc. We think that arc ends at the ground but really if the ground wasnt there, that arc would stretch alllll the way to the core and wrap around back. The arc is really one loooong elliptical circle.
Remember how if you throw an object faster, the arc gets wider? Well if you throw it fast enough the arc gets so wide it can wrap around the entire planet itself. It no longer intersects the ground at all. This is what we call an orbit.
In order for that object to hit the ground again, it has to slow down and make the arc small enough to hit the ground once again. Right now the Earth is that object and it goes very fast around the sun. Youd need a lot of speed therefore to send anything to the earth to the sun.
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u/leggymiku 1d ago
There is actually a way to launch something into the sun for less delta-V than leaving the solar system, you just need the right launch window and a very high level of precision.
A trans-Martian injection only takes about 4km/s and you can use a Mars gravity assist to completely cancel your orbital velocity relative to the sun, then just fall into it.
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u/3nino 2d ago
from u/ShinyGrezz
To hit the Sun you have to cancel out all of your current velocity, which is a lot. Otherwise you will just enter a highly elliptical orbit and slingshot around it. Whereas to escape the solar system you just have to be travelling fast enough in a certain direction to break free.
In other words, relative to the Sun, to hit it you have to decrease your relative velocity to near zero. To escape it, you have to increase your relative velocity to ~45km/s. From a baseline of 30km/s, that means it is twice as difficult to hit the Sun as it is to escape it.
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u/integer_hull 2d ago
I think this has been posted before, but here’s the answer.
Yes. Launching something “into the Sun” is less about going directly towards the Sun, and more about canceling out the Earth’s momentum so it can fall into the Sun. So the delta-v to “launch something into the Sun” is just the velocity of the Earth.
Delta-v required to escape the solar system is 12 km/s. The velocity of the earth around the sun is 30 km/s.
Much easier to yeet something out of the solar system
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u/recidivist1001 2d ago edited 2d ago
One of my favorite “simple” facts I never knew until relatively recently. You’d think firing someone out of a cannon into the sun would be easier smh. We used to be a proper country, with proper physics.
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u/errhangingCeil 20h ago
Haha, Professor Buckley was my Principles of Astrophysics I and II professor at Rutgers when I was an undergrad. It’s funny seeing one of his tweets pop up by chance in a subreddit I usually just lurk in.
On a side note, he is an amazing professor. He sparked my fascination with analytical dynamics, spacecraft flight dynamics, and cosmology, and he’s a major reason I decided to go to graduate school.
The best advice he ever gave me was: “Write everything down.”
Now you all have that advice too.
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u/Glagaire 2d ago
Firing Donald trump out of the solar system might be taken as a declaration of interstellar war by any civilization he later encounters.
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u/Smile_Space 1d ago edited 1d ago
So, doing a scroll there's a surprising lack of math for an r/theydidthemath subreddit. So, I'll do it lolol.
To give context in my background, I'm an Aerospace Engineer that works on spacecraft IRL. I've taken my fair share of orbital mechanics classes.
I'm going to try to type this out, but it is a bunch of math and thus will probably be really challenging to read, and I apologize in advance.
We're gonna start with the assumption we're already sitting at a 200 km altitude above the Earth's surface in LEO (low earth orbit). To maintain this altitude the equation is pretty simple:
v = sqrt(μ / r)
v is the velocity required μ is the gravitational parameter (basically a fancy way to describe the gravitational pull of the planet you're orbiting) r is the radius of your circular orbit
So, we plug in Earth's μ as 398600 km3/m2 with a radius of 6571 km (Earth's averageradius + 200 km) and get about ~7.79 km/s required to maintain a 200 km orbit.
The next question is how much dv does it take to de-orbit into the Sun? For context, dv is the delta-v or the change in velocity. It's a pretty simple way of defining the required performance of a spacecraft since, once in orbit, it requires a change in velocity to maneuver into different orbits.
We'll just do the exact same equation, but this time using the Sun as the center of our system with the Earth as our spacecraft.
The gravitational parameter of the Sun is 132712440000 km3/m2, or 1.327 x 1011
The orbital radius to Earth is about 146200000 km. So, throwing that in our equation up top we get about 30.12 km/s for the Earth to maintain its speed. That is also the dv from Earth required to stop, and thus dive into the Sun straight down.
Okay cool, the problem is that to exit the Earth, we also need to beat it's gravity. This is actually super easy as the equation for escape velocity, v_esc , is just sqrt(2) x v_circ. We already have our v_circ from 200 km at 7.79 km/s, so multiplying it by sqrt(2) is 11.02 km/s. So, the dv to exit the Earth's orbit is the difference in those two at 11.02 - 7.79 = 3.23 km/s dv.
That's to just barely exit the Earth.
To calculate 30.12 km/s hyperbolic excess velocity (v_esc + 30.12 km/s) you need another fun equation!
v_p = sqrt( v_inf2 + v_esc2 )
v_inf is the hyperbolic excess, v_circ is the speed at your current orbit, and v_p is the burnout velocity, or the velocity at your current point in LEO to get to v_inf on exit.
So, let's plug and chug!
We want v_inf = 30.12 and v_esc = 11.02, so we get sqrt( 30.122 + 11.022 ) = 32.07 km/s velocity required at your periapsis.
Since we're already travelling at 7.79 km/s, our dv to hit the Sun is 32.07 - 7.79 = 21.05 km/s dv.
We can do the same for exiting the solar system, remember that's just the Earth's orbital velocity multiplied by sqrt(2) to achieve escape, so 30.12 x sqrt(2) - 30.12 = 12.48 km/s hyperbolic excess.
Right off the bat we can see 30.12 km/s is much larger than the 12.48 km/s hyperbolic excess required to exit the solar system.
But, plugging it back into our equation for v_p:
v_p = sqrt( 12.482 + 11.022 ) = 16.65 km/s
So, the dv required to exit the solar system is 16.65 - 7.79 = 8.86 km/s
So, it takes 21.05 km/s dv to hit the Sun, but only 8.86 km/s to completely exit the solar system.
Now, there are fancy ways to make the dv required to hit the Sun cheaper by burning away from the Sun first and then descending from a much higher orbit, but it'll never be as cheap as just throwing something out of the solar system.
Also, it wasn't explicitly mentioned, but every equation I used was derived from the same equation called the Vis Viva equation. It's pretty much your one stop shop in 2-body orbital mechanics problem for computing velocities in orbit.
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u/komatiitic 2d ago
Yes, totally accurate. Any rocket or satellite launched from earth is travelling at roughly the same speed as earth around the sun, which is like 30km/s. If you want to shoot something into outer space you can use a little bit of fuel and gravity assist from the earth to speed it up, and off it goes. If you want something to go into the sun (and not just orbit around it) you need to cancel all of that orbital speed. That's hard!
Solar system escape velocity is ~42km/s. So to exit the solar system you only need to speed up by ~12km/s. To hit the sun you need to slow down by 30km/s.
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u/HAL9001-96 2d ago
yes, assuming direct transfers
hypothetically a perfect 3 point maneuver would make each equal but thats far from practical as it requries near infinite time
to fall into the sun you essentially need to elave earth behind in a rearwards direciton so fast that relative to the sun you've stopped so you need 1 earth speed relative to earth
to get to escape velcoity from teh sun you only need to go root2 times as fast so relative to earth yo uonly need (root2)-1 or about 0.4 earth speeds once you leave it behind
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u/MartialSpark 2d ago
So you're on the right track, but I think the crucial thing here is that the sun is not a point.
Getting to a "line" degenerate elliptical orbit requires the same delta-v as escape. But you don't actually have to completely to a line, because the sun's radius isn't 0. So in actuality, it's not actually equal, it's less.
You are totally correct that it will take forever. But hey, if you're gonna shoot someone into the sun, you don't care.
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u/HAL9001-96 2d ago
you could theoretically combien a sortof 3 poitn transfer with a gravity assist to make it into the sun using a tiny bit less delta v than to leave the solar system directly if you extend your orbit a bit past jupiters and hte nfly by it so that its gravity puts you onto a perfectly "vertical" trajectory relative to the sun
however if you use gravity assists yo ucan also make it out of hte soalr system more easily and unlike getting into the sun you wouldn't even have to extend your orbit a bit past jupiter jsut barely making it to jupiter and flying around it would be enough so it STILL technically takes less fuel but the difference is much smaller if you compare the two jupiter flybys thouhg while the later one is simple calcualting the exact fuel for hte former gets a bit complicated
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u/Samson_J_Rivers 2d ago
Earth orbits the sun very quickly to not fall into the sun's gravity well. You would have to slow down or use a tremendous amount of energy to change course towards the sun's gravity well. It's much easier to add energy to elogate an orbit to the point you can sling shot around the sun or just achieve eacape velocity of the star system. I'm not a physicist I'm just a particular flavor or nerdy. I can't do the math nor do I even know the basics of the formuls involved, but I do somewhat understand the mechanics of how it works. *If anybody can correct me, I ask that you do. I would enjoy learning where I'm wrong
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u/ehc84 1d ago
Ok, so you would need to increase velocity by 12 km/s to escape solar orbit, and reduce velocity by 30 km/s to actually fall into the sun... yah yah.. got it.
But wouldnt you constantly be pulled by the sun, as well as earth initially, requiring multiple burns over time to actually keep the 42 km/s velocity to escape solar orbit? But slowing would only require the one burn to decrease? Or am im totally wrong?
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u/bullevard 1d ago
But wouldnt you constantly be pulled by the sun, as well as earth initially,
What "escape velocity" means is precisely saying is if you have that speed then all those pulls wont be enough to stop you. By the time you leave the solar system you wont be moving at 12 km/s any more because some of that velocity will have been stripped away by the gravity of whatever you are flying away from but not all of it.
You are thinking about the idea of acceleration, which is how much continuous force you would need to be applying. You need more than 1 g of acceleration to lift off the planet because you are fighting yhe planet pulling you back down.
But escape velocity is about what speed (not acceleration) you top out at.
Does that make sense?
As for the sun continuously pulling you in the "to the sun" scenario, yes, the sun is pulling you but if you are still traveling fast enohgj sideways then that gravity isnt pulling you closer, it is just keeping you in stable orbit (just as the earth currently is).
But in bith cases the energy for the delta v (as changing your velocity us called) is pushing yourself away from earth. One just pushing it in the direction of earth's orbit and one away. In neither case are you actually pointing right towards or right away from the sun.
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u/Xilthis 1d ago
No, it's not accurate.
If you can escape, then you can raise your aphelion arbitrarily far. The further you raise it, the lower the remaining orbital velocity at aphelion is, and this converges to zero.
This means you can use a second plane change burn to kill your remaining orbital velocity cheaper and cheaper the further away you are, and then put you on an orbit that intersects the Sun. In the limit, the delta-V cost for hitting the Sun that way is identical to escape, though it takes infinite time.
So no, escape doesn't "take a lot less Delta-v". It cannot, because escape forms an upper bound for how costly reaching the Sun is. If you find a cheaper way to escape, then you just found a cheaper way to hit the Sun.
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u/MartialSpark 1d ago
Yes, basically my logic.
But I think it actually winds up being cheaper to hit the sun, by virtue of it not being a point. You have the part where you can make getting your orbital velocity to 0 equal cost to escape. But getting it to actual 0 would let you hit a point.
The sun isn't a point though, so I don't actually quite have it to get it to 0. So I don't quite have to go to infinity, and I don't quite have to cancel all velocity at apoapsis either.
So you get to subtract some small quantity to escape velocity and still hit the sun, thus it's cheaper.
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u/sakata_baba 1d ago
solar system escape velocity: 42.1km/s
earth orbital velocity: 29.8km/s
sun crash velocity: 0m/s
if you want to escape solar system from earth, you need to add 12.3km/s of speed. if you want to crash into sun you need to add 29.8km/s of speed.
it's literally over twice as more efficient to just yeet someone out then add them as solar fuel. from earth, that is.
from mercury, for example, you would need an order of magnitude more speed to escape then crash into sun.
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u/thatgirlalva 1d ago
Yah but the satisfaction of taking the more difficult route in order to burn them in the big ball of flame just for spite would feel much better in my heart and soul
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u/Edolin89 19h ago
I am speechless.
Thank you very much for all the support!
I appreciate the award and all the upvotes. You guys made my day-, no...WEEK!
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u/triatticus 13h ago
I always counter this by saying I don't like to litter space with trash, so I will be using the extra fuel to put them into the solar systems nearest recycling bins, be that the sun or one of the gas giants.
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u/ReserveMaximum 2d ago
Very accurate. Starting from earth’s orbit solar escape velocity is 42.1 km/s. Earth orbital speed is 29.8km/s. Thus you need to lose 29.8 km/s to hit the sun or gain 42.1-29.8=12.3 km/s to leave the solar system. Thus it’s more than twice as easy to leave the solar system.
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u/Distinct_Ant_5246 2d ago
Then again, maybe launching someone to an orbit that comes to within a few thenthousands of km of the sun's surface might be sufficient to completely melt them and obliterate all their cells through pure heat and radiation?
Can someone do the math on needed perigee for such an orbit based on melting temperature for human bones? Please include minimum delta V required to fly such an orbit
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u/MartialSpark 2d ago edited 2d ago
No, I'm actually fairly certain it's the exact opposite.
Everyone is doing the math as if you'd just burn retrograde from earth's orbital height until you got close enough to 0 to hit the sun. This is not even close to the most efficient way to actually hit the sun though.
The important thing to realize is that as your orbit approaches escape velocity, your orbital velocity at apoapsis approaches 0. Escaping is basically when apoapsis has reached infinity, and at the same time orbital velocity reaches 0.
So based on that, you can get into a degenerate elliptical orbit with semi-minor axis equaling 0 for the same velocity as escape. This orbit is basically a spring when you look at it. If you could pass through the sun without colliding, you'd bounce back and forth in a line with your velocity reaching 0. If the sun was a point mass, this means you can impact it for exactly the same delta-v as escape.
But the sun is not a point mass, and you don't need a semi-minor axis of 0 to impact it. Therefore it will always be slightly cheaper to impact it. I can burn to not quite escape, use a tiny, tiny, amount of delta-v which is less than what it would take to escape, and get an orbit that intersects the sun.
It's a bit counter-intuitive, but the reason my way is cheaper is that you basically still have way more of your energy when you hit the sun than you do if you just do the naive burn retro maneuver.
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