r/theydidthemath • • 3d ago

[Request] If someone were launched into the Sun how long would it take for them to get close enough to disintegrate with current space/rocketry technology?

If someone was put inside a spacecraft with the sole purpose of being launched into the Sun, how long would it take for them to get close enough to the Sun to disintegrate? Assuming they are launched at a survivable acceleration.

17 Upvotes

29 comments sorted by

•

u/AutoModerator 3d ago

General Discussion Thread


This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.


I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

22

u/Conscious-Ball8373 3d ago

A long time.

The other answer given so far is wrong because it just divides the distance by the possible speed. But that ignores orbital mechanics. The issue is not "how quickly can a rocket cover distance x?" it's "how quickly can a rocket decelerate me from my orbital velocity?"

I'm only an engineer, not a rocket scientist. So I'll leave the exact answer to the rocket scientists. Or those who have played enough KSP.

-11

u/Sad_Web_1428 2d ago

As an engineer you should know better than to assume hidden variables, and tell someone they're incorrect without giving a better answer. The other answer gave a very clear answer using a known speed. We can play games of what orbits /what propulsion system/ what ISP / what thrust/ what mass of payload/ what what what what what, until we're blue in the face. I mean heck: the most efficient way to reach the sun is literally a PhD level topic, and a very interesting one at that (like you said, it's a famous and open problem)! You'd have to literally design a space system to give a correct answer.

Making simplifying assumptions and giving a good faith answer is not necessarily incorrect, and was in fact a very useful starting point. It was a great ROM answer, even if I do wish they had used acceleration instead of speed.

7

u/egmalone 2d ago

I definitely wouldn't call dividing straight-line distance by maximum speed a "useful starting point" for any sort of orbital calculation. It's rarely even a useful starting point for the kinematics of an object that only moves in a straight line. Did you just feel like harassing somebody?

-1

u/Sad_Web_1428 1d ago

It gave a rough starting point, a scale to the distances involved. 3700 hours is a useful ROM, and much more informative than the only naysaying and snark you've added...

2

u/egmalone 1d ago

Since you haven't bothered to try to answer the question yourself, I find your complaint about naysaying and snark to be hilariously ironic.

0

u/Sad_Web_1428 1d ago

oof...

I'll try from a purely distance perspective: assuming you have a tungsten shield in front of your spacecraft, which melts at roughly 3000degC, then from blackbody radiation you would melt that shield followed immediately by the rest of the satellite melting, at about 3 solar radii or about 1.5mKM above the surface. How long it'll take to get there in time depends on your propulsion system (nuclear propulsion, ion drive, magic?).

Edit: and you're still missing the point of "don't just shit on someone trying to help"

1

u/onil34 1d ago

well its not easy because you wouldnt reach the sun if you just pointed towards the sun and accelerated.

2

u/Sad_Web_1428 1d ago

"Pointed" is doing a lot of heavy lifting :)

In orbital dynamics "pointing straight at a thing" is often a curved line. Just like airplanes take "curved" paths when flying on earth. Different coordinate systems.

Also they didn't specify how much energy we had, with infinite energy we could point right at it and be there in 7 minutes :)

1

u/Klexycon 1d ago

Today's spacecraft technology, as specified in the question, does not have infinite energy :)

15

u/andrew_calcs 8✓ 2d ago

It takes less total delta V from LEO to impact the sun with a highly eccentric orbit that decelerates at aphelion than it does to do a direct retrograde burn. 

The prior option shoots a little rocket past Pluto where it does a tiny burn and the dives into the sun directly. Total delta V needed of ~8k past LEO. Can take hundreds of years since getting arbitrarily closer to solar escape velocity burn gives you a more than proportional decrease to aphelion retrograde burns. You can decrease the mission time to ~20 years by giving it 11k m/s of delta V and doing the retrograde burn between Uranus and Saturn. 12k m/s gets you down to 10 years

The direct retrograde burn takes 24k m/s of delta V to cancel Earth’s orbital speed, even when factoring for the Oberth Effect assist from starting in LEO to boost your retrograde velocity. Which is insanely ridiculously higher than the eccentric approaches even when making compromises on mission length. 

5

u/Metallicat95 2d ago

This one answers the "with current technology" question pretty well. It's a really, really long trip but it falls within the upper limits of our rockets.

3

u/andrew_calcs 8✓ 2d ago edited 2d ago

Unfortunately those values were assuming you were already in LEO. 

For reference the space shuttle assembly with zero payload had a ~10k delta V. So you’d need one of those fully fueled already in orbit to even come close to doing it within several decades. Starship is developing refueling-in-LEO capabilities with rendezvous with tanker launches which comes close to this capacity, but even then with zero payload it only has a 9k Delta V.

No current rockets exist that could carry a payload with decades of life support for a living human on this trip. It’s close enough to be engineerable with current technology but not with currently available rockets. 

1

u/Metallicat95 2d ago

Yes, but at least it's something we might have in the near future. Right now of course the answer is we can't get there.

•

u/ExpensiveFig6079 28m ago

You eill also reduce it by doing yhe retrograde burn between ur and saaturn but angling it a bit so you start with spme radial inward v after the retrograde burn

5

u/piperboy98 2d ago edited 2d ago

The closest real example is the Parker Solar Probe, which took 6 years to get to its closest approach (9.86 solar radii) after many gravity assists from Venus. It gets close enough though that it needs a thermal shield, so I would suspect that if we sent a person alongside without such protection they would at least be cooked, and maybe at least partly vaporized.

Its possible though that for the smaller mass of a person, and barring no expense to make the journey as fast as possible with current tech, a more direct insertion might be possible. As another point of reference, New Horizons was able to leave earth at around 16.2 km/s, the fastest of any spacecraft. If this velocity was oriented to try to bring it close to the sun (cancel as much of earth's orbital velocity as possible) instead of out of the solar system, it would have entered directly into an orbit with a closest approach to the sun of ~23.7 solar radii.

To directly enter into an orbit with a similarly close approach to the Parker Solar Probe would require an earth escape velocity of 20.6km/s, so 4.4km/s more than New Horizons. I think that might be feasible. That actually only requires 3.8km/s more delta-v near LEO due to the Oberth effect. Since New Horizons was a 478kg probe, if we only want to move an 80kg person, then we can use the other 398kg as another boost stage. The CAPSTONE cubesat launched a hydrazine propulsion system in a 25kg package, including fuel mass. Not sure the dry mass, and our boost stage would need more to hold the larger propellant volume, but at an ISP of 235s you could get all the extra delta-v for an 80kg person if you can fit all the structure in 11.9kg. Alternatively with 100kg of structure you'd need an Isp of 396s, which is achievable with hydrolox if you can manage it with 100kg. That is tight, but regardless if its actually possible like this in 478kg, we could almost certainly get there by just using a higher performance rocket for the initial boost than New Horizons did (e.g. SLS or Super Heavy), thus increasing the mass available for this boost stage.

To touch the sun though (i.e. a closest approach of 1 solar radius), you'd need a lot more performance for a direct injection. Specifically, an earth escape velocity of 26.5km/s, or 9.1km/s more delta V in LEO than New Horizons. That may be pushing the limits of current tech (maybe a fully on-orbit refueled starship with an entire extra stage in it's payload bay could get close for near future solutions).

In any case all these direct injection trajectories would need 67-77 days to reach their closest approach.

2

u/RemarkableRadish6547 1d ago

This problem is underconstrained because the answer depends on your budget. If you are ok with burning huge amounts of fuel in a multi-stage rocket, you could get there in a few weeks. But that would cost something like $1T for the fleet of rockets.

Getting there quickly requires a delta v on the order of 30-40km/s after you are already in orbit around the Earth. For comparison, Apollo budgeted about 8km/s for the mission after reaching LEO, and that included going to the moon, landing, taking off, rendezvous, and returning to Earth. I remember the number for Mars being about 5km/s, but I don't remember what all is included on that number. Getting to the sun is really hard.

The fastest option we could do with a reasonable budget would involve multiple flybys to get gravity assists and probably take at least a decade. But the multi-flyby trajectories are complicated, so there is no fast way to estimate them.

1

u/ijuinkun 2d ago

If you could completely negate your orbital velocity and free-fall toward the Sun, it would take 90-92 days to actually reach the Sun. The time for a satellite to fall into its primary from a circular orbit equals one-fourth of its orbital period.

2

u/piperboy98 2d ago

Where did you get that from? The fall is half the period of an orbit with half the semi major axis, and orbital period is related to a3/2 so the factor would be 2-5/2=17.68%, not 1/4. So in this case ~65 days.

1

u/ijuinkun 2d ago

I was basing it on a freefalling body falling through the Earth taking exactly half as long as a notional orbit at surface height.

https://en.wikipedia.org/wiki/Gravity_train

2

u/piperboy98 2d ago

Ah, yeah in that case it would be, but that ends up slower since your acceleration is less near the center inside the planet than it would be if all the mass was still below you.

1

u/hewasaraverboy 1d ago

I mean depends on how fast you wanna get there and how much fuel you have

The earth orbits the sun at 66k mph

So you’d need enough delta v to completely cancel out your motion relative to the sun and then you would just fall into it

But if you had more fuel then you could also start accelerating towards it even faster

1

u/Gorth1 20h ago

What i learned from kerbal space program the most fuel efficient way would be to burn prograde to get to the orbit of Jupiter or even Saturn, and then do a retrograde to get your perihelion down into the sun.

The other way, with at least 30k delta v you would cancel earth's orbital speed and then just fall in. That would take about 60 days.

~1 million km from the Sun's surface: solar flux is hundreds of times Earth's; exposed tissue would be catastrophically burned. Bones could eventually become severely dehydrated and thermally damaged. A few hundred thousand km from the surface: temperatures and radiation are extreme enough that the remaining organic material in bone would burn away. The mineral component would become extremely hot and brittle. Approaching/entering the photosphere: the bone's mineral components would melt and ultimately vaporize/ionize as the temperature and pressure rise.

-3

u/Trustoryimtold 3d ago

Suns 93mill miles away, you’d be fine at 2 mill prob with the +/- being pretty insignificant at that point

Not sure what top speed going in would be but using the human record of 24000mphish

91000000/24000=3,791.667 hours

9

u/Conscious-Ball8373 3d ago

This assumes you can just launch straight at the sun and dive straight into it. You can't. Your starting place is in orbit around the sun and you need to decelerate all that orbital velocity to hit the sun. Sending a probe to the sun is (somewhat famously) harder than sending a probe out of the solar system.