# Interestingly counter-intuitive

There are a few people I might like to fire into the heart of the sun, but I hadn’t realized how difficult that was. Here’s a video and simple simulator that lets you try to fire a rocket right into the sun. It took me a few tries to figure out how to do it — you have to launch directly opposite to the direction of Earth’s travel, and cancel out its velocity…and then it will fall into the sun. If you’re a fair bit off, it flies off into a new orbit around the sun that intersects with Earth’s orbit, which is not good. If you’re a teeny tiny bit off, it just scarcely grazes the sun, and then something cool happens: it slingshots around at tremendous velocity and flies off the screen.

I mostly sent rockets off to Alpha Centauri, or something, which is not quite as spectacularly destructive as slamming into a giant radioactive ball of plasma. But still good.

1. Nerull says

Before anyone gets any ideas, the flying off the screen bit is due to integration errors that occur when you pair massive velocity and gravitational forces with a long simulation time step. We couldn’t actually fling something to alpha centuari by sending it past the sun.

2. says

Rats. It just goes off into an absurdly long parabola, or something?

3. Rob Grigjanis says

you have to launch directly opposite to the direction of Earth’s travel, and cancel out its velocity

The component of velocity parallel to Earth’s instantaneous velocity (v) has to be equal and opposite, but it can also have a component at right angles to v, which can be anything from

(a) zero to (less than) the escape velocity from the sun if its outwards
(b) zero to ∞ if its towards the sun

So there’s a continuous range of direction/velocity.

If you throw something on a path that passes near to the sun, it will most likely be a long ellipse. Think comet orbits, although its most distant point from the sun will likely be fairly near to Earth’s orbit. In order to get a parabola, the thing would need to be travelling at solar escape velocity, in which case it really could go to alpha centuari, though its path near the sun wouldn’t have anything to do with it.

Throwing something into the sun is simply putting it on an elliptical orbit that intersects the surface of the sun. Which is not easy.

5. F.O. says

I’m disappointed, I hit the Sun at my very first attempt.
I blame my success on sheer luck, and playing too much Kerbal Space Program.

6. gorobei says

Actually, into an absurdly elongated orbit, I think. If the simulation was good, it would eventually reappear on the same path.

Now, if you had some fuel left, and used it when the craft was moving really, really, fast near the sun, then you might get to Alpha Centauri.

7. kalil says

And everyone who has played Kerbal Space Program is like “Yup, we knew that!”

Cancelling your velocity relative to the surface will effectively cause you to fall straight down – that’s pretty much the trick for landing on any celestial body.

(Pro-tip for landing on the Mun or other atmosphereless bodies : the closer your orbit is to the surface when you kill your velocity, the easier the landing is. …just make sure you’re high enough to clear any mountains you might pass.)

Dr. Myers, I might have a spare KSP steam key, if you’re interesting in learning more about orbital mechanics, as well as seeing some pretty explosions. It’s a lot of fun, and would give you a great comeback to all those physicists who feel the need to weigh in on biology stuff. Lemme know if you’d like a copy.

8. Rob Grigjanis says

gorobei @6: The Corbomite Oberth manoeuvre!

9. eukaryote says

To hit the sun, you want a delta-V that puts your ship onto an orbit that intersects the surface of the sun. There are infinitely many such orbits. Solar orbits are ellipses (Kepler). It is quite unlikely that you’re going to insert onto a line (which is a degenerate ellipse) and fall radially in with no azimuthal velocity component. It might appear so, but it’s probably an ellipse.

Ehh, falling straight down is not the trick for real landings. Inserting into a “straight down” orbit is terribly wasteful of fuel, and one doesn’t waste fuel in space, because there are no gas stations. The last 150 ft of descent on the apollo mission was vertical. See https://www.hq.nasa.gov/alsj/a11/A11_PressKit.pdf. There is a sketch of the descent orbit on pg. 38 or so. On earth, we have the luxury of using parachutes for braking if that is the design. Hohmann transfer orbits conserve fuel.
https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

10. rogerfirth says

Rats. It just goes off into an absurdly long parabola, or something?

No. It’s a numerical artifact of the time-stepping algorithm used to generate the animation. In reality it will leave the sun with exactly the same velocity it had as it approached.

The reason GAMs work off the planets is because the planet is moving. In the sun-relative frame of reference the spacecraft leaves the planet faster than it approached. But in the planet-relative frame of reference the spacecraft leaves at the same velocity as it approached.

I understood all these things mathematically after an graduate orbital mechanics class. But I never really got a gut feel for them until I wrote a little toy to try to boost out of Earth orbit on a Hohmann transfer and brake into Mars orbit. Extremely counterintuitive, and truly impressive that NASA has been able to hit so many holes in one.

11. rogerfirth says

Physics is weird and confusing.

Defintely. But the really really really neat thing about physics, is that all these bizarre counterintuitive things can be boiled down to a few really straightforward principles like Conservation of Mass, Conservation of Energy, Conservation of Momentum, Conservation of Angular Momentum, and I’m sure other conservation laws I’m less familiar with (charge? spin?).

I’ll never forget the day in Prof. Chris Anderson’s undergrad astronomy class at the University of Wisconsin Madison, when he derived Kepler’s Laws from Conservation of Energy and Conservation of (Angular) Momentum. I was truly awed, and I’ve been hooked ever since.

12. F.O. says

Nature is weird and confusing.

13. Nerull says

Another interesting effect, which would actually work at the sun, is that the orbital energy imparted by a given change in velocity is larger the higher your starting velocity. Since the point in an orbit with maximum velocity is the closest point to the gravity well being orbited, this means that engine burns closer to a planet are more effective than engine burns further away from a planet. By doing an engine burn while you were being slung around the sun at ridiculous speeds you could get a massive change in orbital energy with less fuel than you would need to do the same energy change further away from the sun.

I haven’t run the numbers, but I suspect it would be very difficult to make this worth it, however, as you first need to throw away a lot of energy you already had to reach the sun in the first place. That and your ship would melt.

14. OverlappingMagisteria says

“If you’re a teeny tiny bit off, it just scarcely grazes the sun, and then something cool happens: it slingshots around at tremendous velocity and flies off the screen.”
“Rats. It just goes off into an absurdly long parabola, or something?”

Oooyyyy…
You’re forgiven PZ… but you know how you say physicists shouldn’t talk biology? The inverse is true as well…

And #15: The Oberth Effect applies if theres an impulse near a gravitational body (ie thrusters burning) not a free falling object.

15. Nerd of Redhead, Dances OM Trolls says

Nature is weird and confusing.

Just thinking about one of the ISS supply launches from Cape Canaveral can be bewildering.
There is an instantaneous(!) launch window as the ISS passes overhead, and the rockets put the capsules along the same great circle as ISS orbits, with a lower initial perigee, and the apogee at the same altitude as the ISS. Since it takes a few minutes to achieve orbit, the capsule is behind the ISS, which means the apogee is behind the ISS. Since the overall orbit is lower, it will orbit slightly quicker, and eventually catch up to the ISS. By firing thrusters at the apogee, the capsule will increase the perigee, and the burns will take place way from the ISS. After a couple of days, the capsule is in the same orbit as the ISS, and able to approach it safely with minimal use of thrusters.

16. Rob Grigjanis says

rogerfirth @12: Spin is intrinsic angular momentum carried by particles. If we call the orbital angular momentum L, and the spin S, it’s the total angular momentum

J = L + S

which is conserved. So neither L nor S are generally conserved.

17. numerobis says

To get low solar orbit you’ll want to get a very high orbit first, since you’re trying to reduce your semi-major axis by a factor greater than 12.

That or you’ll want some gravity assists, which is how we got to orbit Mercury.

18. AlexanderZ says

If you’re a teeny tiny bit off, it just scarcely grazes the sun, and then something cool happens: it slingshots around at tremendous velocity and flies off the screen.

Presumably to fly off into the past.

19. birgerjohansson says

“you have to launch directly opposite to the direction of Earth’s travel, and cancel out its velocity”
A cheaper way of doing things is to launch the rocket on a Hochmann transfer ellipse to Jupiter.
Then you let Jupiter’s gravity slingshot the craft so it negates the remaining velocity perpendicular to the direction ofthe sun, making it fall straight into the sun. This final journey would take one eight the time of orbiting the sun at the distance of Jupiter, ca. 1,5 years.
— — —
Gorobei @6: “Now, if you had some fuel left, and used it when the craft was moving really, really, fast near the sun, then you might get to Alpha Centauri.”
Vernor Vinge wrote a short story (“Long Shot”) with this premise, 1972. A robotic probe takes 40 000 years to reach Alpha Centauri B, then starts thawing out a frozen embryo…
— — —
Actually, if you travel on aparabolic path to a distance of 16 solar radii, you will have a velocity of 150 km/s. Now start your rocket to get a velocity boost of 10 km/s (entirely within the possibility of current technology). As the probe recedes from the sun, its final velocity will now be 55.7 km/s, or ca. 11 astronomical units (AU) per year, far more than the Voyager probes.
With this speed it would take 4500 years to reach Alpha Centauri.
A better target would be Planet Nine. Some estimates (Malhotra et al) sets it at 665 AU, or 60 years out.

This happens to be the minimum distance for using the Solar Focus for gravity microlensing!
Planet Nine will be hidden under a massive atmosphere and a very deep ocean, but if it has even a single moon, that will serve as a source for raw materials for the von Neumann machines humankind has invented during the time of the journey. (Include advanced 3D printers for the machinery).
Now you can churn out space telescopes with the AI Controls needed to locate the narrow line of the solar focii of the objects they want to study (exoplanets, quasar central Engines, you name it).

I am aware the retro burn at arrival to Planet Nine would require a delta-vee of 55 km/s. This is a job for the (somewhat hazardous) uranium-salt rocket suggested by Zubrin. With a travel time of 50 years the construction robots would have time to modify the reactor/engine assembly for a reliable burn. (You do not want a flawed prototype to try this!)

20. says

@21 let’s recalculate that, shall we?

55.7km/s vs 300 000km/s –> 5400x slower
Alpha Centauri is at 4.2 lightyears away

4.2×5400 = 22680 years to travel to AC at 55.7km/s – don’t know where you got your 4500 years from.

Also not sure how you can get to 55 km/s with a 10 km/s dV regardless of if it happens in Perihelion, a slingshot maneuver works relative to other objects, but doesn’t change your relative velocity to the object you’re slingshotting around any more than straight-up using the same dV to move away from the object, so you’re not gaining anything – at any rate, to get from earth to 16 solar radii, you need a dV close to 30km/s (which is the orbital velocity of earth) for a total dV of 40km/s

And since the Earth is already moving at 30km/s vs the sun, using that same 40km/s dV budget but launching in the direction the earth is moving will give you a departure velocity of 70km/s vs earth (although, admittedly, never more than 40km/s vs the sun – I’d say if you want to quit the solar system, use that dV budget to slingshot around Jupiter (or better still, do a double slingshot around Jupiter & Saturn, though you may have to wait a bit to get the best geometry…)

21. says

Okay, I didn’t take the Oberth effect ( https://en.wikipedia.org/wiki/Oberth_effect ) into account – I haven’t calculated how big it would be so your 55km/s might be correct – however it’ll still be only the difference between 55km/s and about 40km/s, not the 10km/s dV change alone – and it’ll still take tens of millenia to get to Alpha Centauri.

22. says

And note that 40km/s Delta-Vee is far far more than any existing chemical rocket is capable of delivering. Supposing you could put a Saturn V rocket fully fuelled into space, the max delta-V it could pull *without* any payload is around 18 km/s

So basically we currently don’t have any practical way of putting an rocket on a trajectory that gets to within 16 solar radii with enough reactor mass to provide a 10km/s additionnal delta-V *and* have a useful payload.

If we want to explore the stars, something other than chemical propulsion is going to be required (something where a small amount of reaction mass can produce a lot more kinetic energy) – but frustratingly, most anything that produces a lot of kinetic energy for a smaller reaction mass is going to be less useful for profiting off the Oberth effect in a solar slingshot.

And I’ll stop now :)

23. birgerjohansson says

1. Erratum: yes it would take about 22000 years, that is why it helps calculaing stuff with pen and paper instead of just by using memory for digits. My mistake.

2: First a slingshot effect *near Jupiter* so you can travel almost directly towards the sun!
(numerobis @ 19, sorry I did not reference your post. Yes , a Mariner probe made it to Mercury by the mid-1970s that way)

3. 150x 150= 22500 160×160=25600 25600-22500= 3100. Square root of the difference is ca 55,67.

4: Solar focus (and the putative Planet Nine) is ca. 1% of a light year, well short of interstellar, but a good proof-of-concept distance for a robotic mission.

5. Interstellar space has plenty of dark objects (Brown dwarfs, ejected planets, cometary nuclei), the problem is finding them. If you spot a drifting jovian planet (with moons) at 1 light year, you have a target for von Neumann machines. The time spans will be way beyond human life spans but trivial by geological standards. Interstellar travel will be beyond human endurance, no matter what propulsive technologies you use.

6. For no particular reason my PC changes the beginning letters of words to *C*aps which is driving me Trump-style insane, so I will log off now.

24. Matrim says

@AlexanderZ, 20

There be whales here!

25. birgerjohansson says

Matreim,
That could be a reference to Star Trek or (more cruel) the Hitch-Hiker’s Guide to the Galaxy. And let’s not forget the potted plant that crashed into the carcass of the whale.
— — — — — —
I got a bit carried away (I really like the Solar focus idea).
One last thing.
If you use the time span for the various construction phases of Stonehenge as a rule for the maximum time humans can concentrate on one single multi-generational project, you get approximately a millennium and a half. Even with the very long times it takes to move objects in the outer solar system, you can accomplish pretty dramatic things in this time.

Example: If objects like 1996 TL 66 are common, there are a lot of 100-km lumps of ice waiting to be used (for instance, for terraforming Mars). Set aphelion at 130 AU and perihelion at 35 AU, just outside the orbit of Neptune. At 130 AU it will take a delta-vee of less than 0.2 km/ s to move perihelion to 30 AU, the ballpark for Neptune’s orbit. Journey to Neptune: ca 1000 years. Slingshot maneuver at Neptune will send an object en route to the inner solar system (for instance, Mars).

Or you can start off using material from the “trojan” objects in Neptune’s orbit (more mass than the whole main belt of asteroids) if you don’t fancy waiting that long, but I don’t know the velocity changes that would be necessary.

26. says

You know how they say all you need to do is make a grammatical error in a post to get a swarm of commenters speaking up to correct it?

I’ve now figured out how to draw in the physicists.

27. Bill Buckner says

Time for some nit picking.

You will never (talking a two-body system) be on a parabola. That requires infinite precision (eccentricity e = 1, exactly) to place you in between elliptical orbits (e 1). In the same sense you will never be in a circular orbit (e = 0, exactly)

28. Bill Buckner says

(e 1) should read (e < 1)

29. Bill Buckner says

Dammit! Final correction no matter what:

That requires infinite precision (eccentricity e = 1, exactly) to place you in between elliptical orbits (e < 1) and hyperbola (e > 1)

30. birgerjohansson says

Bill,
that is why the infinite improbability drive is so bloody useful.
And if you screw up, you can hide the mistake using the Somebody Else’s Problem field.

31. birgerjohansson says

(OT) Team catalogs most likely ‘second-Earth’ candidates http://phys.org/news/2016-08-team-second-earth-candidates.html
(but the results are skewed towards “bigger-than-Earth- -Earths” because the more suitable smaller worlds rarely show up in the background noise. Also, beware of the solar flares from small stars, they can strip off the atmospheres.)

32. jamiejag says

Also, doesn’t Alpha Centauri, or something, have a giant radioactive ball of plasma to slam in to?

33. kaleberg says

It sounds like they’ve implemented the original Spacewar game from the early 60s. We used to play that at night when no one else was using the PDP-1X, so we learned a lot about orbital dynamics. The graphics were minimal, but there was nothing like zipping around in a little spaceship to get a sense of how gravity works.

34. says

@rogerfirth:

An even cooler thing about physics is that there is a one-to-one correspondence between each of these conservation laws and a symmetry in the equations of mechanics (Noether’s theorem). For instance, conservation of energy arises from the fact that the equations are invariant under translation in time. See: https://en.m.wikipedia.org/wiki/Noether%27s_theorem

35. Crimson Clupeidae says

This is just a two body gravitational problem, it completely ignores the gravity of the Earth, which potentially makes a big difference. I have found better, similar, simulators around on the web, but haven’t played with them in years.

36. Rob Grigjanis says

Ivo @36:

there is a one-to-one correspondence between each of these conservation laws and a symmetry in the equations of mechanics (Noether’s theorem)

Worth quibbling about, IMO. The symmetry is in the action, which is also used to derive the equations of motion, via the principle of least action. A sine qua non for understanding our physics theories, I think.