Science and Science Fiction: Neutron Star by Larry Niven

April 6th, 2010

There are spoilers ahead concerning the story “Neutron Star” by Larry Niven.   Be warned.   If you want to download and read the story for under a dollar, check it out on fictionwise.com.   If you’re not going to jump out and read the story any time soon, you can familiarize or remind yourself about it at the wikipedia entry for “Neutron Star.”

Here is Wiki’s plot summary:

Beowulf Shaeffer, a native of the planet We Made It and unemployed for the last eight months due to a stock market crash, is contracted by a Pierson’s Puppeteer, the Regional President of General Products on We Made It, to pilot a General Products-hulled starship, in a close approach about neutron star BVS-1. The Puppeteers want to determine why two previous researchers, Peter and Sonya Laskin, were killed during the previous attempt on a similar mission. Shaeffer has no intention of even attempting the dangerous mission, but agrees anyway – he has other plans. He has the Puppeteers construct what he dubs the Skydiver to his precise specifications, supposedly to ensure he survives to return with the relevant data: an advanced sensor package, a high-powered thruster – and a high-powered laser. It is thus the only warship ever constructed by the cowardly and paranoid alien race – a prize beyond value and a perfect means of escape. However, he is forced into compliance by an operative of the U.N.’s Bureau of Alien Affairs, Sigmund Ausfaller, who has had the Puppeteers install a bomb somewhere inside the Skydiver. Ausfaller informs Schaeffer that if he does not attempt the mission he will be sent to debtors prison, and that if he attempts to escape in the ship the bomb will be detonated within a week – well before he could even reach another planet, let alone find a buyer for the ship. Shaeffer, realizing he is trapped, agrees to fly the mission.

The Skydiver reaches the neutron star, and the ship’s autopilot puts the Skydiver into a hyperbolic orbit that will take 24 hours to reach periapsis with BVS-1, passing a mile above its surface. During the descent Schaeffer notices many unusual things: the stars ahead of him began to turn blue from Doppler shift as his speed increases enormously; the stars behind him, rather than being red-shifted, were blue too as their light accelerated with him into the gravity well of the neutron star. The nose of the ship is pulled towards the neutron star even when he tries to move the ship to view his surroundings.

As the mysterious pull exceeds one Earth gravity, Shaeffer accelerates the Skydiver to compensate for the unknown X-force until he is in free fall (though the accelerometer only registers 1.2 gees). Shaeffer eventually realizes what the X-force is: the tidal force. The strong tidal pull of the neutron star is trying to force the ends of the ship (and Shaeffer himself) into two separate orbits. Shaeffer programs the autopilot in a thrust pattern that allows him to reach the center of mass of the ship in effective freefall, though he nearly fails to do so. The ship reaches perigee where tidal forces nearly pull Shaeffer apart anyway, but he manages to hold himself in the access space at the ship’s center of mass and survives.

After returning to We Made It, Shaeffer is hospitalized (he has received a sunburn by starlight blue-shifted into the ultraviolet) for observation at the Puppeteer’s insistence. While explaining tidal forces to the Puppeteer, Schaeffer realizes the alien had no knowledge of tides, something that would be elementary for a sentient species living on a world with a moon. The Puppeteers are extremely cautious when dealing with other races, and keep all details about their homeworld secret. When Schaeffer mentions that he can tell reporters the fact that the Puppeteer’s world has no moon, the Puppeteer agrees to give Shaeffer a million stars (an incredible fortune in galactic currency) in return for his silence. Shaeffer asks the alien how he likes being blackmailed for a change.

First, let me say I first read this story when I was in high school and loved it, and have read it a number of times since.   It’s a classic Hugo winner that has a plot point turn on a knowledge and understanding of astrophysics, and also, unfortunately, the surprise murderer can also be ruined by too much knowledge of astrophysics.   Conceptually, this is a great story to me.   I got my first introduction to tidal forces from this story, which is cool.   Gravitational force depends on distance, and tidal forces describe how an object pulls more strongly on one side of an object than the other.   Tidal forces are a subtle thing to most readers who are not physics or astronomy majors, and neutron stars extreme objects that really exist and have large tidal forces.   There’s a problem with the story that Niven acknowledges, however.   Also from Wiki:

In the “Afterthoughts” section of the Tales of Known Space collection, Niven writes: “I keep meeting people who have done mathematical treatments of the problem raised in the short story ‘Neutron Star‘, …. Alas and dammit, Shaeffer can’t survive. It turns out that his ship leaves the star spinning, and keeps the spin.” If this is true, it does more than kill Shaeffer: it kills the entire story premise, for the Laskins’ ship also would have acquired and kept a similar spin, which the puppeteers could hardly have failed to notice. It is also unclear how the Laskins’ ship returned to its starting point; unless the puppeteers sent another ship to retrieve it, it would have had to do so through normal space, a journey of years.

So, some plot holes and holes in his physics.   That seems to happen to Niven a lot, which isn’t a bad thing.   It means he’s pushing some limits, and there’s always the opportunity to come back to a story and do it right one way or another.   Niven’s famous creation Ringwold (AKA Halo to younger generations) isn’t instrinsically stable.   Niven was able to come back and write a sequal to Ringworld, The Ringworld Engineers, in which the stability issue suddenly becomes a plot point for an entire novel.   When I write a science fiction story and I come up with a problem with the basic physics, I know look to see if there’s an engineering solution to the issue that can become a plot element in my story.   I did that with Spider Star. There was no way to make a human-breathable atmosphere for my dark matter planet over the range of alitutdes I wanted — not a natural way, in any event.   Sufficiently advanced alien engineering could do it, however, and the reasons why aliens would do this became plot elements.

Now, Niven brings up the spin issue and the return flight issue.   Something I always meant to do, and haven’t done until now, was just to quantitatively calculate the magnitude of the tidal forces, making some assumptions based on information in the story.   OK, minimum alititude is only one mile above the surface, which is somewhat signficant compared to the radius of a neutron star.   For modern values of a typical neutron star, and these are somewhat model dependent, I assume a raduis of about 10 kilometers and a mass of 2 solar masses (see wiki for some more information, although I’m going from one of my textbooks).   1 mile makes the distance above such a neutron star about 6.6 km.   We can compute the tidal force exerted…it’s not as simple as this, but the primary thing to consider is just the axial component and its magnitude (there is also a transverse squeezing term in addition to this axial stretching term).   This is not so hard to compute.   And it’s more useful to compute the acceleration rather than the force, and put it in Earth gravities, which is something I have some intuitive feeling for.

\vec a_t(axial) ~ \approx ~ \pm ~ \hat r ~ 2 \Delta r ~ G ~ \frac{M}{R^3}

That’s from wiki.   The direction is axial.   The delta r term is the size of the body (a couple of meters for a tall human stretched out along the direction toward the neutron star, maybe half a meter curled up in a ball).   Capital M is the mass of the neutron star, R is the distance from the center of the neutron star, and G is Newton’s gravitational constant.   Watching the units, we can get an answer based on the values of M and R above.   Uh oh…I’m getting an answer like 2 billion meters per second squared per meter of separation, or about 200 million Earth gravities.   Even if you could lay perfectly flat, and assume a tenth of a meter between front and back, that’s still 20 million Earth gravities.   That’s large.   You don’t sruvive that kind of force.   Niven, in the story, suggests that there are “hundreds of gravities” present in the ship, and he’s only off by a factor of a million or so.   Still, it’s better than the surface gravity of a neutron star, which is about a hundred billion times that of Earth…

Now, I’m guessing that back in the 1960s, neutron star sizes were not well understood, but the mass should have been known to be on the order of a solar mass and a half or higher, and Niven gets the size right by saying it is “11 miles across”).   I mean, a neutron star is about the size of a small town like Laramie, which is pretty far out.   Anyway, any pilot this close to a neutron star gets pulped, with no hope for survival, regardless of ship spin issues.   The only way to fix this would be to change the perigee altitude, or do something very science fictional like make the pilot microscopic or shield the tidal force somehow.

The story doesn’t stand up today, quantitatively, although the concept is cool and could perhaps be reworked.   That might be a fun project, although today you’d have to assume that the audience had read “Neutron Star” and the new story would have to be a response in some clever way…I’m going to think about that.

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