by Andy Love, Jr.

This story is a good introduction to the concept of tidal forces, and also (more subtly) introduces the concept of the scientific method and the empirical approach to life. The story contains no sex, or objectionable language, and is written in a straightforward style (with some flashbacks). There is some gore and death in the story, but no scenes of violent conflict between sentient beings. The story is available in the collection called Neutron Star, which is still in print (?) [Editor's note: The collection is now out of print; see "What to Read First" for how to find a copy.], and belongs in Larry Niven's "Known Space"

future history as are all the stories in the collection (actually most of these stories belong to a subset of the "Known Space" future history that ould be called "The Tales of Beowulf Shaeffer").

Study Questions/Notes:

1. Science fiction stories often begin with a unusual/unfamiliar situation in the first few sentences, requiring the reader to spend a few moments figuring out what is going on. The challenge for the writer is to give the reader the information she needs without leading her to give up on the story. What is going on as the story begins? How does the author try to "hook the reader in" in the opening paragraph?
2. Neutron stars are real and basically as Niven describes (both here in the beginning of the story and later on).
3. A hyperbola orbit is an orbit that is not closed, so an object in such an orbit will approach its focus once and then depart forever at high speed (for more information on orbits, see here).
4. Niven follows the first scene, which establishes that the main character is in a dangerous situation, with a flashback to tell how the main character got into that situation. What familiar activity was the main character performing when the flashback begins?
5. What does a puppeteer look like? Cecil the Seasick Sea Serpent was a puppet character in a children's television program called "Time For Beany" (for information about it see here). In another story, Niven actually establishes that the first person to see a puppeteer had just seen a revival of that program, so this reference to a television show centuries before the story's action isn’t as silly as it might seem. For artists' renditions of puppeteers and much background information, see The Pierson's Puppeteer Home Page [Note the menu along the top].
6. Note that when the author introduces the puppeteer, he gives a range of possible occupations, "from a dockworker, to a jeweler, to the president of General Products." Two paragraphs later, the reference to a jeweler pays off when the exquisite skillfulness of the puppeteer mouth is mentioned and a paragraph later when General Products is mentioned again, the reader knows without having to be explicitly told, that General Products is a big, successful company.
7. The author drops in two references to advanced technology in rapid succession. From context, what is a "lift belt" and what is a "displacement booth"? Note while introducing these items, the author also refers to a familiar image from the Great Depression: businessmen jumping from windows.
8. How does Beowulf Shaeffer keep his creditors from demanding their money immediately?
9. "Neutron Star" is basically a puzzle story, in which the protagonist is placed in a trap of some sort, and can't get out until he or she has some insight. The conversation between Beowulf and the puppeteer starts to set up the puzzle. Why do the puppeteers need someone to visit BVS-1? What was the purpose of the initial visit? What happened to the Laskins?
10. No neutron stars had been observed in 1966 when this story was written (although they had been predicted as early as the 1960s) and as the author suggests, it was considered unlikely that they could be observed. However, in 1968, shortly after theoreticians predicted that the magnetic fields of rotating neutron stars would produce observable pulses of radio waves, the first pulsars were observed. The high-energy radio waves would likely kill Beowulf unless they were blocked by the General Products hull.
11. The next couple of scenes complete the trap inherent in a puzzle story. Why does Beowulf accept the puppeteers' offer of a job? Do you think the puppeteers knew what Beowulf planned, knowing that someone like Ausfaller would take care of the loopholes in their arrangement with Beowulf for them? In what ways does the name "puppeteer" fit them, other than in appearance? Ausfaller calls the puppeteers cowards, but they do seem to get what they want. If you read other "Known Space" stories you will see that asymmetrical beards are a style worn on a particular planet.
12. To understand this puzzle, some background on "free fall" is necessary. Any object moving solely under the influence of gravity is in free fall, including dropped objects in a vacuum, or objects in orbit. A person in free fall doesn’t sense a force moving him or her around, and unless he or she can see some nearby object that’s not in free fall, he or she will be unable to distinguish his or her situation from being in "zero-gravity" (this is the "principle of equivalence"). Beowulf and the space ship are both in free fall, dropping towards the neutron star, so he expects to sense no motion relative to the ship, except when he moves himself.
13. Read through to the end of the story, but try to figure out what the X-force is and how to avoid being killed by it, before Beowulf figures it out. What is the first effect of the X-force? Before Beowulf figures out what it is, he figures out how it works. What is his strategy for survival? A mathematical/physical explanation of what is happening throughout the story with regards to tides is given below.
14. Consider how Beowulf dealt with the tides even before he knew what they were. How does this strategy compare with the scientific method? Note in particular that Beowulf always tried to find the rules that the X-force followed and that once he figures out the rules, the ultimate source of the X-force is almost irrelevant.
15. Do you think it likely that a species as advanced as the puppeteers would not know about tides, even if their world had no moon? In a later story, collected in the book Crashlander, Beowulf comes up with a reason for the puppeteers to pretend not to know about tides. This is known as "retconning".

Tides

As Beowulf said, when an object is close enough to a strong gravity source, individual parts of the object feel different forces, and would end up in significantly different orbits, but for the forces holding the object together. There’s not quite enough information about the orbit that Beowulf and his ship are in to calculate the maximum tidal force trying to pull him apart, but we can do something nearly as good— we can figure out the tidal force if the ship was in a circular orbit. First I’ll give a conceptual explanation (with a little math), and then I’ll work through the math in more detail and show how the tidal force fits in the plot.

For a circular orbit, the vis-viva equation works out to , where v is the velocity of the spaceship, G is the gravitational constant, M is the mass of the neutron star, and R is distance from the center of the star to the spaceship. The equation means that the closer the ship gets to the star, the faster it is goes. The illustration below and on the left shows the spaceship in its orbit around the BVS-1 (obviously the ship and star are much exaggerated in size).

Consider the outer part of the ship. It's moving at the same velocity as the center of the ship, which is faster than it would be going if it were independent of the rest of the ship (because it's further from the star than the center is). The extra velocity leads to a force pulling the outer part of the ship further outward (towards the distance from the star appropriate for its velocity). Meanwhile the inner part of the ship is moving too slowly for its distance from BVS-1; it feels a force pulling it inward towards its proper orbit nearer the star. Both forces tend to orient the ship so that it’s pointing towards the star (as in the figure on the right). When Beowulf complains that the ship keeps turning toward the star, this is what’s happening, and the same thing is happening to Beowulf— he's constantly pulled away from the center of the ship towards one end or the other.

How big does the force get? To figure out that, consider the centrifugal acceleration produced just by rotating the ship around in a circle (imagine the ship is on a string) very fast. The centrifugal acceleration is , where R is the distance from the center of the star to the center of the ship, and r is the distance from the center of the ship to whatever point in the ship we care about. We already have an equation for v; when we substitute that in, we get a centrifugal acceleration of . This acceleration is always outward from the star. Now we add the acceleration of gravity, which is always inward; it's . Obviously at the center of the ship the total acceleration felt is zero, but everywhere else in the ship the force is  outward from the center of the ship. What's the magnitude of the force? The mass of BVS-1 is approximately 1.3 times the mass of the Sun, which has a mass of 2 x 10³⁰ kg. The gravitational constant is . The closest to the center of BVS-1 that Beowulf originally plans to get is 6.5 miles or about 10,000 meters, and Beowulf is about 2.1 meters tall (really!), while the ship is about 90 meters long. Putting all this information together, the tidal force at the ends of the ship is 700 million times stronger than Earth's gravity and Beowulf's feet would be feeling a force about 16 million times stronger than earth's even when Beowulf was at the center of the ship (unless he’s curled up into a ball, which he probably should be!). Among Beowulf's adjustments to the autopilot must have been changes to his closest approach. If closest approach had been 100 kilometers, the force on Beowulf's feet reduces to a mere 18 thousand times Earth’s gravity, and if it were 500 kilometers, it's down to 150 gees (unless I’m doing the calculation wrong, or the fact that Beowulf is in a hyperbolic orbit, not a circular one, makes a big difference).

So what's happening in the story?

The first effect of the tides is to make Beowulf clumsy in the ship. Then the ship starts pointing towards the star no matter how much Beowulf tries to keep it pointing in another direction, again due to the tide. Beowulf starts feeling a perceptible force next, even though the ship's accelerometer senses nothing; the accelerometer is in the exact center of the ship, where the tidal force is zero. Things keep getting worse as the tidal force gets stronger, but Beowulf learns he can use the ship's thrusters to cause an acceleration that balances the tide in the part of the ship where he is. Unfortunately, this also means he's accelerating towards BVS-1. Beowulf's strategy to get to the safest part of the ship (the center) is to have the autopilot first accelerate the ship so that the total force at his position is zero, then to gradually reduce the acceleration so that the 'zone of safety' where Beowulf can move relatively easily gradually moves towards the center of the ship. Once in the center of the ship, Beowulf must simply endure the tide's attempt to tear him apart.