Table of Links
Abstract and 1 Introduction
2. Summary of the Story
3. Observables
4. Possible Scenarios and Consequences
The other Suns
Simulation
Conclusion and References
SIMULATION
We have written a program computer program that simulates a stellar system. We have not attempted to match the scale of the system, this is only a demonstration. The user inputs the initial positions and velocities of the stars, as well as a precision parameter which determines how often forces and velocities of the individual bodies are updated and recalculated. The simulation is based on Newton’s laws of motion:
where ‘r’ and ‘r0’ are the instantaneous and initial positions, ‘v’ and ‘v0’ are the instantaneous and initial velocities, ‘a’ is the instantaneous acceleration and ‘dt’[1] is the time step in seconds. The smaller the value of dt, the better the simulation but the longer the simulation length.
KALGASH 2 DISTANCE
We will suppose that Kalgash 2 is a gaseous moon slightly less dense than Saturn (0.687g/cm3). Since it has the same mass as the earth, it will have a diameter of 26,540 km. It also subtends an angle of 26”. This means that Kalgash 2 is at a distance of 3.04 million kilometres. However, both the planet and the moon are light compared to the stars and we can ignore them in the simulation.
As discussed above, the stellar system of Asimov’s Nightfall has 6 stars but with two sets of binaries (Trey-Patru and Tano-Sitha), which we treat as single point masses. Although different stable configurations may be possible, we have worked out one possible configuration[2] which we found to be stable for a few hundred years. We further arrange these stars into three sets of 2-star systems. First, Onos and Dovim (circling each other) as one independent system, then Tano-Sitha and Onos-Dovim (Figure 5), where the forces act on the centre of masses of the two binaries. And finally, Trey-Patru and Onos-Dovim-Tano-Sitha.
The graph is similar to a velocity graph of a binary star (in this case Onos-Dovim is the binary, since we have treated TS as a single star). The amplitudes of the oscillation slowly increase, but this is within the limits of the precision settings of our program. Also the amplitudes increase over a period of several hundred years: the people of Kalgash need have no fear of being swallowed by a sun!
Next, we add Trey-Patru. Now we suspect that the addition of Trey-Patru will quickly rip the system. To counter this, we make sure that Trey-Patru is not close to Onos-Dovim for large periods of time. This is done by giving TP an opposite angular velocity as the following image shows:
The addition of TP increases the tidal forces on Onos-Dovim. However, for the duration of the story (about 2 years) these effects will not be perceptible. (Though subsequent generations of the Kalgash people will face dangerous scenarios.)
The Kalgash people measured the universe to be 110 light minutes across. Perhaps, they made this measurement at a very specific time in the evolution of the system.
Luckily for them, the hottest binary star maintains a safe distance from them. The large amplitudes mean that at some later time, the “stars” might be become visible.
CONCLUSION
We have explored several aspects of Asimov’s novel. We have found that the suns, especially Dovim are bright enough to blot out the stars. Kalgash 2 can eclipse Dovim for a period of 9 hours.
We also tested one possible star configuration and after running some simulations, we found that the system is possible for short periods of time. Several other configurations might exist and have to be explored more fully.
REFERENCES
Asimov, I., 1941. Nightfall. [Online] Available at: https://www.uni.edu/morgans/astro/course/nightfall. pdf [Accessed April 2014].
Asimov, I. & Silverberg, R., 1991. Nightfall. New York, NY: Bantam Books.
Jens Buus, J. M., n.d. Latitude Dependence of the Maximum Duration of a total Solar Eclipse. [Online] Available at: www.eclipsechasers.com/papers/Maximum_duration.pdf [Accessed 11 July 2014].
Meeus, J., 2003. The Maximum Possible Duration of a Total Solar Eclipse. Journal of the British Astronomical Association, 113(6), pp. 343-348.
Orosz, J. A. et al., 2012. Sciencemag. [Online] Available at: https://www.sciencemag.org/content/337/6101/1511. short [Accessed May 2014].
Roatsch, T., Jaumann, R. & Thomas, P., 2009. Wikipedia – Cartographic Mapping of the Icy Satellites Using ISS and VIMS Data. [Online]
Available at: http://en.wikipedia.org/wiki/Tethys_%28moon%29 [Accessed 11 July 2014].
Sagan, C., 1992. Nature. [Online] Available at: http://www.nature.com/nature/journal/v357/n6374/ pdf/357113a0.pdf [Accessed May 2014].
Wikipedia, 2014. Apparent Magnitude. [Online] Available at: http://en.wikipedia.org/wiki/Apparent_magnitude [Accessed July 2014].
Williams, D. D. R., 2004. Wikipedia. [Online] Available at: http://en.wikipedia.org/wiki/Apparent_magnitude [Accessed May 2014].
Williams, D. D. R., 2014. Nasa. [Online] Available at: http://nssdc.gsfc.nasa.gov/planetary/factsheet/index.h tml [Accessed 11 July 2014].
Williams, D. R., 2006. Wikipedia. [Online] Available at: http://en.wikipedia.org/wiki/Saturn [Accessed 11 July 2014].
[1] The value of dt is critical in the simulations. We have used 1000sec. This means that the errors will become significant over large periods of time. The simulations here just give an approximate idea of the system stability. [2] In this configuration we have changed some distances to allow a stable configuration.
