AActa Prima Aprilia • April 2015 • Vol. I
Beyond the New Horizon: The Futureof Pluto M ichael B. L und
Vanderbilt [email protected]
Abstract
Since its discovery in 1930, Pluto’s mass has been a value that has repeatedly been calculated. Additionally,the search for Planet X prior to Pluto’s discovery results in mass calculations that date back severaldecades earlier. Over its observed history, the mass of Pluto has consistently decreased. We reassess earlierpredictions of Pluto’s fate, and rule out the hypothesis that Pluto’s mass has been constant over the lastcentury. We are able to fit linear and quadratic equations to Pluto’s mass as a function of both time anddistance. The observations that will be made by New Horizons will help to determine if we can expectPluto to continue to shrink until it has negative mass, or if it will begin to increase in mass again.
I. I ntroduction T h e search for planets in the outer solarsystem has been an active endeavor inastronomy, especially after the discoveryof the first planet to be added to the classicalplanets with the discovery of Uranus in 1781by William Hershel. The discovery of Neptunein 1851 by Johann Gottfried Galle and Hein-rich Louis d’Arrest in 1846, using predictionsmade by Urbain Le Verrier, demonstrated theability to discover objects in the solar systemindirectly by locating their effect on alreadyknown planets. The most controversial object,both in the scientific and public realm, wouldbe the discovery of Pluto in 1930. Prior to thistime, the existance of an additional planet hadbeen suggested by multiple authors and thesearch for Planet X was well under way, in-cluding predictions of its mass (Pickering andPickering, 1909; Lowell and Observatory, 1915).This provides an over 80 year baseline of ob-servations post-discovery, and even more if theinferred masses are included in this analysis.Over this time, the mass calculated for Plutohas changed from estimates on the order of themass of the earth around the time of discoveryto the current mass estimates that are only afraction of the earth’s mass. Here, we consider that this data may still be useful and worthyof consideration. The idea that Pluto could beshrinking is not new (Disney, 1935; Dessler andRussell, 1980), and we revisit that concept tosee how more recent observations help us con-strain Pluto’s evolution over the last centuryand what this can tell us about the origins ofPluto. II. D ata
With a long history of mass calculations, welook at 75 years of published masses for Pluto(1931 to 2006), as well as including two masscalculations for Planet X. We supplement thisdata with heliocentric distance calculations forPluto that have been gathered with the Stellar-ium software . Our full data set is in Table 1. III. A nalysis
We consider two simple possible functions inthis work; the first is that the mass is a functionof time, and the second is that the mass is afunction of heliocentric distance. The conven-tional model we include is that the mass ofPluto over the last century has actually been a Available from Sourced from Weintraub (2014) a r X i v : . [ phy s i c s . pop - ph ] A p r cta Prima Aprilia • April 2015 • Vol. I
Table 1:
Pluto Masses and Distances
Year Distance (AU) Mass ( M earth ) Citation1909 45.6 2 Pickering and Pickering (1909)1915 44.52 6.67 Lowell and Observatory (1915)1931 41.09 0.94 Nicholson and Mayall (1931)1931 41.09 0.75 Pickering (1931)1942 38.38 0.91 Wylie M = [ cos π ( t − ) ] π (1)We also look at the validity of using thePlanet X values for this fit, and so we attemptto fit the data using both the data from 1909and 1915, and only the data following the offi-cial discovery of Pluto. I. Mass as a Function of Time
We conduct an analysis of the mass as a func-tion of time by attempting to fit to the databoth with and without the Planet X mass val-ues. We display these two fits in Figure 1. Witheach of these fits, we then also calculate thevalues for the χ and p values for each of thesemodels, displayed in Table 2 and Table 3.We don’t compare the function that wasproposed by Dessler and Russell (1980), astheir proposal was that Pluto would have animaginary mass after 1984, which appears tobe inconsistent with the real masses that havebeen measured in the last 20 years. However,the χ is not a value we can calculate, but we feel that further indicates that this model canbe discarded.In both cases, we find that the least likelymodel for the observed mass history of Plutois that Pluto has had a constant mass. Wefind that linear, quadratic, and power-law fitsare all robust in the Pluto-only data, howeverwhen we include the Planet X data as well,the quadratic fit may be the most likely. It isparticularly persuasive that the quadratic fitwe find when we include the Planet X massesappears to have a minimum around the samepoint where Dessler and Russell (1980) had alsopredicted that Pluto’s mass would drop belowzero. The starkest difference will be whether ornot the small increase we see in Pluto’s massfrom the early 1990s (Binzel, 1989; Null et al.,1993) to the late 1990s and early 2000s (Foustet al., 1997; Buie et al., 2006) continues into thefuture as a quadratic function would predict,or if this is an aberration in an otherwise lineartrend. II. Mass as a Function of Distance
For our analysis of mass as a function of dis-tance, we are not able to get suitable fits for thePower Law fit, and so we omit that equation.Additionally, the Dessler-Russell equation wasspecifically set to be a function of time, and so2cta Prima Aprilia • April 2015 • Vol. I
Figure 1:
Best fit lines for functions as determined by the Pluto masses on left, and Pluto and Planet X masses on theright.
Table 2:
Quality of Fits to Pluto-only Data
Model Constant Value Linear Fit Quadratic Fit Power Law Fit χ p -value 0.8290 >0.9999 0.9997 0.9868 Table 3:
Quality of Fits to Pluto & Planet X Data
Model Constant Value Linear Fit Quadratic Fit Power Law Fit χ p -value <0.0001 0.5644 0.8660 0.4900as it isn’t applicable here we exclude it as well,limiting our consideration to only the constantvalue, linear, and quadratic fits. We displaythese fits in Figure 2. With each of these fits,we then also calculate the values for the χ and p values for each of these models, displayed inTable 4 and Table 5.Again, we see that we get better fits for thelinear and quadratic equations than we get forPluto as a constant value. Beyond that, wedo see that there is a very good relation be-tween the mass and the distance, in this casestronger (although not statistically more signif-icant) than what we observed for the mass asa function of time. It is worth noting that adistance-dependent mass does provide a natu-ral limit on the mass, preventing it from becom-ing smaller than Pluto was at perihelion (and potentially prohibiting negative masses) as wellas an upper limit when Pluto is at aphelion (re-moving the possibility of a mass runaway inthe future). IV. D iscussion
The strong evidence we provide as an indica-tion that Pluto has changed mass over the lastcentury gives a very natural explanation as towhy the status of Pluto has been of such greatdebate over the last decade. It remains to beseen if we are observing Pluto at a local min-ima, in which case it may increase to planetstatus again in the future, or if it will continueto shrink until such a point as its planet statusis irrelevant or otherwise unquestioned. Thepossibility that Pluto’s mass may increase in3cta Prima Aprilia • April 2015 • Vol. I
Figure 2:
Best fit lines for functions as determined by the Pluto masses on left, and Pluto and Planet X masses on theright.
Table 4:
Quality of Fits to Pluto-only Data
Model Constant Value Linear Fit Quadratic Fit χ p -value 0.8290 >0.9999 >0.9999 Table 5:
Quality of Fits to Pluto & Planet X Data
Model Constant Value Linear Fit Quadratic Fit χ p -value <0.0001 0.7034 0.8748the future is not a result that was consideredby Dessler and Russell (1980), however the pre-dictions that could be made from a linear fitfor Pluto’s mass could give somewhat similarpredictions of the disappearance of Pluto (orthe realization of a negative mass) somewherein the near future.The physical meaning of a distance-dependant mass would need further analysis tounderstand, and so we leave that to further con-tributions from the community. This solutionis of note, however, as it will provide a mini-mum and maximum mass for Pluto that elimi-nates negative or infinite masses. We can betteraddress the question of time-dependent mass-loss, as this is not an unknown phenomenon.It has been seen in high mass planets already,such as the large mass loss that has been ob- served in WASP-43b(Czesla, S. et al., 2013).There are also measurements made for themass-loss of solar system bodies, includingPluto itself (Johnson et al., 2015) and cometsthrough multiple physical channels (Napier,2015).We can further surmise that as the masshas decreased over time, we can also imaginethat prior to the speculation of Planet X, thatPluto’s mass was already decreasing. As itwould be unrealistic to presume that Pluto hada very large mass in the mass (on the order ofNeptune) without causing Neptune’s orbit toexhibit something distinctly non-circular, thiswould imply that Pluto has not been in its cur-rent orbit until relatively recently. This wouldbe consistent with the idea that Pluto’s orbit isstill not stable, and so is undergoing some scale4cta Prima Aprilia • April 2015 • Vol. Iof evolution (Sussman and Wisdom, 1988). Fur-ther constraining this function will allow us toinfer more about the dynamic history of Pluto.
V. S ummary
While we are in broad agreement with Desslerand Russell (1980) that Pluto has decreasedin mass over the last century, we don’t findtheir proposal for the function that best repre-sents this mass loss. Our best indications arethat the mass loss should be represented bya linear or quadratic fit. New Horizons willhelp provide great insight to this, as a linear fitwould indicate that Pluto would have reachedzero mass somewhere after 1994, and would becontinuing to shrink. The quadratic fit for thenear future, when we exclude Planet X, wouldsimilarly be negative for the near future. TheNew Horizons observations that will be madeby Pluto in the next year will be very useful inconstraining which of these functional formsis most accurate, and may provide further evi-dence that Pluto’s mass is distance-dependentrather than time-dependent. R eferences Binzel, R. P. (1989). Pluto-Charon mutualevents.
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