---
abstract: 'December Monocerotids and November Orionids are weak but established annual meteor showers active throughout November and December. Analysis of a high quality orbits subset of the SonotaCo video meteor database shows that the distribution of orbital elements, geocentric velocity and also the orbital evolution of the meteors and potential parent body may imply a common origin for these meteors coming from the parent comet C/1917 F1 Mellish. This is also confirmed by the physical properties and activity of these shower meteors. An assumed release of meteoroids at the perihelion of the comet in the past and the sky-plane radiant distribution reveal that the December Monocerotid stream might be younger than the November Orionids. A meteoroid transversal component of ejection velocity at the perihelion must be larger than 100m/s. A few authors have also associated December Canis Minorids with the comet C/1917 F1 Mellish. However, we did not find any connection.'
date: Released 2010 Xxxxx XX
title: 'Meteor showers of comet C/1917 F1 Mellish'
---

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comets, individual: C/1917 F1 Mellish – meteors, meteoroids – celestial mechanics – catalogues

Introduction
============

The comet C/1917 F1 Mellish, formerly designated as $1917\,\,a\,\,(Mellish)$ or $Mellish\,\,1917\,\,I$, was discovered by J.E. Mellish on March 20, 1917 and was observed for 96 days [@ask23; @ask32] from many places on the Earth. In the southern hemisphere, the comet reached up to +1 magnitude. Astronomer J.F. Skjellerup noted that the brightness of the cometary head was about +3 magnitude, with the diffuse coma and narrow tail about 10$^\circ$ long on April 19, 1917 [@orch03]. The comet is a Halley-type comet, with a relatively low inclination, and has one of the smallest perihelion distances. It was observed only at one apparition. Despite the relatively long observational arc, the precision of the orbital elements is questionable. @ask32 published a slightly modified orbit of the comet and noted that the orbit is given with a period of $145\pm0.8$yr [@cham97]. The nominal orbital elements, according to JPL Solar System Dynamics database [@cham97], are presented in Table 1. Although the ascending and descending node of the nominal orbit are currently far away from the orbit of the Earth, we noted a small difference in the eccentricity (e.g. $\Delta e\sim$ $-0.002$) would change the orbit into an Earth-crossing orbit as the heliocentric distance of the ascending node would become equal to 1AU. The orbit has a notably small perihelion distance ($0.19$AU). Several authors [@por52; @has62] determined that the comet–Earth distance is close enough to observe a meteor shower and predicted the radiant positions and activity of the shower on Dec. 15 (Dec. 20 respectively) and the geocentric velocity of meteors $\sim40\,$km/s. The first few meteors associated with the comet C/1917 F1 Mellish were obtained by the Harvard Super Schmidt photographic survey [@whip54; @mcc61]. Several candidates of this meteor stream, later designated as the December Monocerotids (MON), were also detected and distinguished by radar surveys [@nil64; @sek73]. Another study connecting the December Monocerotids with the comet C/1917 F1 Mellish was made by @drum81 [@olson87]. Surprisingly, the radar data published by @nil64 and @sek73 revealed that the meteors having similar radiant positions, activity and geocentric velocities appear to have 10$^\circ$ lower inclinations. @kres74 noted that December Monocerotids seem to have 2 components. The author also speculates that the stream may have a common origin with the Geminid meteor stream. Moreover, Harvard radio data revealed a possible meteor stream with low inclined orbits but almost the same orbital elements as the December Monocerotids, active between November 27 - December 7 [@nil64; @sek73]. The possible genetic connection between the comet and the December Monocerotids was studied by @fox85.

Various photographic searches confirmed the existence of a weak stream at $RA=90.6$$^\circ$, $DEC=15.7$$^\circ$ on November 27, with $v_{g}=43.7$km/s [@lind71]. The stream was named as $\xi$-Orionids (Xi-Orionids, $\omega-$Orionids), currently recognized as established meteor shower November Orionids (NOO) within the IAU Meteor Data Center (IAU MDC) catalogue [@oh89] and later by @lind99. Moreover, other photographic December Monocerotids were published [@oh89] and complex analysis of December Monocerotids and $\xi$-Orionids done by @lind90. Even some historical records of fireballs might confirm that December Monocerotids were active in past centuries [@fox85; @has99].

In [-@hind69], @hind69 published his telescopic meteor observation from Dec. 11, 1964 and assigned 5 meteors to the new stream called 11 Canis Minorids. @hind69 computed that these meteors have parabolic orbits and much higher inclinations (over 100$^\circ$). A year later, the author suggested a connection between the shower and comet C/1917 F1 Mellish [@hind70] and determined the activity during December 9-14. @kres74 revealed that 9 meteors that create the second component of the December Monocerotids might be 11 Canis Minorids activity within December 4-15. Their inclination was determined as $i=29.1$$^\circ$ and the perihelion distance as $q=0.092$, which is closer to the Sun compared to the nominal orbit of the comet C/1917 F1 Mellish. The radiants might look like an extension of the MON activity, however, the shower might be active during the MON activity. The geocentric velocity is similar $v_{g}\sim 40$km/s. The maximum activity of 11 Canis Minorids is expected at $L_{\odot}=252.4$$^\circ$ (December 3).

Now, the December Monocetorids and November Orionids are weak (few meteors per hour at maximum) but annual established meteor showers. The shower 11 Canis Minorids, (December Canis Minorid according to IAU nomenclature) is classified as a “working” shower. Despite several investigations, past publications analyzed only a small number of orbits and provided disperse data on the mean orbit, the position of radiant, the activity and precision of orbits, and did not reveal the orbital evolution of the meteoroid particles released from the parent comet, in order to explain the current state of these meteor showers. A significant number of the analyzed orbits are hyperbolic or parabolic.

This work uses recent and precise video multi-station orbits, obtained by the SonotaCo video network in Japan, which provide the highest number of relatively precise meteor orbits detected continually between the years $2007-2009$. The network operates with over 25 similar video-optical systems and uses the same software for meteor detection and orbit analysis (UFOCapture, UFOAnalyser and UFOOrbit; @sonota09). Our goal is to provide a more complex description of meteor showers related to the comet C/1917 F1 Mellish and reveal some of their obscured characteristics. The eventual objective is the investigation of the orbital evolution of meteors and the parent comet, and determination of ejection velocities near the perihelion.

![Orbits of December Monocerotids and November Orionids selected from the SonotaCo database of video orbits.](fig1-a.eps){width="8cm"}

![Orbits of December Monocerotids and November Orionids selected from the SonotaCo database of video orbits.](fig1-b.eps){width="8cm"}

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![image](fig2-a.eps){width="7.2cm"} ![image](fig2-e.eps){width="7.2cm"}

![image](fig2-i.eps){width="7.2cm"} ![image](fig2-q.eps){width="7.2cm"}

![image](fig2-vg.eps){width="7.2cm"} ![image](fig2-lonperi.eps){width="7.2cm"}

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                   element                          value
  ------------------------------------------ -------------------
                      a                         27.6473325 AU
                      e                           0.993121
                      q                          0.190186 AU
                      i                        32.6828$^\circ$
                   $\omega$                   121.3190$^\circ$
                   $\Omega$                    88.6683$^\circ$
                      M                       0.0259325$^\circ$
                  epoch (JD)                      2421334.0
   heliocentric distance of Ascending Node       0.783556 AU
   heliocentric distance of Descending Node      0.250005 AU

  : Orbital elements of the comet C/1917 F1 Mellish in equinox J2000 reference frame (JPL).[]{data-label="t1"}

December Monocerotids and November Orionids from SonotaCo database
==================================================================

The freely accessible database of the meteors detected by the SonotaCo network contains $64 540$ multi-station meteor orbits with additional parameters such as the beginning and terminal height, absolute magnitude, equatoreal and ecliptical coordinates of the radiant, the stream assignment, etc. Although the SonotaCo method uses its own shower assignment algorithm, we have demonstrated (@veres10) that its results are consistent with the widely-used Southworth-Hawkins D-criterion $D_{SH}$ (@south63) for meteor stream identification. In accordance with several restriction criteria developed in our previous work (@veres10), we selected a high quality subset of orbits for further analysis. The criteria fulfilled $111$ of $250$ December Monocerotids and $110$ of $333$ November Orionids detected in the years 2007-2009.

Of 111 MON meteors, only 8 have hyperbolic orbits and among 110 NOO meteors, 14 have semimajor axes larger than 100AU or eccentricity higher than $1.0$. We also employed $D_{SH}$ to distinguish possible rogue sporadic meteors among MON and NOO assigned to the showers by SonotaCo. In comparison with the nominal orbit of the comet C/1917 F1 Mellish, all MON and NOO meteors fall within $D_{SH}<0.4$. Even within stricter $D_{SH}<0.15$, 105 MON and 97 NOO are found (according to SonotaCo shower assignment). Independently, we selected the MON and NOO shower members by using the iteration procedure according to @por94. In the iteration for the $D_{SH}$=0.15, 105 MON and 97 NOO were identified. This result is almost identical to SonotaCo assignment of both shower members. The showers appear very narrow in the orbital element space. The mean orbits are presented in Table 2, in comparison with the mean orbits by other authors. Each orbital element was calculated as the median, with given standard deviation. The photometric mass was computed for each meteor according to @bet99 and its mean value for the showers is mentioned in Table 2. The orbits of the meteor showers are given in Figure 1. Figure 2 depicts selected orbital elements of both meteor showers. Figure 3 shows the $q-i$ phase space of individual meteors and nominal orbit of the comet C/1917 F1 Mellish.

The semimajor axes of both shower meteors seem to be much smaller than the nominal semimajor axis of the comet or even the range of semimajor axes derived from the 5000yr orbital evolution of cometary clones (the orbital evolution is described in chapter 3). The eccentricity, the perihelion distance and the inclination of MON are very close to the cometary orbit: the NOO meteors exhibit slightly lower but still high eccentricities, notably lower inclinations and lower perihelion distances. Generally, the orbits of MON and NOO are very similar. In $e$ and $q$ the values are the same within the standard deviation: a notable difference is seen only in the inclination. The gap between the MON and NOO is also visible in Figure 1. The $q-i$ phase space and the dispersion of orbits from the mean orbit of each shower imply that the NOO exhibit wider dispersion. The cometary orbit is located within MON elements and, therefore, the NOO meteoroids seem to be older than MON. The inclination exhibits interesting behavior. The nominal orbit of the parent comet lies within the MON orbits, while the NOO orbits are less inclined and are apparently well separated from the MON orbits. There seems to be no overlapping in the inclination between the two clumps representing the MON and NOO in Figure 2.

   elements     a       e        q        i     $\omega$   $\Omega$   $v_{g}$\[km/s\]   mass\[g\]      activity       No     author
  ---------- ------- -------- -------- ------- ---------- ---------- ----------------- ----------- ----------------- ----- -----------
   **MON**    8.86    0.979    0.186    34.7     129.6       77.9          41.2            0.6      Nov 26 - Dec 21   111   this work
    s.dev             0.018    0.029     3.9      4.3        5.4            1.7                                            
              19.88   0.991    0.188    34.9     128.9       80.1          41.6                                       15      OH89
    s.dev     7.49    0.026    0.012     3.1      2.1        2.2            1.8                                            
              20.79   0.990    0.187    34.9     128.9       80.4          41.82                    Nov 27 - Dec 17   12     LIND90
   **NOO**    11.36   0.989    0.125    23.51    139.3       69.3          42.0            0.4      Nov 16 - Dec 16   110   this work
    s.dev             0.019    0.033    4.47      5.8        5.9            2.1                                            
              12.86   0.9915   0.1093   24.7     140.4       67.2          42.6                     Nov 16 - Dec 7    38     LIND99
              12.7             0.088    26.9     145.8       60.0          43.3                     Nov 16 - Nov 29   16      JEN06

![December Monocerotids, November Orionids and the comet C/1917 F1 Mellish in the phase space of perihelion distance and inclination.[]{data-label="F2"}](fig3.eps){width="8.0cm"}

As seen in Table 2 and Figures 1-3, the orbital distribution of the December Monocerotids and November Orionids have common features. There is good agreement in the geocentric velocity and minimal difference in the angular elements and eccentricity. The perihelion distance of the November Orionids is generally lower. It is worth pointing out that the perihelion distance of the MON and NOO showers is one of the lowest observed. Only a few meteor showers, among them the prominent Geminids, have such close perihelion distances. The dispersion of the MON and NOO orbital elements is relatively low, which gives the chance for good definition and differentiation of these showers.

The cumulative absolute magnitude distribution in Figure 4 shows that the population index of both showers is almost identical. However, NOO contains smaller particles, according to Figure 4. This finding is consistent with the radar data, where NOO are more significant than MON (@nil64, @sek73).

We determined the maximum activity of the MON for the longitude of the Sun $L_{\odot}=259.5$$^\circ$ (December 11) with the duration of the shower from November 26 to December 21. The maximum of MON occurs one day earlier in the SonotaCo data than in the IAU MDC catalogue. The radiant position during the maximum activity was determined as $RA=98.8$$^\circ$, $DEC=8.6$$^\circ$ and the daily motion is given by the following equations in the equatoreal and ecliptical coordinates:

$$\begin{array}{l}
 \displaystyle RA=(101.4\pm0.1)\,^\circ + (0.65\pm0.01)~(L_{\odot}-259.5\,^\circ)\\
 \displaystyle DC=(~8.0\pm0.1)\,^\circ ~~ - (0.14\pm0.02)~(L_{\odot}-259.5\,^\circ)\\
\end{array}
\label{eq:xdef}$$

$$\begin{array}{l}
 \displaystyle \lambda=(101.7\pm0.1)~+(0.67\pm0.01)~(L_{\odot}-259.5\,^\circ)\\
 \displaystyle \beta=(-14.9\pm0.1)-(0.09\pm0.01)~(L_{\odot}-259.5\,^\circ),\\
\end{array}
\label{eq:xdef}$$

where 259.5$^\circ$ represents the solar longitude of the December Monocerotid’s maximum, derived from the SonotaCo data (eq.2000.0).

According to SonotaCo data, the maximum activity of the NOO occurs on $L_{\odot}=249.5$$^\circ$ (December 1) and it is active from November 16 until December 16. The maximum occurrs 4 days after the maximum predicted by the IAU MDC catalogue ($L_{\odot}=245.0$$^\circ$). The motion of the radiant is given by equations (3) and (4):

$$\begin{array}{l}
\displaystyle RA=(92.6\pm0.2)\,^\circ + (0.62\pm0.03)~(L_{\odot}-249.5\,^\circ)\\
 \displaystyle DC=(15.3\pm0.1)\,^\circ - (0.06\pm0.02)~(L_{\odot}-249.5\,^\circ)\\
\end{array}
\label{eq:xdef}$$

$$\begin{array}{l}
 \displaystyle \lambda=(92.5\pm0.1)\,^\circ ~+ (0.60\pm0.02)~(L_{\odot}-249.5\,^\circ)\\
 \displaystyle \beta=(-8.1\pm0.1)\,^\circ - (0.06\pm0.02)~(L_{\odot}-249.5\,^\circ).\\
\end{array}
\label{eq:xdef}$$

The sky-plane positions of the radiants in the equatoreal and ecliptical grid are depicted in Figure 5. The radiant positions calculated using the nominal orbit of the comet C/1917 F1 Mellish and computed by several methods by DOSMETH software (@nes98) are shown as well.

![Cumulative distribution of absolute magnitudes of December Monocerotids and November Orionids.[]{data-label="F4"}](fig4.eps){width="8.0cm"}

![Equatoreal and ecliptical radiants (Eq. 2000.0) of December Monocerotids and November Orionids. Upper and lower right graphs show the radiants corrected for daily motion and reduced to the solar longitude of the activity maximum. Theoretical geocentric radiants derived by DOSMETH from the nominal orbit of C/1917 F1 Mellish are displayed as well (open circles).[]{data-label="F5"}](fig5.eps){width="8.0cm"}

A possible common origin of both meteor showers can also be inferred from Figure 6 depicting the heliocentric distance of the ascending and descending nodes of the MON and NOO as a function of solar longitude. As expected, the ascending node lies very close to the value of 1AU but the descending node gradually rises with the solar longitude and both meteor showers overlap without any gap or visible difference in the descending node.

Other common properties might be derived from the beginning and terminal heights of individual meteors. Figure 7 shows clearly that heights of the MON and NOO are practically identical. The geocentric velocity and entry geometry is almost the same for both meteor showers; therefore, the beginning and terminal height would mostly depend on the physical properties of meteoroids, such as the mass, the bulk density and internal structure. The heights are given in Table 3 and the heights as a function of photometric mass in Figure 7. In Table, 3 we also compare the heights of MON and NOO with the high quality Geminids orbits from the SonotaCo database. Geminids from the SonotaCo database have beginning and terminal heights 5km lower than other video observations made by similar techniques (@koten04). MON and NOO meteors have beginning heights 6–7km higher than Geminids, which could indicate that meteors from C/1917 F1 Mellish have lower bulk densities and are more fragile. On the other, hand Geminids with similar geocentric velocities belong to the densest and most rigid meteors observed (@ren04).

   shower   beginning height\[km\]   terminal height\[km\]
  -------- ------------------------ -----------------------
    MON         $102.6\pm2.7$            $86.1\pm4.8$
    NOO         $101.5\pm3.9$            $85.1\pm5.3$
    GEM          $95.6\pm3.3$            $80.2\pm7.0$

  : The beginning and terminal heights of the December Monocerotids and November Orionids in comparison with the Geminids using the high quality SonotaCo data.[]{data-label="t3"}

![The heliocentric distances of the ascending and descending nodes of the December Monocerotids and November Orionids as a function of the longitude of the Sun, compared with the ascending and descending nodes of the comet C/1917 F1 Mellish. Range of the theoretical radiants computed by DOSMETH for the parent comet is displayed with a heavy line. Vertical lines represent the maxima of the meteor showers.[]{data-label="F6"}](fig6.eps){width="8.0cm"}

  ------------- --------------- --------------- ------------ --------------- -------------- -------------- ------------- ----------- ----------
    a \[AU\]           e           q \[AU\]          i          $\omega$        $\Omega$       $v_{g}$      $L_{\odot}$      RA          DC
   $1.8\pm1.5$   $0.95\pm0.02$   $0.11\pm0.02$   $30.2\pm7$   $144.7\pm4.9$   $78.6\pm3.1$   $39.7\pm2.4$   254.1-261.6   $107\pm4$   $14\pm2$
  ------------- --------------- --------------- ------------ --------------- -------------- -------------- ------------- ----------- ----------

![The beginning and terminal heights of the December Monocerotids and November Orionids as a function of the photometric mass.[]{data-label="F7"}](fig7.eps){width="8.0cm"}

The database does not contain any December Canis Minorids, yet we tried to find some representatives among the high quality data set. The published mean orbit of December Canis Minorids has a very low semimajor axis, $\omega$ similar to a previously published value, and $i$ and $\Omega$ similar to MON. According to SonotaCo , the shower might be active from November 30 until December 9, with the maximum on December 4. Nevertheless, the database does not contain any meteors of this stream. Because of the little information there is about the stream, we tried to select candidates from the high quality subset of orbits. The subset was selected using the iteration method [@por94] with respect to the IAU MDC catalogue shower parameters. Only 6 meteors fulfilled our criteria (Table 4). Meteors were detected during the activity of both MON and NOO. The D-criterion of meteors was on average greater than 0.3 with respect to the assumed parent comet. It is even doubtful if the December Canis Minorids is a regular shower or if it is only an occasional shower observed when the Earth crosses a narrow filament of the meteoroid particles, or these meteors are just scattered meteors of the MON-NOO complex; or that even these meteors belong to the sporadic background.

Orbital evolution of the comet and meteoroids
=============================================

The first orbital evolution analysis of the comet C/1917 F1 Mellish 800yr to the past [@car84] revealed that its orbit evolves slowly: notably, the nodes evolve very slowly. The inclined orbit avoids giant planet encounters and there is only a little chance of substantial gravitational interaction with the terrestrial planets near the perihelion. @fox85 and @has99 studied the option that the ancient fireballs observed between December 6 and 18 apparently emanated from the same radiant. They worked out that these bolides could not be connected to the Geminid meteor stream because of its rapid orbital evolution but might belong to the MON. @fox85 confirmed the slow evolution of the ascending node in the 2400yr integration of the cometary orbit to the past. Their work also confirmed that the heliocentric distance of the MON ascending node is stable as well and is close to 1AU one thousand years to the past or to the future.

![The orbital evolution of the heliocentric distance of the ascending and descending nodes of the nominal orbit of the comet C/1917 F1 Mellish (solid line) and its clones (points). Up - clones generated within the 0.8yr orbital period error, down - clones altered in order to put ascending node close to 1AU at the present day.[]{data-label="F8"}](fig8-a.eps){width="8.0cm"}

![The orbital evolution of the heliocentric distance of the ascending and descending nodes of the nominal orbit of the comet C/1917 F1 Mellish (solid line) and its clones (points). Up - clones generated within the 0.8yr orbital period error, down - clones altered in order to put ascending node close to 1AU at the present day.[]{data-label="F8"}](fig8-b.eps){width="8.0cm"}

![image](fig9-a.eps){width="7.0cm"} ![image](fig9-q.eps){width="7.0cm"}

![image](fig9-i.eps){width="7.0cm"} ![image](fig9-lonperi.eps){width="7.0cm"}

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![image](fig10-Ma.eps){width="7.0cm"} ![image](fig10-Na.eps){width="7.0cm"}

![image](fig10-Me.eps){width="7.0cm"} ![image](fig10-Ne.eps){width="7.0cm"}

![image](fig10-Mq.eps){width="7.0cm"} ![image](fig10-Nq.eps){width="7.0cm"}

![image](fig10-Mi.eps){width="7.0cm"} ![image](fig10-Ni.eps){width="7.0cm"}

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![image](fig10-Mlonperi.eps){width="7.0cm"} ![image](fig10-Nlonperi.eps){width="7.0cm"}

![image](fig10-Masc.eps){width="7.0cm"} ![image](fig10-Nasc.eps){width="7.0cm"}

![image](fig10-Mdesc.eps){width="7.0cm"} ![image](fig10-Ndesc.eps){width="7.0cm"}

\[F11\]

As mentioned previously, the orbit of the parent comet was determined with a low precision. In our study, we set out to calculate the orbital evolution of nominal and cloned orbits of the parent comet. We created 100 clones within the 0.8yr uncertainty of the orbital period [@ask32], with fixed perihelion distance and altered semimajor axis and eccentricity accordingly. We could not modify other orbital elements because their uncertainties are unknown. Another set of 100 clones was made in order to create orbits with the heliocentric distance of ascending node close to 1AU while neither nominal orbit nor first 100 clones have the ascending node close enough to the orbit of the Earth to create an observed meteor shower. In this case, the eccentricity, the semimajor axis and the perihelion distance were altered. The beginning of the integration was set at the epoch of the perihelion passage of C/1917 F1 Mellish (JD 2421334.0, Eq. 2000.0). The multistep Adams-Bashforth-Moulton type up to 12th order numerical integrator, with variable step-width, was used. All planets were considered as perturbing bodies and the Earth and Moon were treated separately.

The integration shows that both sets of clones behave in a similar way. Figure 8 depicts the heliocentric distance of the ascending and descending node of the nominal orbit and the clones integrated 5000 years to the past. The ascending node of the nominal orbit gradually falls and retreats from the orbit of the Earth to $\sim0.4-0.6$AU from the Sun. The descending node is initially close to the Sun ($\sim0.25$AU) and rises slowly to ($\sim0.3\pm0.1$AU). Clones of the altered orbit, that start with the ascending node at the orbit of the Earth, behave the same way but remain within 0.05AU of the Earth’s orbit about 2000yr to the past.

The evolution of the orbital elements of the comet and its clones is depicted in Figure 9. The most probable value (1$\sigma$) of the semimajor axes of cloned orbits is in the range of $a\subset(25;30)$AU, while the nominal semimajor axis rises up to 40AU 2500 BC. The inclination of both clones and the nominal orbit falls from initial 32$^\circ$ down to $i\subset(26;30)$$^\circ$. Even at 3000yr BC, the inclination is not low enough to explain the low inclination of the NOO ($i\sim23.5$). The perihelion distance remains in the small heliocentric distances ($q\subset(0.14;0.23)$AU) and the summation of angular elements (longitude of perihelion – $\pi$) rises gradually from 210$^\circ$ to $\pi\subset(212;218)^\circ$ after 5000yr integration to the past. Clones derived from the uncertain orbital period did not encounter the Earth but had close flybies within the Hill sphere of Venus ($2\%$) and Mercury ($0.5\%$). This gives a non-zero chance that comet C/1917 F1 Mellish might encounter Venus or Mercury. In fact, this could cause a sudden change in its inclination at least within 5000yr in the past.

We also studied the orbital evolution of the MON and NOO meteors from the SonotaCo database. For a chosen subset of high quality orbits (non-hyperbolic, $a<100$AU), the integration uses a beta parameter representing the solar radiation pressure (@kla04) for each particle ($\beta=2\cdot10^{-5}$) derived from an assumed low bulk density ($\varrho=750\,kg/m^3$) and the typical photometric mass of observed meteors (0.5g) and starts for the epoch and the orbital elements valid for the moment of the meteor observation. The numerical integration computed the orbital evolution for 5000yr to the past (Figure 10 and Figure 11).

Unlike @fox85, perturbed orbits of the MON and NOO reduced their heliocentric distance of the ascending nodes as time goes to the past. It seems that it takes only two or three hundreds years until the ascending node reaches the nominal orbit of the parent comet. On the contrary, the semimajor axes of both the MON and NOO are generally constant over 5000yr, which might be due to low perturbations of giant planets and higher inclinations. Even with the beta parameter, the semimajor axes remain far away from the nominal or even cloned orbits of the parent comet. Meteoroids could be injected to these orbits directly after the ejection from the cometary core. The inclination of the MON is quite consistent with the current orbital inclination of the comet C/1917 F1 Mellish. The orbital evolution in inclination implies that MON were released recently, generally hundreds, or at most, 3000 years in the past. On the contrary, the NOO meteoroids have lower inclinations in the present day. The orbital evolution reveals that NOO meteoroids could have departed from the comet mostly 4000 years prior and almost all low inclined NOO could be explained by an orbital evolution within the last 5000 years – most of the NOO inclinations intersected the comet evolution path of its inclination. The longitudes of the perihelia of the MON attain the same values as the nominal cometary orbit in the recent centuries and then disperse. On the other hand, the longitudes of the perihelia of the NOO remain much longer along the evolved nominal orbit of the comet and disperse slowly after thousands of years, which could support the younger age of MON as well. A similar feature is visible for the perihelion distance of both showers. Currently the perihelion distance of MON fits well with the current orbit of the comet but gets more dispersed around 500 B.C. The perihelion distance of NOO is slightly different during the last 2000 years but generally intercepts the perihelion distance of the comet earlier than 1000 B.C. The eccentricity of MON is dispersed much more in the past than in the case of NOO. The heliocentric distance of the ascending node of MON lies close to the current ascending node of the comet but disperses fast in the past. This distance is currently lower for NOO but could be explained by the orbital evolution (Figure 11). These implications of the orbital evolution suggest that the NOO shower is older than the MON shower and both streams may originate from the same parent comet.

Resulting from the nodal distances of the comet and the relatively fast evolution of the ascending nodes of the showers (centuries), there is a possibility that we observe the outer edge of a widely evolved complex stream. The streams (MON and NOO) might be observed as two streams as a result of a geometric selection effect. Meteoroids with inclinations between the MON and NOO might have nodes on non-Earth crossing orbits.

Ejection of meteoroid particles from the parent comet
=====================================================

The relatively large heliocentric distance of the ascending node of the parent comet and the much lower and stable semimajor axes of the meteors indicate that these particles were injected into these orbits immediately after ejection from the comet, while the comet might not have been on the same orbit at that time. The derivation of the ejection velocity depends on the model used. If we assume a spherical cometary nucleus with an albedo of $0.04$, active surface $0.15\%$ (@ma02, bulk density $750\,kg/m^3$, a radius of the nucleus 3.1km (@jen06), ejection at the perihelion $q\sim0.19$AU; and if the meteoroids are escaping only from the Sun-facing hemisphere with the Gaussian distribution of velocities with the center on the subsolar point, the maximum ejection velocity might range from 5m/s [@imp01] to 112m/s [@crifo; @ma02]. The escape velocity of the meteoroid particle changes its orbital elements so that we may calculate according to @pec97.

On the other hand, if we know the orbital elements of the comet (before the ejection of the meteoroid) and the meteoroid after the ejection (assuming that the observed meteoroid escaped the comet recently and did not undergo rapid orbital changes due to gravitational and non-gravitational perturbations), we may directly derive the ejection velocities from equations by @pec97 as a low estimate. The ejection velocity affects, at most, the semimajor axis. In the perihelion, the semimajor axis change is ruled by the transversal component of the velocity vector $\Delta v_{t}$. The range of ejection velocities derived according to mean, the peak and minimum-maximum values of the semimajor axis (Figure 2) of each meteor shower, in comparison with the range of semimajor axes of the cometary clones, integrated 2000yr to the past is presented in Table 5. The mean and peak values of the transversal ejection velocity components are in good agreement with the ejection model by @ma02. While the eccentricity, the inclination and angular elements of the MON lie within the cometary clones’ range, the derivation of the radial and normal components of the velocity vector are ambiguous, following equations by @pec97. On the other hand, a difference in the inclination, the eccentricity and angular elements of the NOO could not be explained by the direct ejection of the particles into current orbits, but only by the following orbital evolution.

   shower   method   a \[AU\]   $-\Delta\,v_{t}$ \[m/s\]
  -------- -------- ---------- --------------------------
    MON      mean      8.8             $104\pm8$
             peak      6.5             $117\pm8$
            range      3-17             $50-145$
    NOO      mean     11.36             $90\pm8$
             peak      6.5             $117\pm8$
            range      2-17             $50-150$

  : The transversal component of the meteoroid ejection velocity derived from the the difference of the semimajor axis of meteor showers and the parent comet. The range of cometary semimajor axis lies within $a\subset(26;29)$AU.[]{data-label="t4"}

Conclusions
===========

We demonstrated that the December Monocerotids and November Orionids obtained from the SonotaCo database of 3 year observations (2007-2009) have most likely a common origin and come from the comet C/1917 F1 Mellish. The common origin is supported by their similar orbital characteristics, the activity, physical properties assumed from the beginning, and the terminal heights of the meteors, the descending nodes of both showers as a function of the solar longitude, and the narrow Southworth-Hawkins D-criterion for most December Monocerotids and November Orionids with respect to the parent comet ($D_{SH}<0.15$). Direct modeling of the stream was not an option, while the orbit uncertainty of the comet avoids the selection of reliable and real starting point of the numerical integration from the past to the current date. Therefore, we studied the orbital evolution of the nominal orbit of the comet, cometary clones within the known orbital uncertainties, and the orbital evolution of precise meteor orbits. The dispersion of the orbital elements, the radiants and nominal orbit of the parent comet, currently beyond the orbital elements, suggest that the November Orionids is an older stream than December Monocerotids. The orbital evolution of both streams, the nominal orbit of the comet and its clones imply that the orbital evolution is causing November Orionids to have 10$^\circ$ lower inclinations than December Monocerotids. There is a non-zero chance of a close encounter of the comet with Venus or Mercury which could cause a sudden change in the inclination of the parent comet. Furthermore, a close encounter with a planet might cause the tidal breakup of the comet and create a significant release of matter. The scenario of the cometary core disintegration might also be supported by the extremely low perihelion distance of the parent comet and both meteor showers.

Another option is a gradual shift in the inclination, demonstrated in the simulation. But a change in the inclination of more than $10\circ$ of the parent comet would be solved only through a longer orbital evolution. This option is also obscured while we do not observe any orbits between relatively well defined clumps of the December Monocerotids and November Orionids in the $q-i$ phase space and radiant sky-plane distributions. Eventually there is a wide and massive stream of the meteoroids but only some of them have ascending nodes close to the Earth’s orbit; and due to selectional effects, we may observe two distinguished streams and only the distant edge of the stream. The nodal distance of the comet is currently more than 0.2AU from the Earth’s orbit and it retreated in the past increasingly, as well as the ascending nodes of the observed meteors. The observed shower meteors might have left the cometary nucleus a few centuries ago but, due to the stable orbit of the comet, both streams might be replenished regularly and weak shower activity might be observed each year. The semimajor axes of both meteor streams are much lower than the nominal orbit of the comet or its clones’ evolution 5000yr to the past. Almost no change of the semimajor axes of meteoroids within the orbital evolution suggests that these particles were injected directly into these orbits right after ejection from the cometary nucleus. We determined that transversal component of the ejection velocity would be about $100 m/s$ if the ejection occurred at the perihelion. Further precise orbits and physical data of the December Monocerotids and November Orionids are needed for additional research.

The key question is the accuracy of the C/1917 F1 Mellish orbit. A new measurements of the photographic plates of the comet might reveal a more precise orbit and bring new light onto the orbital evolution of the comet and its meteors. Our work did not confirm any December Canis Minorids meteors in the SonotaCo database; however, 6 candidates were selected. Their connection to the comet C/1917 F1 Mellish is uncertain.

Acknowledgments {#acknowledgments .unnumbered}
===============

This work was supported by Slovak Grant Agency VEGA, No. 1/0636/09 and by a grant of Comenius Uviversity, No. UK/245/2010.

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