Oort Cloud Comet Encounters with Mars, Earth, Venus and Mercury

46th Lunar and Planetary Science Conference (2015) 2467.pdf

OORT CLOUD COMET ENCOUNTERS WITH MARS, EARTH, VENUS AND MERCURY. Renu Mal- hotra (Lunar and Planetary Laboratory, The University of Arizona, Tucson, AZ 85721; [email protected])

Introduction: The close encounter of Mars with an Oort Cloud comet Siding Spring C/2013 A1 on Oc- tober 19, 2014 was of great interest for its transient and

long term effects on the planet’s atmosphere. What is Mars the frequency of such events in the inner solar system? 0.03 A rough estimate for the mean time between encoun- Earth ters of parabolic comets with terrestrial planets – Mars, Venus Earth, Venus and Mercury – is obtained here. 0.02 Parabolic comet encounter frequency: Oort Mercury Cloud comets (also known as ‘long period comets’ or

‘new comets’) in the inner solar system have a nearly 0.01 isotropic distribution of orbital planes, nearly parabolic orbits, and an approximately uniform distribution of perihelion distances; the rate of new parabolic comets (of absolute magnitude brighter than about 10) entering 0 the Earth’s orbit is approximately 3 per 4 years [1]. 0 50 100 encounter velocity (km/s) From these observations, we can estimate that the rate of such comets crossing Mars’ orbit is approximately 1.14 per year. The mean residence time of such para- Figure 1. Distribution of encounter velocities of parabolic comets within Mars' orbit is about 0.34 years. bolic comets with Mars (red curve), with Earth (green This yields the steady state number of parabolic com- curve), with Venus (magenta) and with Mercury (blue ets within 1.52 AU of the Sun of about 0.39. There- curve). We approximate the orbits of the planets as fore, the steady-state number density of parabolic circular orbits. comets in Mars crossing orbits is about 0.026 per cubic AU; we will denote this by �. The relative velocity during a Mars' encounter of such parabolic comets is approximately in the range of 20-60 km s-1 (see Figure 1000

1). We can estimate the mean time between encounters 100 by imagining that such comets appear randomly in the 10 space near Mars, with a mean speed V = 40 km s-1 relative to Mars. Then the mean time between encounters 1 2 at flyby distances up to d is given by T♂(d) ≈ 1/(�d V�) 0.1 6 5 -2 ≈ 3.3x10 yr (d/10 km) (see Figure 2). For Siding 0.01 Spring C/2013’s flyby distance (d ≈ 140,000 km), the mean time of encounters is ~1.7 myr. 0.001 0.0001 For Earth, Venus and Mercury, a similar calcula- tion finds that the mean time for encounters with parabolic comets is 2.1 myr x (d/105 km)-2, 1.5 myr x (d/105 0.1 1 10 100 1000 -2 5 -2 km) , 0.8 myr (d/10 km) , respectively (see Figure d / 100,000 km 2).

Figure 2. The mean time of encounters of parabolic Comet tail lengths typically exceed 106 km. Para- comets as a function of encounter distance with Mars bolic comet encounters with the terrestrial planets, (red curve), with Earth (green curve), with Venus (ma- with flyby distances of less than 106 km, occur with a genta) and with Mercury (blue curve). The Mars en- frequency of about one per ten thousand years. counter distance of Siding Spring C/2013 A1 is indi- cated by the vertical dotted line. 46th Lunar and Planetary Science Conference (2015) 2467.pdf

Encounters with periodic, ‘short period’ comets (including the so-called Jupiter-family comets and Hal- ley family comets) require different considerations than presented above: periodic comets are rather more predictable than the random, unpredictable encounters with long period comets.

References: [1] Fernandez, J., Comets - Nature, Dynamics, Origin and their Cosmological Relevance, Astrophysics Space Science Library, volume 328, Springer, Dordrecht (2005).