Origin of the Martian Moons Joe Burns Cornell University

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Presentation transcript:

Origin of the Martian Moons Joe Burns Cornell University October 26, 2015 I thank the organizers (Dan Britt, Jim Head, Carle Pieters, Ken Ramsley). for their invitation. I had hoped to visit Providence and Brown (always enjoyed) but not in new world. Good to see Phobos and Deimos finally getting their due. My story: First real extraterrestrial bodies (how bizarre? What a preview for how surprising satellites have been seen to be via planetary exploration. Wrote dynamical review before Mariner 9, in orbit on Nov 1971 Had written paper for Mars in early 90s. Reviewed by Stan Peale (who died six months ago) and Dan Britt/Scott Murchie. Different opinions from the dynamicist and the planetary geologists.

Surfaces are cratered, dark albedoes, no strong spectral absorptions. Porous densities (formed in low g envir). P’s Orbit first suggested in ’45 to evolve. Might P&D be captured, and be evolving via tides? But low e and i argue against. Nico S, Andy Rivkin and Sascha Basilevsky all stated these are ancient surfaces but still 40 years on distinguieh. Dessicated phyllosilicates or space weathered surface? Still two possibilities

Orbital Characteristics Note: Orbits lie in orbit plane and are nearly circular: Like mid-sized satellites of giant planets, normally ascribed to growth in the nebulae. Not captured, like irregular satellites of giant planets (high e, I, large a). Or like our Moon, formed from impact-derived ejecta disk. Orbits lie within and exterior to synchronous, at 6.02 R. From recent measurements, mostly Mars Express: Q ~100; k2 ~0.16 r ~ 1.87, 1.48 g/cm3

Tides Tides are (differential) gravitational forces caused by an external body. They distort the object’s shape. The Earth feels tides from the Sun & Moon. But the Earth is not a point; some places closer to the Moon than others. Let’s discuss the plausibility of capture at an elementary level. Tides provide a natural simple explanation for the evolution that is noted already. Of course, same true for Martian moons, and these forces are reciprocal: Moon distorts just like Earth does. Moreover, we’re used to thinking in terms of fluid tides but in solid body too, altho not distorted as much. Differential implies closer is (much) better (i.e., Moon vs Sun). But also for Phobos. And Phobos much more affected than Deimos, Differential => ~(r/R)(1/R2) ~ r/R3(

Difference in local gravity relative to that needed for orbit determines distortion. Top: Not quite right, b/c total orce should be equal, but also every place feels force Far side too, but less Much of this gravitational attraction is needed to cause synchronous orbit, as shown at bottom right It’s the difference that matters, to our current story.

Gravity difference leads to semidiurnal tide Error: As body distorts, it must keep total volume, so should be shown as polar flattening. Complications: 1)The actual distortion depends on interior strength 2) As body distorts (greatly exagerated here), it no longer is a point mass. Example of Rhode Island coast. half-spin period due to Earth’s rotation

PHOBOS’ TIDAL DISTORTION Here we have added the potentials of point mass Mars, ellipsoidal Phobos, and centrifugal potential due to spin of coordinate system. Dobrovolskis & Burns, 1980 Tidal Strain ~ k2(m/M)(r/R)3. where k2 = Love no. ~Gr2 r2/m

Tidal Effects Planet does not respond instantaneousls; max distortion occurs after max force. Tidal bulge leads (trails for n>W) by sin 2e ~ 1/Q. Non-aligned bulge causes torque b/w Moon & Earth By conservation of angular momentum, planet’s rotation slows, and moon is pulled forward, so it recedes from planet. But little transfer of angular momentum to Mars; spin constant (Deimos) Q ~100 > n Q~100

Tidal Effects: Phobos vs. Deimos Recall Phobos is at 2.7 R, Deimos at 6.9 R; synchronous at 6.02R Burns, In Mars, 1992.

Phobos’ Rotational State Tidal distortion of Phobos.~k2 (m/M)(r/a))3 r ~ 10 m Rotational slowing = (9/8)( k2 G m2 /2wQ)(R5/a6) Time for tidal de-spin = 104k2/ Q yrs PHOBOS = 107 k2/ Q yrs DEIMOS Peale, 1977 Synchronous rotation and quick damping to align with minimum energy state (long axis to Mars) Because of Phobos’ small mass, little effect on Mars’ spin, unlike Earth-Moon case. Libration due to forcing by uneven speed along satellite’s eccentric orbit =>( B-A)/C (natural libration freq),which suggests homogeneous interior

Many others from Mars Express, More recently. After Mars Express : Willner, Shi & Oberst (P&SS, 2013) get 1.14o Witasse et al. (P&SS, 2013) also get 1.2 (+/- 0.15)o. Oberst et al. (P&SS, 2014) get 1.09o Many others from Mars Express, P&SS, 2014 From M. Tiscareno, 2011 EGS

Orbital Evolution Orbital Energy = KE + PE = - GM/2a = E ORBIT SIZE da/dt =(2a2/GM)dE/dt= (2a2/GM) v.dF , work done Energy Loss => Smaller orbits, even if loss causes orbital speed-up. Forces in Orbit plane (in direction of velocity; i.e., power) only affect a Orbital Collapse with energy loss (atmospheric drag, tidal drag, PR drag) ---------- Orbital Angular Momentum = H = [Gma (1- e2)]1/2 ORBIT SHAPE or … de/dt = (e2-1)(2H’/H + E’/E)/(2e) or… Orbits circularize when H is constant and E is lost (satellite tides) Only Forces in orbit plane can change shape. Burns, Am. Jnl. Phys. 1976 Note planetary tides usually cause e’>0

Tidal Evolution of Circular Orbits da/dt = 3 (G/M)1/2 m k2 a-11/2R5/Q (a/ao)13/2 =1 – (13/3) (n’o/no) (t – to) ~ tens of millions of years for Phobos, much longer for Deimos

Phobos a, e Planetary tides Satellite tides, too

Tidal Evolution (Higher-Order Terms) e runs away

Phobos a, e Planetary tides Satellite tides, too

Deimos a, e

…but high eccentricity orbits cannot have happened. Once orbits become interlaced, mutual collisions occur quickly. Yoder, 1982 Szeto, 1983

Resonance Passage Effects on Evolution 2:1 solar evection Moon tides; e-0 3:1 spin:orbit 2:1 spin: orbit The eccentricities that we see today are not primordial. Rather they are remnants of past resonance passages. Yoder, Icarus, 1982

Orbit Orientation Orbit tilt depends on Angular Momentum’s direction. Moments change orientation; Just forces normal to orbit plane cause such reorientations. Not important in tides. Gas drag forces the body’s orbit to adopt that of medium. If orbit evolves slowly, it keeps a constant angle relative to mean (Laplace) plane. Distant orbits precess around planet’s heliocentric orbit plane; close-in orbits precess around equatorial plane. Thus moon orbits follow Mars’ axial precession and its chaotic obliquity oscillations.

Approach (Relative) Velocity In slow tidal evolution, orbit inclination relative to Laplace plane is roughly constant (Goldreich 1965) because orbit precession (oblateness or solar tides) is relatively fast . Orbital evolution under tides suggests low inclinations (relative to Mars’ orbit plane) when captured in the past. Low inclinations on capture are very rare (poles of orbit planes fill little solid angle). Relative velocity: asteroid Think meteor streams (Draconids: Oct 8; Orionids: Oct 21-22; Taurids: early Nov; Leonids: Nov 17-18); Do they all arrive on equator?? Mars DV

Phobos’ Inclination History A. Cazenave et al. Icarus, 1980 F. Mignard, MNRAS, 1981

Phobos a, e, i N.B. small inclinations

Deimos a, e, i

Atmospheric Drag Exponential decay V = Vi e –b Cd Pollack, Burns, Tauber Icarus, 1979 Hunten, Icarus, 1979 Sasaki, LPSC, 1990 Can capture quickly w/ dense disk, but orbit evolves quickly too. Periodic impacts into disk cause energy loss (lower a), drop angular momentum (lower e) and regularize i. Cuk & Burns 2004

Bottom Line: in situ origin Capture is difficult, at best, whether tidally or thru atmospheric drag. Hard to dissipate energy and to circularize/flatten orbit to equator. Tidal scenarios suggest both Martian moons formed closer to synchronous orbit and with e & i ~ 0 Formation by impact or within disk (cf. Canup)

Tidal Effects This model of tides on the Earth is oversimplified: Earth not completely covered by oceans. The solid Earth distorts and bulges from tides as well. The Earth distorts the Moon into an ellipsoid. Tidal forces change the Earth-Moon system: Tidal Friction is slowing the Earth's spin (~ msec/century). Conservation of angular momentum, which is transferred from Earth’s rotation to lunar orbit: Moon is receding from Earth (3.8 cm/year). Tides can affect the spin and internal heating of some solar system bodies.