Earth - (1685) Toro Asteroid Resonance

The asteroid (1685) Toro is in an 8:5 resonance with earth. This simply means that it makes 8 rotations about the sun in the same time as the earth makes 5 rotations.

The orbital elements of (1685) Toro show that its daily mean motion n = 0.61646079 deg /day

Thus its rotational period is 360 deg / (0.61646079 deg /day) * (1 yr/365.25 days)= 1.60 yr

5 rotations of Toro takes 2919.894 days or 8.0 years, the same time as 8 earth rotations.

(1685) Toro is also in an 13:5 resonance with Venus, but Earth predominates with a stronger restoration force to its orbit.

The synodic period of Venus is 224.70069 days
5 rotations of Toro takes 2919.894 days or 13 Venus rotations.

From orbital elements for Toro

a 1.3673061 AU
e 0.4358292

perihelion distance q = a - ae = a(1 - e) = 0.7713942 AU
aphelion distance Q = a + ae = a(1 + e) = 1.9632180 AU

a_Mars 1.52371034 AU
a_EM Barycenter 1.00000261 AU
a_Venus 0.72333566 AU

As Toro orbits the sun, it crosses the orbits of Earth and Mars, passing near the orbit of Venus at its perihelion. Over long periods of time Venus, Earth, and Mars will influence its orbit perturbing it as the asteroid approaches and receeds to and from each planet with tidal forces that affect th asteroid's angular momentum and causes its orbit to osculate. This causes precession in its longitude of perihelion. Its orbit librates (or oscillates) with respect to Earth and Venus. The effect of earth's gravity provides an impulsive force on its orbit during every close encounter which stabilizes the resonance with Earth. Encounters with Venus and Mars will disturb this until it encounters Earth again. This is like the earth's pull on the pendulum in a grandfather clock.

Other small perturbing solar system bodies usually considered in perturbation calculations include: Ceres, Pallas, Vesta, which are the most massive asteroids.

Perturbed orbital elements for an object like Toro will only be valid near the Epoch they are calculated for.

Toro is an Apollo type NEO with Earth MOID = 0.0504725 AU
Tholen spectral type: S
SMASSII spectral type: S
Absolute magnitude H: 14.23
Geometric albedo: 0.31
Diameter: 3.4 km
Rotation period: 10.196 h
Color index B-V: 0.880 mag
Color index U-B: 0.470 mag
Discovered 1948-Jul-17 by Wirtanen, C. A. at Mount Hamilton
T_jup = 4.716

Perihelion T: 2455025.524942745145 (2009-Jul-13.02494275)

Since this object's Earth MOID is greater than 0.05 AU, it is NOT classified as a Potentially hazardous Asteroid (PHA).
Its last encounter with earth was 2008-Jan-24 16:03 at a nominal distance of 0.19634 AU.
Its next encounter with Earth is at 2012-Jul-28 22:16 at a nominal distance of 0.3017 AU.
It has an impact probability of 0. This object has been well observed over 60 years which includes radar observations. It just passed its perihelion on July 13, 2009. Currently it is at magnitude 18.0, slowly fading, in the early morning sky at RA: 13 07 39.3 DEC: -14 44 47

References:

Minor Planet Ephemeris Service: http://scully.cfa.harvard.edu/~cgi/MPEph2

JPL Small-Body Database Browser:
http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1685;orb=0;cov=0;log=0;cad=0#elem

Alfvén, Hannes; Arrhenius, Gustaf; SP-345: Evolution of the Solar System, Scientific and Technical Information Office, NASA, Washington, D.C., 1976: http://history.nasa.gov/SP-345/ch8.htm

http://history.nasa.gov/SP-345/ch8.htm

Hazards due to Comets and Asteroids (1994), Ed. T. Gehrels, pp.540-543

EAR-A-5-DDR-TAXONOMY-V4.1

Venus Fact Sheet:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
Mars fact Sheet:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html
Earth Fact Sheet:
http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html