PX282 - J8 - orbits

• planets show secular resonances, which are oscillations in eccentricity and inclination
• mercury has the most eccentric and advance of perihelion
• this led to the first test of general relativity

rotation

• earth and mars rotate rapidly, whereas mercury and venus rotate very slowly due to tidal interactions (synchronization) with the sun

• tides are also slowing the rotation of earth, seen directly in sea shell fossil records

• the true rotation period is the sidereal day* , while the solar day for earth is slightly longer (4 min) due to orbital motion

image: Carrol & Ostile, An Introduction to Modern Astrophysics, 2007

• the difference is much more for slowly rotating planets

• for mercury, it is thrice longer than its spin period

• venus has a very slow retrograde rotation due to faster retrograde circulation of the atmosphere driven by solar heating

• mercury's rotation is stuck in $3:2$ resonance with its eccentric orbit (spins $1.5$ times per orbit), keeping its small permanent deformation aligned with the sun at perihelion (where tidal forces are the strongest)

image: Carrol & Ostile, An Introduction to Modern Astrophysics, 2007

obliquity

• obliquity is the angle at which the spin axis is tipped

• mercury and venus have very small obliquities due to tidal synchronizations

• earth and mars have an obliquity $\sim 23\mathrm{°}$

• this is the reason for seasons

• since the earth is slightly oblate, ie. bulges around the equator, there is a torque due to solar gravity

• this causes the spin axis to rotate - precession

• the obliquity of mars varies due to small torques from the planets

• this leads to large climate variations

• torque due to the moon stabilizes earth's obliquity

• there are small variations, together with secular resonances in $e$ and $i$, that lead to milankovich cycles in earth's climate

image: Laskar (1993)