Lecture 4Lecture 4Physics in the solar systemPhysics in the solar system

TidesTides

•Tides are due to differential gravitational forces on a body. Consider the Earth and Moon: the gravitational force on the

Moon due to Earth is stronger on the near side than on the far side.

This net difference in force will cause the body to stretch along the line between the bodies.

Tidal ForcesTidal ForcesWhat force is exerted on body M1, by the tidal bulges raised on body M2?

r12

M2M1

•Tides result in a net force which slows Earth’s rotation and speeds the Moon’s orbital velocity.

Tidal FrictionTidal Friction

•As a result the day is getting longer by ~1 second/century and the distance between the Earth and Moon is increasing. There is evidence for this in the fossil record on Earth

Tidal FrictionTidal Friction

In the past, when the moon was 0.25 as far from Earth as it is now:

a) How much more massive was Earth’s average tidal bulge?b) How much stronger was the net accelerating effect of this

bulge on the moon?

Synchronous RotationSynchronous Rotation

• How does tidal drag explain the fact that the Moon always shows the same face to Earth?

This effect causes Pluto and Charon to always show the same face to one another

Similarly, Mercury rotates exactly 3 times for every two orbits of the Sun.

Roche limitRoche limit

•The tidal force gets very large as the distance between objects decreases.

•At a critical distance, the tidal forces will exceed the gravitational force holding the satellite together, and it will be torn apart.

Roche limitRoche limit

Calculate the Roche limit for two equal-mass particles, just touching and with their centres separated by a distance dr. If these particles are a distance r away from a much larger mass M, at what distance (the Roche limit) will tidal forces overwhelm the gravitational force holding them together?

dr

Mm m

r

Tidal heatingTidal heating

•A tidal bulge is raised on Io, due to Jupiter.

Other large moons perturb Io’s orbit, which cause it to vary its distance to Jupiter

• This causes the tidal bulge to rise and fall, generating internal heat

BreakBreak

RingsRings

•The rings of Uranus are thin, narrow, and dark compared to other planetary ring systems.

Rings of Neptune show thin ringlets, and ring arcs

The “gosssamer” ring of Jupiter is very faint

Many gaps – large and small – in Saturn’s ring structure.

RingsRings

• Ring features (gaps, edges) due primarily to resonant perturbations

• In densest regions, ring particles collide with one another every few hours.

• Extend out to Roche limit: these are swarms of debris which cannot coalesce to form a moon

• In Jupiter and Saturn systems, small moonlets are associated with the outer ring edges, near the Roche limit.

Thinness of ringsThinness of rings• Saturn’s rings are very thin: only a few tens of metres thick (270,000 km in diameter)• Why?

Shepherding satellitesShepherding satellites

•Narrow rings can be maintained by gravitational action of small moons in or between rings.

Two small moons on either side of Saturn’s narrow F ring

Two shepherding moons straddling the brightest ring around Uranus

Shepherding moons: PandoraShepherding moons: Pandora

•Pandora is a shepherding moon of Saturn’s F ring.•Craters on Pandora appear to be covered over by some sort

of material, providing a smooth appearance. Curious grooves and ridges also appear to cross the surface of the small moon.

Gap MoonsGap Moons•Gap moons have the opposite effect: clearing a gap in the

ring structure

Rings of UranusRings of Uranus

•several distinct rings, mostly narrow

•dark, sooty particles•some banded

structure•only tens of metres

thick•mass ~1/4000

Saturn’s system

Rings of JupiterRings of Jupiter

Jupiter has two ring systems, likely produced by material ejected from moons following meteorite impacts

Radiation pressureRadiation pressure

• Photons carry momentum: can push an object away from the Sun

• If object has a large surface area but small mass, radiation pressure can overcome gravity

• Imagine a typical stone (~3000 kg/m3) with radius a, a distance r from the Sun. Under what conditions will radiation pressure balance the gravitational attraction to the Sun?

r

Qac

fF 2