Transcript Lecture 4 Physics in the solar system Tides • Tides are due to differential gravitational forces on a body.  Consider the Earth.

Lecture 4
Physics in the solar system
Tides
• 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 Forces
What force is exerted on body M1, by the tidal bulges raised on
body M2?
r12
M1
M2
Tidal Friction
• Tides result in a net force which slows Earth’s rotation and speeds the
Moon’s orbital velocity.
• 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 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 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 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 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?
r
m
m
M
dr
Tidal 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
Break
Rings
The “gosssamer” ring
of Jupiter is very
faint
Many gaps – large and
small – in Saturn’s ring
structure.
•The rings of Uranus are thin, narrow,
and dark compared to other planetary
ring systems.
Rings of
Neptune show
thin ringlets,
and ring arcs
Rings
• 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 rings
• Saturn’s rings are very thin: only a few tens of metres thick (270,000 km in diameter)
• Why?
Shepherding satellites
• Narrow rings can be maintained by gravitational action of small
moons in or between rings.
Two shepherding moons straddling
the brightest ring around Uranus
Two small moons on either side of
Saturn’s narrow F ring
Shepherding 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 Moons
• Gap moons have the opposite effect: clearing a gap in the ring
structure
Rings 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 Jupiter
Jupiter has two ring systems, likely produced by material ejected
from moons following meteorite impacts
Radiation 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 (r~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?
f 2
F  a Q
c
r