A) Neptune
 
 

1. Data: Radius equatorial = 24,765 km, polar = 24,340 km. Mass = 1,03 x 1029 g. Density = 1.64 g cm-3. Albedo = 0.29. Year = 164.1 yr. Day = 16h 6m. Distance from Sun = 30.1 AU.

2. Properties: Neptune is very similar to Uranus in both mass and radius; yet there seem to be subtle differences in internal structure. Neptune is appreciably denser than Uranus. Neptune has a sizable internal heat source while Uranus doesn't. On the other hand, the moments of inertia seem to be similar, and the magnetic fields are more similar to each other than to the other giant planets. Are there fundamental differences in their internal structure, and if so, what caused them? One possibility is the large tilt of Uranus' axis of rotation.  The belief is that the planet was hit by a large body early in its history, and that caused the tilt.  Did it cause some subtle internal changes as well? It could affect the computed gravitational moments by inducing differential rotation. It could affect the internal temperature distribution by perhaps setting up layered convection. Our understanding of these two bodies is far from complete.

B) Pluto
 

1. Data: Radius = 1152 km Mass = 1.28 x 1025 g. Density = 2.0 g cm-3. Albedo = 0.3 Year = 248.5 yr. Day = 6d 9h 18m

Distance from Sun = 39.8 AU on average, but since its orbital eccentricity is 0.254, it can get as close as 29.7 AU to the Sun, closer than Neptune (it does this for about 20 years every revolution, currently it is from 1979 to 1999).  At its farthest it is 49.9 AU from the Sun.

2. Properties: Pluto is unusual in a number of respects. It is a very small planet, considerably smaller than our moon.  If we had discovered it now we would probably call it a large asteroid, but when it was first discovered it was thought to be even larger than Mercury, so it earned the name "planet".  In addition, when it was discovered there were no known asteroids outside the asteroid belt.  We now know that there are asteroids in many different parts of the solar system. Pluto is made up largely of ice.  Its small mass means that pressure will not affect the density very much, so the material comprising it must be mostly ice and rock.  This too is unlike the composition of any of the other planets. Pluto has a large companion, Charon, which is about half its radius.  This is so large a fraction, that it can really be considered a double planet rather than a planet-moon system.  The density (and therefore probably the composition) of Charon is very similar to that of Pluto.  Pluto and Charon both keep the same face to each other throughout their rotation.  The axis of rotation is tilted to the plane of the orbit by only 28°, much like Uranus. Possibly Pluto belongs to the newly discovered family of Kuiper belt objects.  This makes Pluto (and Charon) more like giant comets rather than small planets.

C) Satellites.
 

1. We have already seen the Earth's moon. 2. Mars' moons. 2.1 Jonathan Swift in Gulliver’s Travels first mentions Mars’s moons, about a century before they were actually discovered.  This is often cited as one of the mysteries of astronomy, but, in fact, Kepler predicted two moons a century before Swift, based on curious reasoning: Mercury is the “moon” of the Sun, Venus has no moons, Earth has one, so Mars must have two! 2.2 The moons are small, have low densities, and have low albedos.  They exhibit evidence of collisions such as craters (and in the case of Phobos, grooves), which may have their origins in such collisions.  They are very similar in appearance to asteroids, and may be captured asteroids. 2.3 Phobos is inside the synchronous orbit of Mars, so it appears to move from west to east.  In addition, there is some evidence that its orbit is decaying, and it may crash into Mars in some 30 million years.  2.4 Deimos is outside the synchronous orbit radius and is actually getting further from Mars as time goes on.  This gives another possibility for their origin.  They may have been part of a larger body that was orbiting Mars near the synchronous orbit radius.  A large collision could have split it, and sent one object inward and the second outward. 2.5 Further details can be found in the table below.

3. Jupiter's moons. 3.1 The details of Jupiter's moons are given in the table below The first two moons are probably associated with Jupiter's dust ring, and may supply the dust. Amalthea is small and red, and was known before Voyager.  The red color may come from sulfur dust sputtered from Io.  Thebe is not well known. The four large moons were discovered by Galileo in 1610, and can be easily seen with binoculars.  They decrease in density going outward from the planet.  Io has a density of 3.5 g cm-3 corresponding to rock.  The other moons have densities, respectively of 2.9, 1.9, and 1.8 g cm-3.  This seems to be due to an increasing fraction of ice that was deposited in larger amounts on those moons that were further away from an originally hot Jupiter. Io is in an eccentric orbit and is tidally heated by Jupiter.  This is the cause of the volcanoes seen on its surface.  Europa shows surface features that are very similar to those seen on ice over liquid water, and it is suspected that liquid water may exist there as well.  This could have important implications for the possibility of life.  Ganymede is bigger than Mercury, and seems to have a magnetic field.  It has dark old craters and light younger ones, and shows surface cracks that may be caused by internal melting and convection of water ice. Callisto has an old surface, with no sign of tectonics.  The dark areas on both Ganymede and Callisto have a larger fraction of rock than would be expected from their densities, and it may be dust that was picked up from space. The next four satellites (all with names ending in a) have very similar orbits, and may have been historically associated.  They are all regular in the sense that they orbit Jupiter prograde, have small orbital eccentricities, and small orbital inclinations. The next four satellites are irregular.  Their orbits are all retrograde, and the eccentricities are large and differ from each other.  The orbits are also highly inclined to the equatorial plane.  They may be captured asteroids.

4. Saturn's moons   The first three moons are small shepherds.  They are larger than the shepherds found in the inner ring system.  Possibly because they are further from the planet. The next two orbit just outside the ring system.  All appear to be made of ice. Mimas is large enough to be round, and is insturmental in forming the Cassini division in the rings.  Enceladus has an albedo close to 1, which means it has recently been resurfaced.  There are clear signs of such resurfacing.  It has a density of nearly 1 g cm-3.  Tethys has a large crater that is about 1/8 the circumference of the moon.  Mimas too has a crater that is about 1/8 of its circumference.  It seems this is as large as a crater can get before the body itself is shattered.  There is also a large crack on the opposite side of the moon that may have been caused by the impact that formed the crater. Dione and Rhea also show heavily cratered surfaces and possibly cracks.  They are all composed mostly of ice. Titan has a substantial atmosphere composed mostly of N2.  There is also a few percent of CH4 and A.  Ultraviolet photolysis of the methane forms polymers of C2H2 and C2H4 as well as other organic compounds.  These polymers, in turn, form aerosols whose scattering gives the planet its red color.  The nature of these aerosols (i.e. their size or mixing ratio in the gas) changes as the seasons on Titan change, and this makes the upper hemisphere of Titan have a different reflectivity from the lower hemisphere.  Hyperion is a body about 400 km long and about 250 km wide.  It is large enough to behave like a fluid and be spherical, but it is not. One explanation is that it got its present shape as the result of a collision in the not too distant past, and is in the course of reverting to spherical form, but has not yet completed the process.  At the low temperatures in the outer solar system, ice has a very high viscosity, and changes in shape take a long time.  Support for the collision theory comes from the fact that although its orbit has a small inclination, it has a far higher eccentricity (e = 0.104) than any of the other satellites except for Phoebe. Iapetus has a leading hemisphere that is 7 times darker than the icy trailing hemisphere.  One explanation is that dust from Phoebe, which spirals towards Saturn due to the Poynting - Robertson effect falls on Iapetus and covers the leading hemisphere.  The reflectivity of the dark side of Iapetus is similar to that of Phoebe but not identical.  Another possibility is that high-energy particles impinging on the ice causes the formation of dark organic compounds.  Phoebe is retrograde and is in an eccentric orbit (e = 0.163).  It is probably a captured asteroid. Helene is a small satellite at Dione's Lagrangian point.  Calypso is at the trailing Lagrangian point of Tethys, and Telesto is at its leading Lagrangian point.

5. Uranus' moons The inner moons are small and dark and were discovered by Voyager. Miranda has a very strange surface, including chasms up to 15 kilometers deep.  This is more than 6% of the radius of the body.  On Earth this would correspond to a depth of over 400 km.  It also shows "chevron" patterns.  One idea is that Miranda was completely broken up, and reformed in orbit.  Ariel shows evidence of a young surface.  No craters larger than 50 km, icy flows, cracks that may be due to tidal distortion. Umbriel seems to have an old surface.  There are many large craters, and the surface is relatively dark. Titania is similar to Ariel, with smaller craters and an apparently young surface, while Oberon is more like Umbriel, dark, and heavily cratered.

6. Neptune's moons Little is known about the inner satellites. Triton is a large satellite with a retrograde, but very circular orbit.  It seems to be a captured body (probably from the Kuiper belt) and this would be consistent with its orbital inclination of 157°.  Strong tidal damping of its orbit would circularize it and cause internal heating.  This may be the source of the cryovolcanism observed.  Because Triton's albedo is so high, its surface temperature is even lower than that of Pluto, and can be as low as 35 K.  The surface is probably covered by frozen methane and nitrogen. Nereid has a very eccentric orbit (e = 0.75), which may be due to an earlier interaction with Triton.  Little is known about this body.

7. Pluto's moon, Charon, is not much smaller than Pluto itself (R = 615 km), and the pair can be called a double planet.

D) Origin of the Solar System
 

1. What properties of the solar system does a theory have to reproduce? All planets orbit in the same direction. All planets (except Pluto) orbit in nearly the same plane. All planets have nearly circular orbits. Inner planets are rocky, outer planets are gaseous. Inner planets have basically no satellites; outer planets have whole families of them. Most of the mass of the solar system (98%) is in the sun. Most of the angular momentum of the solar system (over 90%) is in the planets.

2. What do we know about other solar systems? Since most of the mass of the solar system is in the sun, the formation of the solar system is really the story of the formation of the sun. The galaxy is filled with clouds of gas that are typically tens of light years across.  We also see that many stars are formed in loose clusters, or associations.  It seems reasonable to assume that the clouds of gas, called diffuse nebulae, somehow serve as the birthplace of these open clusters of stars.

3. How do we turn a gas cloud into a star? 3.1 The cloud wants to collapse because of gravity, but its temperature and pressure keep it from collapsing.  There is a balance between its thermal energy and its gravitational energy.  The gravitational energy of a spherical cloud of mass M and radius R is given roughly by If the volume of the sphere is decreased, the gravitational energy becomes more negative by the amount This volume change will also increase the thermal energy by -PdV, or where m is the mass of a gas molecule.  Note that Egrav goes like R2 while Etherm is independent of R.  As a result, for a given mass and temperature, if R is small enough, the thermal energy will be increase more quickly than the gravitational energy, and the sphere will re-expand.  But, if R is large enough, the gravitational energy will increase more quickly, and the sphere will contract.  The critical radius is Actually, a more careful calculation gives a somewhat different numerical coefficient, but the dependence on temperature and density remains the same.  What this means is that a gas cloud of a given temperature and density will be unstable to gravitational collapse if its radius exceeds a certain critical value, called the Jeans radius. 3.2 We can suppose that when a region of a diffuse nebula has a density and temperature that makes it unstable, it will begin to collapse. During the collapse angular momentum will be conserved, so that the cloud fragment will rotate.  As a result, those portions of the cloud nearer to the axis of rotation will feel a small centrifugal force, while those regions farther from that axis (in the equatorial plane) will feel a greater force.  The collapse will tend to form a disk.  Such disks are indeed seen around young stars.  3.3 There is a class of stars called a T-Tauri variable that is a very young star and behaves in a manner consistent with such a disk.  There are different types of T-Tauri stars, and I won't get into the details here, but they are believed to be newly formed stars that are going through the processes I am describing.  3.4 As the cloud fragment collapses, a central condensation quickly forms.  This is the protostar.  The disk gas orbits the protostar with a speed that is determined by the balance between the protostar's gravitational pull, and the pressure and centrifugal forces in the gas.  Gas at different distances, orbits at different speeds, and there is friction between adjacent layers.  This frictional force on the one hand slows the inner gas and causes it to fall into the protostar.  On the other hand, it causes angular momentum to pass to the outer portions of the nebula.  This can account for the fact that most of the mass of the solar system is in the sun, while most of the angular momentum is in the planets.

4. How do planets form in this environment? 4.1 The composition of the gas is solar.  Nearest to the sun where the temperature is high, everything is a gas.  Further from the sun, the temperature drops, and different species condense.  These solids are the building blocks of the planets.  4.2 There are two issues:  The chemical composition, and the phase of the species.  The chemical composition is generally computed by calculating the expected composition for chemical equilibrium at a given pressure and temperature. Since there are gas currents in the nebula, and the material is moving from place to place, will it really be in equilibrium? How long does it take to get to equilibrium compared to how long it takes to move from one part of the nebula to another? 4.3 Of the abundant elements Fe and Mg will generally form oxides such as MgO or silicates such as Fe2SiO4 and Mg2SiO4 (olivine) or FeSiO3 and MgSiO3 (enstatite).  Since there is more O than Fe, Mg, or Si, the remaining O will combine with H to form H2O.  Similarly, C and N will combine with H to form CH4 and NH3. 4.4 This is the result of equilibrium at low temperature.  The minor species most often collide with H and combine with it.  4.5 At high temperatures the collisions are more violent, and although most are with H, the molecule formed will often break up again because the bond between C and H or N and H is relatively weak.  If a C and O collide, the resultant bond is much stronger, and the molecule survives.  The same is true for an N - N bond.  Thus even though collisions with H are much more common, collisions between C and O or N and N are much more stable.  At low temperatures the bond strength doesn't matter much, but at high temperatures it is the bond strength that determines the composition.  4.6 Since there is only a little less C than O in solar composition, low temperature equilibrium gives roughly equal amounts of H2O and CH4.  High temperature equilibrium gives lots of CO and any extra O as H2O.  4.7 Near the sun the temperature is so high that everything is gas.  Further from the sun, the temperature drops and different species condense from the gas.  Near the sun the solids are Fe, olivine, and other "rocky" materials.  Further from the sun where the temperature drops to around 150 K water ice begins to condense.  Still further from the sun (around 80 K) NH3 condenses, and at around 60 K CH4 condenses... if that is the correct composition.  If not, then everything is the same, except that CO and N2 condense only at around 20 K, and the amount of H2O available is much less, so there is less ice condensed than in the first case.  4.8 For a solar composition gas, the mass ratio of "ice" to "rock" will be about 3:1 if "ice" is composed of water, methane and ammonia.  If CO and N2 are formed, "ice" will be composed of only a small amount of water, and the ice to rock ratio will be 0.5.  Since planets are formed by accretion of these solids, the composition of the planets should hold clues to the conditions in the solar nebula.  4.9 In any given region of the nebula, the solids will initially be in small grains with radii around 10-4 cm.  These grains will feel a gravitational force from the sun that has a radial component and a vertical component.  The radial component will cause them to orbit the sun and the vertical component will cause them to fall towards midplane.  4.10 As the particles drift towards midplane, particles will collide because of Brownian motion,  and also because larger particles will overtake smaller ones.  If the particles stick, there will be growth.  Detailed computations show that it takes about 104 years to reach midplane, and by then the particles are of the order of centimeters in radius.  4.11 When the particle density in the midplane gets high enough, instability develops similar to the Jeans instability and the particles form gravitational associations of the order of kilometers in radius or more.  This is called the Goldreich-Ward-Safronov (GWS) instability.  It is very useful for bridging the gap between micron sized dust and kilometer sized planetesimals.  With one proviso.  4.12 If the gas is turbulent, the dust layer will never get thin enough for the instability to set in.  This is still an unsolved problem.  But, assuming that everything is correct up till here, what happens next is as follows:  4.13 The GWS instability causes the formation of gravitationally bound objects with radii of tens of kilometers.  These can collide with one another and form even larger bodies.  If one of these protoplanets grows more quickly than its neighbors, it will begin to accrete much more quickly.  The reason for this can be seen from the following analysis.  4.14 Suppose that a particle with a speed at infinity of v0 is captured by a protoplanet.  If the impact parameter (the closest approach distance between the particle and the center of the planet in the absence of gravity) is b, the mass of the particle is m, the mass of the protoplanet is M, and the radius of the protoplanet is R, then conservation of energy tells us that while conservation of momentum tells us that if the particle hits the planet at the very last possible place, then v0b = vR.  We are interested in the capture cross section, which is ob2.  We get and, from the energy equation,  where vesc = (2GM/R)1/2 is the escape speed from the body.  This gives where Θ is the so-called Safronov parameter, which is defined as where m1 and r1 are the mass and radius of the largest particle in the planetesimal size distribution.  4.15 If we assume that the random velocities of the planetesimals are caused by the interaction with the biggest body in the swarm, then we would expect them to get velocities somewhat lower than the escape velocity from the biggest body.  In other words, the Safronov parameter should be of the order of 1.  Typical early computations took it to be around 2 - 5.  4.16 We can use this idea where P is the period of revolution around the Sun, and r0 is the initial surface density of material in that region.  The time it takes to get to z = 1 is infinite, since the density of material goes to zero as the body is built, and it takes longer and longer to pick up the last few pieces.  The time to get to z = 0.99 is about t = 6 τ0, where While the details of this derivation are not important for us here, the functional dependence bears looking at.  The larger the surface density of solid material the faster one can build the planet.  The longer the time it takes to move through the feeding zone, the longer it takes to build the planet.  The lower the random velocities (the higher the Safronov parameter) the easier it is to build the planet.  If we take z = 0.99, and put in the numbers for the Earth, we find that τ0 is of the order of 108 years, which is a bit long, but not obviously wrong.  For Jupiter, we get something like 109 years, which is too high.  For Neptune the time is orders of magnitude longer than the age of the solar system, so something is clearly wrong.  4.17 It is possible to raise the surface density somewhat, but not too much, because we would then need to find a mechanism for getting rid of the excess mass.  4.18 A much more reasonable way of shortening the time comes from the concept of runaway accretion.  One of the basic assumptions was that the random velocities come from gravitational stirring by the largest body.  But this stirring is not instantaneous.  It is possible that after the largest body stirs a group of planetesimals, and leaves their immediate vicinity, it grows substantially.  When it returns to that vicinity, the planetesimals are moving with a velocity relevant to the previous mass of the protoplanet.  This can be considerably lower than the escape velocity from the current protoplanet.  In this case the value of the Safronov parameter will be much higher than 5, and may even reach values of 104.  This will lower the formation time by a corresponding factor.  4.19 A third factor that comes into play is due to the fact that the outer planets all contain substantial amounts of gas.  The mechanism we have described here is only for the accretion of solids.  We believe the outer planets were built in two stages.  In the first stage a solid core was accreted, as was the case for the terrestrial planets.  This core sat in a nebula of mostly hydrogen and helium.  As it grew it slowly accreted gas from the surroundings by gravitational attraction.  This process was slow at first because the core mass was low.  As the accreted gas joined the core, however, the total mass of the body grew, both by accumulation of solids and of gases.  The more the mass of the protoplanet increased, the more efficiently it could attract additional gas.  Modeling of this process shows that when the core reaches a critical mass of some 10 – 15 Earth masses, instability develops, and the gas collapses, quasi-statically onto the core.  A great deal of mass is thus added in a relatively short time.  This also dramatically decreases the formation times of the outer planets.  Models show that Jupiter and Saturn can be accreted in some ten million years.  This is about the length of time that the solar nebula is in place.  4.20 The time for Uranus and Neptune to reach the critical mass is longer than this, and the nebula dissipates before they reach the stage of quasi-static collapse.  This would explain why they have relatively little hydrogen and helium compared to Jupiter and Saturn.

5. Formation of comets. 5.1 The planetesimals that form the outer planets are similar to comets in size and composition, and this is most likely the source for many comets.  If these planetesimals fail to be captured by the protoplanet, they may be given additional kinetic energy, and thrown into orbits far from the Sun.  Although these orbits are initially very elliptical and lie in the plane of the planets, the perihelia are so large, that distances of 104 - 105 AU may be reached.  At these distances even nearby passing stars, or interactions with interstellar clouds can affect the orbits, and they quickly get scattered into a ball around the Sun.  This ball is called the Oort cloud.  It is the source of long period comets with orbits that can be highly inclined to the plane of the planets.  5.2 Neptune does most of this gravitational scattering.  In giving up kinetic energy to the planetesimals, Neptune loses orbital energy and drifts inwards towards the Sun.  It may be that this is the reason its orbital distance is so much less than predicted by the Titius Bode law.  5.3 Comets can also be formed further from the Sun, in the so-called Kuiper belt.  This region is not much influenced by gravitational interactions with the planets, and the bodies formed there stay in this region.  The Kuiper belt is the source of short period comets whose orbits lie in the ecliptic plane.  Recently numbers of Kuiper belt objects have been discovered, and Pluto may actually be considered to be one of the innermost of these objects.