Download ASTR 330: The Solar System Example Dr Conor Nixon Fall 2006

ASTR 330: The Solar System
Lecture 4:
The Planets:
Overview
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Solar System To Scale
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Density
• What do we mean by the density of an object?
 Density is defined as the amount of mass in a given volume:
Mass
Density 
Volume

If mass is in grams (g) and volume is in cubic centimeters (cm3)
then density is in grams per cubic centimeter: g/cm3.

This is a very convenient unit, because the density of water in
these units is 1.0 g/cm3.

We can then easily compare the densities of different materials
to the density of water.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Measuring Densities
• To measure the density of a planet, we need to know:
1. the size (diameter), and
2. the mass.
• To determine the actual size, we need to know:
1(a): the distance (from parallax), and
1(b): the angular size of the planet.
• To determine the mass (from Kepler’s third law) we need to know:
2(a): the distance (from parallax),
2(b): the angular size of the planet’s orbit,
2(c): the orbital period.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Planet Diameter Determination
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Planet Mass Determination
• In practice, this method is inaccurate for planetary orbits around the
Sun, because MS>>mp. Use satellite orbits around planet instead.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Example
• Calculate the diameter of Mars at closest approach to the Earth
using the formula D= 2dA/360, given that the distance d (from
parallax) = 78x109 m and A=0.005 degrees. You do it!
• Answer: d=6.807x106 m.
• Determine the mass of Mars using the formula:
m+M=(5.916x1011) a3/T2
applied to the orbit of Phobos, with a=9.377x106 m, T=27,576 s.
Assume that the mass of Phobos m can be ignored.
• Answer: M=6.414x1023 kg.
• Now calculate the volume (V=4r3/3) and density =M/V of Mars.
• Answer: =3885 kg/m3 (a tiny bit too low)
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Densities of the Planets
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Categories of Planets
• From consideration of size and density alone, we can divide the nine
planets into three main categories:
TERRESTRIAL PLANETS: characterized by small size, high density,
and also found in the inner solar system:
Mercury, Venus, Earth and Moon, and Mars.
GIANT PLANETS: characterized by large size, low density, and
found in the outer solar system:
Jupiter, Saturn, Uranus, Neptune.
DWARF PLANETS: Pluto, its moon, Charon, and Ceres, the
largest of the asteroids have been recently
named ‘dwarf planets’ as they have enough
mass to become round, but do not dominate
their orbital regions of space.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Terrestrial
Planets
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Compression vs Composition:
The Inner Planets
• From their densities, the inner planets are likely to be composed of rock
and some metal in the cores.
• We might expect that planets less massive than the Earth would have
lesser densities, because they are less compressed at the center by
gravity, right?
• Amongst the terrestrial planets, this is true for both Mars and the Moon,
which are both smaller and less dense than the Earth.
• Venus is roughly the same size and density, as the Earth. So far, so
good…
• BUT, Mercury is both less massive, and more dense than the Earth!
WHY?
We must conclude that Mercury has a different composition
than the Earth.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Giant
Planets
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Compression vs Composition:
The Outer Planets
• What about the densities of the outer planets?
• We would expect the outer planets, which are more massive, to be
much more compressed than the inner planets, and so more dense,
correct?
• In fact, these heavier bodies are less dense than the inner, terrestrial
planets.
• The only composition which we can use to construct such massive
bodies with such low densities is a mixture of hydrogen and helium, the
two lightest elements.
• The composition of the outer planets is hence more similar to the Sun
and stars than to the inner planets!
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Densities and Compositions of
Other Solar System Bodies
• Among the moons of Jupiter we find a similar trend of decreasing
density with distance from the primary body:
Satellite
• Io
• Europa
• Ganymede
• Callisto
Distance from Jupiter
0.42 million km
0.76 million km
1.07 million km
1.88 million km
Density
3.3 g/cm3
3.0 g/cm3
1.9 g/cm3
1.8 g/cm3
Why could this be?
• Less is known about asteroids and comets:
Asteroids: thought to be mainly rock composition.
Comets: mainly ice composition.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Chemistry
• Hydrogen and oxygen are the most important chemical elements: they
are both highly abundant, and chemically reactive.
• Each can form compounds with many other elements, including each
other! (What is the most common hydrogen-oxygen combination?)
E.g.:
hydrogen with carbon can form CH4 (methane)
oxygen with carbon can form CO2 (carbon dioxide).
• If hydrogen atoms predominate, as in the giant planets, then most
elements form compounds with hydrogen. This is known as a reducing
environment.
• If oxygen atoms predominate, many oxygen compounds form. This is
called an oxidizing environment. This is the case in the inner solar
system.
• Why is hydrogen less abundant in the inner solar system?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Types Of Matter
• We can categorize the forms of matter in various ways:
• To the ancient Greeks there were 4 ‘elements’: Fire, Air, Water, Earth.
• We now know that there are in fact ~92 naturally occurring elements.
• Elements and compounds may be found in one of 4 physical states,
depending on temperature and pressure: solid, liquid, gas and plasma.
• However, it will be useful for our investigation of the planets to define
four types of common physical-chemical combinations:
gas, ice (solid), rock, metal.
• In what physical state will rock and metal be most commonly found?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Announcements 9/14/06
• Homework #1 - no grades yet.
• Yellow forms - any more?
• Assessment forms.
• New materials on website: Lecture 5 - Planetary
Astronomy
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Quick Quiz
1. Define density. What is the density of water?
2. What are the (i) least dense and (ii) most dense planets?
3. What differences are there between the terrestrial and
giant planets?
4. Why does Pluto not fit in either of the previous
categories?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Gas
• Gas is what makes up the atmosphere of a planet.
• For the Earth, we have a unique atmosphere of nitrogen (N2 78%) and
oxygen (O2 20%). Oxygen gas would not exist without plants!
• For Mars and Venus, the main atmospheric gas is carbon dioxide, CO2.
Without life on Earth, our atmosphere would have a lot more CO2.
• For Jupiter and Saturn, the largest gas giants, the atmosphere is mostly
hydrogen gas (H2) and helium gas (He). In this sense, they are like the
Sun. The outer parts of the Sun most resemble the original solar nebula
in composition, out of which the solar system formed.
• Uranus and Neptune also have large amounts of hydrogen and helium
gas, but their densities are greater, indicating more heavy elements as
well.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Ice
• Volatiles are molecules that are liquid or gaseous at moderate
temperatures, but form solid crystals, called ices, at low temperatures.
• They may melt or sublime (vaporize from solid), and later re-freeze at
moderate temperatures, hence phase changes will be common.
• The main volatile species on the Earth is … what?
• On Mars, CO2 is the main volatile, but recently water ice has been found.
• Other volatiles include carbon monoxide (CO), ammonia (NH3), and
methane (CH4).
• Volatiles are the main component of comets and most planetary
satellites.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Polar Caps
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rock
• At higher temperatures, the volatiles are completely evaporated and the
remaining matter is typically rock.
• The Moon is almost
entirely rock, as is most of
the Earth.
• The most common rocks
are silicates: oxides of
silicon, aluminum and
magnesium.
Image: Apollo 17 Astronaut Harrison Schmidt; NASA JSC Archives
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Metal
• At still higher temperatures, rock itself is transformed.
• The metallic elements in the rock may separate out: typically iron,
magnesium and nickel.
• The core of the Earth is
metallic: as is 3/4 of
Mercury!
• Some asteroids are
nearly pure nickel and
iron.
Image: Gibeon Meteorite, FMM Museum, Russian Academy of Sciences
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Chemical Trends
• Let us re-cap some of our conclusions so far.
• Trends from the inner to the outer solar system:
Quantity
Inner Planets
Proportions of H and He lower (escaped)
Outer Planets
higher (retained)
compared to Sun
Proportion of oxygen
compared to Sun
higher
lower
Atmospheric chemistry oxidising
reducing
Atmospheres
Heavy volatiles
Light volatiles; H2; He
Cores
Rock; metal
Rock; ice
Composition compared more evolved
to original nebula
(more changed)
less evolved
(less changed)
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rocks and Minerals: Definitions
• A rock is an assembly of compounds or elements, called minerals.
 A mineral is a single substance (homogenous).
 A rock is a mixture of different mineral pieces (inhomogeneous).
 A elemental mineral contains only one element, e.g. Gold (Au),
graphite or diamond (C) , or sulphur (S).
 A compound mineral is comprised of multiple elements bonded
together: e.g. quartz (SiO2), hematite (Fe2O3).
• Pure elemental minerals are rare in nature hence most minerals are
compounds.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Types Of Rocks
•
Rocks may be divided into three main categories depending on
origin:
1. Igneous: rocks that have formed directly by cooling from a molten
state, e.g. basalts. Igneous rocks make up 2/3 of the Earth’s crust.
2. Sedimentary: composed of rocks or shells that have been ground
down and then re-deposited again in layers, e.g. limestone (from
shells) and sandstone (from silicates).
3. Metamorphic: originally igneous or sedimentary rocks which were
buried far beneath the Earth, processed by high pressures and
temperatures, and then re-exposed again at the surface, e.g. marble
can be made from limestone which is ‘cooked’ at high temperature.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rock Formation Summary
• This diagram shows the three rock formation processes in action:
Figure: msnucleus.org
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rock Formation Pictures
IGNEOUS ROCK FORMATION:
lava flowing on Mauna Loa, Hawaii
(picture: R.W. Decker, U.S.G.S.)
SEDIMENTARY ROCK FORMATION:
The Grand Canyon, Arizona.
(picture: Matthew Nyman, TERC)
METAMORPHIC ROCK FORMATION: These
Arizona rocks show sedimentary rocks
squeezed into new formations
(picture: R.W. Decker, U.S.G.S.)
Web source: earthsci.terc.edu
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Primitive Rocks
• The three types of rocks we have just discussed have all been created
at some point in the Earth’s history, from either molten rock (magma,
lava) or other rocks.
• But, is there such a thing as primitive rock, which formed at the
beginning of the solar system and has remained unaltered?
• Yes, in fact there is. But not on Earth! As the primitive rocks which were
to become the Earth gravitated together to form the planet, a lot of heat
was released, partly from impacts and partly from radioactivity.
• The Earth became hot enough for the center to become molten: the
rocks melted and became a liquid. Denser materials then gravitated to
the center, a process called differentiation.
•Where might we look to find primitive rocks?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Atmospheric Differences
• When we consider the solar system, we see a wide variation in the
planets and moons in terms of atmospheres.
 The Earth is much smaller and denser then Jupiter, yet both have
an atmosphere, although they are very different.
Photos: The Nine Planets, LPL Arizona
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Atmospheric Differences
 Titan and Ganymede are similar sizes, yet only Titan has an
atmosphere. How can we explain this difference?
Photos: The Nine Planets, LPL Arizona
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Acquiring An Atmosphere
•
We can imagine two main ways in which a planet may acquire an
atmosphere and oceans:
1. Direct capture (primordial): the volatile gases were captured by
the planet’s gravity from the original gas nebula.
2. Outgassed (secondary): the gases were released from solids
and liquids (e.g. rocks and ices) in the planet after formation was
complete.
3. Impacts (secondary): the volatiles were brought by cometary
impacts.
• In the case of the outer planets, the most likely explanation is a
combination of (1) and (2). For the inner planets, which were most
important?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Losing An Atmosphere
•
Once a planet has acquired an atmosphere, it must hold on to it, by
gravity. But there are forces at work which will tend to remove gases:
1. Impacts: from comets and meteorites may impart enough energy
to remove gas from smaller bodies.
2. Thermal escape: if the random motions in the warm gas are
great enough to equal the escape velocity, then the molecules of
the gas can leave the planet!
3. Charged particles: e.g. the solar wind may scour the outer
atmosphere and strip particles from the planet.
• Thermal escape happens in a layer called the exosphere, where the
atmosphere is so thin that a molecule moving upward will not
encounter another molecule before escaping.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Differential Escape
• For a given temperature (energy), lighter gas molecules will have
higher velocities than heavier ones (imagine an eight-ball ricocheting off
a bowling ball).
• Also, the escape velocity depends on gravity, i.e. the mass of the
object.
• Therefore, smaller and warmer bodies will tend to lose more gas
species than larger, cooler ones.
• For example, in the outer planets, we see Jupiter and Saturn holding on
to almost all their original hydrogen and helium, which have mass
numbers of 2 and 4.
• Whereas, the Earth holds on to heavier gases such as nitrogen and
oxygen, with mass numbers of 28 and 32.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Summary of Atmospheric Diversity
•
Let us summarize the main reasons for the differences between the
atmospheres of the various planets and moons:
1. Initial capture from solar nebula.:
- Large outer planets were able to capture and hold all gases from the
initial solar nebula, and hence exhibit compositions like the Sun.
- Small inner planets were not able to hold on to the lighter gases.
2. Later out-gassing:
- Both outer and inner planets out-gassed part of their atmospheres,
but for the inner planets, out-gassing is the dominant mechanism.
3. Biological agents: only on the Earth has biology substantially
changed the atmosphere, which would otherwise be more similar to
the composition of Mars and Venus.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rock Type Quiz
IGNEOUS
• Be a geologist!
Can you identify
which types these
rocks belong to?
METAMORPHIC

SEDIMENTARY
Photos: University of North Dakota, Grand Forks
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Quiz - Summary
1. Give three examples of volatile species in the solar
system, and say where they could be found.
2. What is the difference between a rock and a mineral?
3. Name the three main categories of rocks found on Earth,
and give an example of each.
4. What is a primitive rock, and where might one be found?
5. What processes lead to the formation of planetary
atmospheres?
6. What processes lead to the loss of atmospheres?
Dr Conor Nixon Fall 2006