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The Sun and Planets
Lecture Notes 1.
Spring Semester 2017
Prof Dr Ravit Helled
Lecture 1
Introduction to Planetary Science
Units in Planetary Science
S.I. Units (“Systeme Internationale”)
length unit:
time unit:
mass unit:
meter
second
kilogram
(m)
(s)
(kg)
Table — Astronomical Units
Unit
light-year
astronomical unit
Abb.
ly
AU
S.I. Equivalent
9.461 × 1015 m
1.496 × 1011 m
Description
distance that light travels in one year
average Sun-Earth distance
Note that it is also common in planetary science to report measurements in units of a
particular object (e.g., Earth radii, Jupiter masses, etc.). An example of these units would
be: 1 AU = 215 R (solar radii).
Basic Astronomical Objects
star — A large, glowing ball of gas that generates heat and light through nuclear fusion
in its core. The Sun is a star.
planet — A moderately large object that orbits a star and shines primarily by reflecting
light from its star. According to the 2006 definition of the IAU (International Astronomical Union), an object can be considered a planet only if it:
1. orbits a star
2. is large enough for its own gravity to make it round
3. has cleared most other objects from its orbital path
An object that meets the first two criteria, but has not cleared its orbital path, is a “dwarf
planet” (e.g. Pluto).
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exoplanet — A moderately large object that orbits a star and shines primarily by reflecting light from its star. According to the 2006 definition of the IAU (International
Astronomical Union), an object can be considered an exoplanet only if it:
1. orbits a star (or stellar remnant)
2. has a mass lower than the mass required for deuterium burning
3. fulfils the mass/size criteria of planets in the solar system
moon (or satellite) — An object that orbits a planet. The term satellite is also used
more generally to refer to any object orbiting another object.
asteroid — A relatively small and rocky object that orbits a star. Asteroids are “small
solar system bodies”
comet — A relatively small and ice-rich object that orbits a star. Like asteroids, comets
are considered “small solar system bodies”.
The Solar System
The Sun — An average star at the center of the solar system. The Sun is a G-class star
with a surface temperature of 5’800 K and a central temperature of 15 million K.
The Planets — Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune
The Asteroid Belt — A ring of small bodies between Mars and Jupiter with a combined
mass of ∼ 3 × 1021 kg. The largest asteroid in the belt, Ceres, accounts for 1/3 13 of the
asteroid belt’s mass.
The Comets — The two reservoirs (sources) of comets in the solar system are the Kuiper
belt (35–1’000 AU) and Oort cloud (30’000–100’000 AU).
Age
The age of the solar system is approx. 4.567 Gyr. Most of the objects in the solar
system show a similar age.
Mass
The Sun contains most of the mass in the solar system: Sun 99.85%, Planets 0.135%,
Comets 0.01%, Satellites 0.00005%. The planets account for less than 0.2% of the solar
system’s mass. The outer planets (Jupiter, Saturn, Uranus, Neptune) are much more
massive than the inner planets (Mercury, Venus, Earth, Mars).
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Orbits
The orbits of the planets are ellipses with the Sun at one focus. The orbits of the planets
are all more or less in the same plane (this plane is called the ecliptic). The planets
orbits are prograde (i.e., they orbit in the same direction as the Sun rotates) and roughly
circular. All of the planets’ orbits lie within approx. 30 AU of the Sun. The spacing
between the planets is large.
Angular Momentum
Over 98% of the angular momentum in the solar system is found in the orbital motions
of the giant planets, whereas 99% of the mass is found in the Sun.
Composition
Planets differ in composition, with a definite trend with distance from the Sun. Planets
closer to the Sun are denser and have higher metal contents. H and He abundances in
the giant planets decrease with distance from the Sun. The asteroids are mostly rocky.
The moons of the outer planets, as well as Kuiper belt objects, consist of rock and ice.
Kepler’s Laws
Kepler’s 1st Law Planets travel in an ellipse with the Sun at one focus.
Kepler’s 2nd Law The planet sweeps out equal areas in equal times (the planet
goes faster when nearer the Sun).
Kepler’s 3rd Law The square of the orbital period P of any planet is proportional
to the cube of the planet’s average distance from the Sun:
a3 = kP 2
If a is expressed in Astronomical Units (AU) and P in Julian (i.e. Earth) years,
then the constant of proportionality is k = 1.
Newton’s Laws
Newton’s 1st Law Every object in a state of uniform motion tends to remain in
that state of motion unless acted on by an external force.
Newton’s 2nd Law The relationship between an object’s mass m, its acceleration
α, and the force F applied upon it is F = mα.
Newton’s 3rd Law For every action there is an equal and opposite reaction.
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Gravitation
Newton’s law of universal gravitation states that an object attracts another object using a
force that is directly proportional to the product of their masses and inversely proportional
to the square of the distance between them:
F1 = F2 =
Gm1 m2
,
r2
where G = 6.67428 × 10−11 m3 kg−1 s−2 is Newton’s Gravitational Constant, m1 and m2
are the masses of the objects, and r is the distance between the objects. Both objects feel
the same force.
Gravity is a central force, meaning that the force depends on the distance from the center
[of mass]. This is why massive objects are round.
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