Download Lecture 23: Jupiter Solar System Jupiter`s Orbit

Lecture 23: Jupiter
Solar System
Jupiter’s Orbit
•The semi-major axis of Jupiter’s orbit is a = 5.2 AU
Jupiter
Sun
a
•Kepler’s third law relates the semi-major axis to the orbital
period
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Jupiter’s Orbit
•Kepler’s third law relates the semi-major axis a to the orbital
period P
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⎛ P ⎞ ⎛ a ⎞
⎜⎜
⎟⎟ = ⎜
⎟
⎝ years ⎠ ⎝ AU ⎠
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•Solving for the period P yields
⎛ P ⎞ ⎛ a ⎞
⎜⎜ years ⎟⎟ = ⎜ AU ⎟
⎠
⎠ ⎝
⎝
3/ 2
•Since a = 5.2 AU for Jupiter, we obtain P = 11.9 Earth years
•Jupiter’s orbit has eccentricity e = 0.048
Jupiter’s Orbit
•The distance from the Sun varies by about 10% during an orbit
™Dperihelion = 4.95 AU
™Daphelion = 5.45 AU
•Like Mars, Jupiter is easiest to observe during favorable opposition
•At this time, the Earth-Jupiter distance is only about 3.95 AU
Jupiter
(perihelion)
Earth
Sun
Jupiter
(aphelion)
•Jupiter appears full during favorable opposition
Bulk Properties of Jupiter
•Jupiter is the largest planet in the solar system
•We have for the radius and mass of Jupiter
™Rjupiter = 71,400 km = 11.2 Rearth
™Mjupiter = 1.9 x 1030 g = 318 Mearth
•The volume of Jupiter is therefore given by
Vjupiter =
4
π R 3jupiter
3
•Hence Vjupiter = 1.5 x 1030 cm3
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Bulk Properties of Jupiter
•The average density of Jupiter is therefore
ρ jupiter =
M jupiter
Vjupiter
=
1.9 × 1030 g
1.5 ×1030 cm 3
•We obtain
ρ jupiter = 1.24 g cm −3
•This is much less than the average density of the Earth
•Hence there is little if any iron and no dense core inside Jupiter
Bulk Properties of Jupiter
•The average density of the Earth is equal to
ρ ⊕ = 6 g cm −3
•The density of water is:
ρ water = 1 g cm −3
•The density of rock is:
ρ rock = 2 − 4 g cm −3
Bulk Properties of Jupiter
•The average density of Jupiter is about that of water…
ρ water = 1 g cm −3
ρ jupiter = 1.24 g cm −3
•Jupiter is composed mostly of hydrogen gas
•It has a relatively small, rocky core
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Surface Gravity
•We can compute the surface acceleration on a planet or moon
using Newton’s laws of motion and gravitation:
F = mA =
- GMm
R2
•Solving for the surface acceleration A yields
A=
- GM
R2
Surface Gravity
•Using values for the Earth, Moon, Mercury, and Jupiter, we
obtain for the surface accelerations
A earth =
A mercury =
- GM earth
= 9.8 m s − 2
2
R earth
GM
A moon = − 2 moon = 1.7 m s − 2
R moon
- GM mercury
R 2mercury
= 3.7 m s − 2
A jupiter =
- GM jupiter
R 2jupiter
= 24.9 m s − 2
•The acceleration at the cloud level on Jupiter is over twice that
on the Earth’s surface
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Jupiter’s Spin
•We can try to determine the rotation (spin) period of Jupiter by
tracking the motions of its colorful clouds
•The rotation period is different for clouds in bands A, B, and C
•Jupiter does not rotate as a solid body!
•This is called differential rotation
•Is there any way to find a single, meaningful rotation period for
the entire planet?
Video of Jupiter’s Atmosphere
Jupiter’s Spin
•The strong magnetic field rotates with a period of about 10 hours
•This probably indicates the rotation period of the planet’s deep
interior
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Auroras
on
Jupiter
Jupiter’s Spin
•This is a very short rotation period; the shortest in the solar
system!
•The centripetal force due to the spin produces a bulge of about
5,000 km at Jupiter’s equator
•The rapid spin produces a huge Coriolis force that affects the
atmospheric circulation
Jupiter’s Spin
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Atmosphere of Jupiter
•Atmospheric composition:
•Earth:
™H2
-- 86.1%
™Nitrogen: 78%
™He
-- 13.8%
™Oxygen: 21%
™CH4
-- trace
™Argon: 0.4%
™NH3
-- trace
™Carbon dioxide: 0.03%
™H2O
-- trace
™Water vapor: 0.1-3%
™Water ice clouds
™Ammonia ice clouds
•This is totally different from the terrestrial planetary atmospheres
•Jupiter is massive enough and cold enough to retain its primordial
hydrogen gas (primary atmosphere)
Atmosphere of Jupiter
•In terms of its composition, Jupiter closely resembles the Sun
•In fact, Jupiter could have been a star if it’s mass were about
1,000 times larger
•The various colorful cloud layers have different compositions and
physical properties
•The band and cloud patterns change with location and time due to
™Flows of gas
™Local chemical processes
™Changes in physical conditions
•The different colors occur at
different depths in the atmosphere
Atmosphere of Jupiter
•The temperature at the
cloud tops on Jupiter is
about 125 K
•The expected equilibrium
temperature at Jupiter’s
distance from the Sun is
only about 105 K
•Consequently, Jupiter is
radiating about twice as
much energy as it receives
from the Sun
•Where is the extra heat
coming from?
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Atmosphere of Jupiter
•Heating due to the
radioactive decay of heavy
elements is not strong
enough to explain the
temperature of Jupiter
•We think that the heat is
leftover from the initial
“squeeze” when Jupiter
collapsed under the
influence of gravity
•Because Jupiter is a very
large planet, this “heat of
formation” has not all
leaked out into space yet
Atmosphere of Jupiter
•Jupiter’s atmosphere shows very complex patterns of motion
•There are bands, clouds, and storms
•The bands display shear flow
•The Great Red Spot is a storm a few times the size of Earth that
has lasted for hundreds of years
•The complex motions are explained by the combination of solar
heating, the rapid spin, the 3o tilt of Jupiter’s spin axis, and the
heat of formation escaping from the interior
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Interior of Jupiter
•With a radius of 71,500 km
and thickness of 100 km, the
atmosphere is mostly
molecular hydrogen gas, H2
•A huge shell of metallic
hydrogen under great
pressure exists below a radius
of 50,000 km
•Farther inside lies the rocky
core, with a radius of about
10,000 km
•The temperature at the center
is about 40,000 K and the
pressure is about 50 million
bars
Jupiter’s Moons
•A small telescope reveals the four Galilean moons:
•Io
422,000 km orbit
•Europa
671,000 km orbit
•Ganymede
1,070,000 km orbit
•Callisto
1,880,000 km orbit
JPL’s Jupiter Website
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Primary Solar System Moons
Jupiter’s Moons
•There are dozens of moons orbiting Jupiter
•The primary, or Galilean, satellites are Io, Europa, Ganymede,
and Callisto
•Most are in synchronous orbits and are frozen solid
•An exception is Io, which has many active volcanoes
Io
Europa
Ganymede
Callisto
Jupiter’s Moons
•The moons of Jupiter form something like a “miniature Solar
system” around Jupiter
•The properties of Jupiter’s moons vary with the distance from
the planet
Io
Europa
Ganymede
Callisto
•The densities of the moons decrease with increasing distance
from Jupiter
•This is called “differentiation” and it is similar to what we find in
the Solar System
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Jupiter’s Moons
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Galileo at Jupiter
•Galileo (1989-2003)
Cassini at Jupiter
•Cassini (1997-2004)
•Cassini movies
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Jupiter’s Moons
•There is a trend towards more ice and less differentiation as we
work our way out through the Jovian system of satellites:
Satellite
Composition
™Io
iron, rock
Structure
differentiated
™Europa
icy crust, rock
differentiated
™Ganymede
ice and rock
differentiated
™Callisto
ice/rock mixture
undifferentiated
Io
Europa
Ganymede
Callisto
Jupiter’s Moons
•Next we compare the bulk properties of the Galilean moons:
Satellite
Mass
™Io
1.22 x lunar
3.6 g cm-3
™Europa
0.65 x lunar
3.0 g cm-3
™Ganymede
2.02 x lunar
1.9 g cm-3
™Callisto
1.47 x lunar
1.9 g cm-3
Io
Europa
Density
Ganymede
Callisto
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Jupiter’s Moons
•Io is similar in size, mass, and density to Earth’s moon, but it has
active volcanoes!
•The heating of Io is due to the strong tidal force of nearby Jupiter
•Why isn’t Io in a synchronous orbit?
•Because it’s orbit is elliptical, due to the gravitational influence of
Europa
Jupiter
Io
Europa
Europa
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Ganymede
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Io
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Callisto
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Jupiter’s Moons/Rings
•The pattern of more ice and less differentiation as we
work our way out through the Jovian system indicates
that the satellites experienced less heating during their
formation the farther they were from Jupiter
Io
Europa
Ganymede
Callisto
•We will see that this is similar to the pattern we see in the
solar system itself
•Jupiter also has a ring, although much smaller than
Saturn’s…
Jupiter’s Ring
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