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 1
Jupiter s Orbit Kepler s third law relates the semi-major axis a to the orbital period P 2 P years Solving for the period P yields 3 a = AU 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 The distance from the Sun varies by about 10% during an orbit D perihelion = 4.95 AU D aphelion = 5.45 AU Jupiter s Orbit 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 R jupiter = 71,400 km = 11.2 R earth M jupiter = 1.9 x 10 30 g = 318 M earth The volume of Jupiter is therefore given by V 4 = π 3 Hence V jupiter = 1.5 x 10 30 cm 3 3 jupiter R jupiter 2
Bulk Properties of Jupiter The average density of Jupiter is therefore ρ jupiter M = V jupiter jupiter 30 1.9 10 g = 30 1.5 10 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 3
Surface Gravity We can compute the surface acceleration on a planet or moon using Newton s laws of motion and gravitation: - GMm F = ma = 2 R Solving for the surface acceleration A yields - GM A = 2 R A earth - GM = R Surface Gravity Using values for the Earth, Moon, Mercury, and Jupiter, we obtain for the surface accelerations A mercury - GM = R earth 2 earth mercury 2 mercury = 9.8ms A moon = 3.7 ms A 2 GM = R jupiter 2 moon 2 moon - GM = R jupiter 2 jupiter = 1.7 ms 2 = 24.9 ms 2 The acceleration at the cloud level on Jupiter is over twice that on the Earth s surface 4
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 5
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 6
Atmosphere of Jupiter Atmospheric composition: Earth: H 2 -- 86.1% Nitrogen: 78% He -- 13.8% Oxygen: 21% CH 4 -- trace Argon: 0.4% NH 3 -- trace Carbon dioxide: 0.03% H 2 O -- 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 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? Atmosphere of Jupiter 7
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 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 3 o tilt of Jupiter s spin axis, and the heat of formation escaping from the interior 8
9
With a radius of 71,500 km and thickness of 100 km, the atmosphere is mostly molecular hydrogen gas, H 2 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 Interior of Jupiter Jupiter s Moons A small telescope reveals the four Galilean moons: Io Europa Ganymede Callisto JPL s Jupiter Website 422,000 km orbit 671,000 km orbit 1,070,000 km orbit 1,880,000 km orbit 10
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 11
Jupiter s Moons 12
Galileo at Jupiter Galileo (1989-2003) Cassini at Jupiter Cassini (1997-2004) Cassini movies 13
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 Structure Io iron, rock 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 Density 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 Ganymede Callisto 14
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 15
Ganymede 16
Io 17
Callisto 18
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 19