Lecture 20 - Uranus and Neptune Lecture Notes

Uranus and Neptune

Discoveries of Uranus and Neptune

• Uranus and Neptune are the 7th and 8th planets from the Sun, respectively.
• They are gas giants (Jovian planets), similar to Jupiter and Saturn.
• These planets are so far away that ancient astronomers were unaware of them.
• Uranus was discovered in 1781 by William Herschel using a telescope, marking the first planet discovered in over 2000 years.
  • It is barely bright enough to be seen without a telescope, and only under ideal conditions if you know exactly where to look.
• Herschel noticed an object that moved relative to background stars and realized it was not a star or comet.
• Voyager 2 flew by Uranus in 1986, providing the first up-close images of the planet.
  • The upper atmosphere appeared nearly featureless, with only a few wispy clouds in the northern hemisphere.
• The orbit of Uranus was found to deviate from a perfect ellipse; the discrepancy grew to 15 arc-seconds over 50 years.
• In 1845-6, John Adams and Urbain Le Verrier independently deduced that another body was causing the orbital anomaly of Uranus.
  • They used Newton's Laws to predict the location of an eighth planet.
  • In late 1846, astronomer Johann Galle discovered Neptune within one or two degrees of the predicted location.
  • The mathematicians, Adams and Le Verrier, received credit for the discovery, and the planet was named Neptune.
• Like Uranus, details of Neptune cannot be discerned from Earth-based telescopes.
• Voyager 2 flew by Neptune in 1989, providing the first close-up pictures.
  • Neptune's upper atmosphere shows more features than that of Uranus, including cloud streaks ranging from 50 km to 200 km wide.

Orbital and Physical Properties

• The period of Uranus' orbit is $P = 83.75$ Earth years.
• Kepler's Third Law can be used to calculate Uranus' semimajor axis, $a$, using the formula: $P^2 \text{ (in Earth years)} = a^3 \text{ (in AU)}$.
  • Solving for $a$ gives: $a = (83.75)^{2/3} \text{ AU} = 19.2 \text{ AU}$.
• Uranus' orbit has an eccentricity of $e = 0.047$.
  • The distance from Uranus to the Sun varies by about 10% during its orbit.
  • Perihelion: 18.3 AU
  • Aphelion: 20.1 AU
• Observations of parallax of Neptune show that its semimajor axis is $a = 30.1 \text{ AU}$.
• Kepler's Third Law can be used to calculate Neptune's orbital period, $P$.
  • Solving for $P$ gives: $P = (30.1)^{3/2} \text{ years} = 164 \text{ years}$.
• Neptune's orbit has an eccentricity of $e = 0.009$.
  • The distance from Neptune to the Sun varies by about 2% during its orbit.
  • Perihelion: 29.8 AU
  • Aphelion: 30.3 AU
• Neptune's orbital period is 164 years.
  • Since its discovery in 1846 (173 years ago), Neptune has completed just over one orbit around the Sun.
• Like other Jovian planets, Uranus and Neptune rotate quickly and exhibit differential rotation.
• The rotation period of Uranus is 17.2 hours, based on magnetic field measurements.
• Unlike other Jovian planets, Uranus' spin axis is tilted by 98 degrees, which is almost perpendicular to its orbital axis.
• The rotation period of Neptune is 16.1 hours, based on observations of its magnetic field, and the tilt of Neptune's spin axis is 29.6 degrees.
• Due to Uranus' axial tilt of 98°, the planet experiences extreme seasons.
  • Its equatorial regions have two summers at the equinoxes (42 years apart) and two winters at the solstices, with its poles plunged into darkness for 42 years at a time.
• During Uranus' solstices, when the northern hemisphere points toward the Sun, almost the entire southern hemisphere is in total darkness (and vice versa).
• The reason for Uranus' large axial tilt is not well understood but might be the result of collisions during the solar system's formation.
• Uranus' physical properties:
  • Radius: 25,559 km = 4.0 R⊕
  • Mass: $8.68 × 10^{25} \text{ kg} = 14.5 M⊕$
  • Density: 1270 kg/m3
  • 27 moons (as of 2021)
  • Faint rings discovered from Earth
• Neptune’s physical properties:
  • Radius: 24,766 km = 3.9 R⊕
  • Mass: $1.02 × 10^{26} \text{ kg} = 17.1 M⊕$
  • Density: 1640 kg/m3
  • 14 moons (as of 2021)
  • Faint rings discovered by Voyager 2
• Neptune and Uranus are very similar.

Atmospheres of Uranus and Neptune

• Spectroscopic studies of reflected sunlight show that the outer atmospheres of Uranus and Neptune have a similar composition to those of Jupiter and Saturn, but with more methane ($\text{CH}_4$).
  • Hydrogen ($\text{H}_2$): 84 %
  • Helium (He): 14 %
  • Methane ($\text{CH}_4$): 2 %
  • Almost no Ammonia ($\text{NH}_3$)
• Abundances of ammonia ($\text{NH}<em>3$) and methane ($\text{CH}</em>4$) vary systematically across the Jovian planets.
  • Jupiter has more gaseous ammonia than methane.
  • Uranus has more gaseous methane than ammonia.
  • As distance from the Sun increases, the amount of ammonia in a planet's atmosphere decreases relative to methane.
  • Temperature is the reason: ammonia freezes into crystals at 70 K.
  • Since the upper atmosphere of Uranus is 58 K, ammonia does not exist as a gas, but as ice.
• Methane is a good absorber at longer wavelengths (red light).
  • A higher concentration of methane means more red light is absorbed by the atmosphere, so the planet has a more bluish color.
  • The blue-green color of Uranus results from methane in its atmosphere.
• The cloud-top temperature on Uranus is around 58 K, which is below the freezing point of ammonia.
  • This temperature is close to the predicted equilibrium value at that distance from the Sun.
  • Unlike the other Jovian planets, Uranus lacks an internal heat source.
• Low amounts of high-level clouds mean that weather patterns (storms) cannot readily be seen, as they are blocked by high atmospheric haze.
• High winds (200 km/h to 500 km/h) form bands like Jupiter, but are buried deeper in the atmosphere.
• Uranus' atmosphere is efficient at transporting energy around the planet; the temperature difference between winter and summer sides is only a few K.
• Wind speeds near the poles are higher than at the equator, probably due to the higher amount of sunlight these regions receive.
• Composition of Neptune's atmosphere:
  • Hydrogen ($\text{H}_2$): 86.1 %
  • Helium (He): 13.8 %
  • Methane ($\text{CH}_4$): 3%
  • Almost no Ammonia ($\text{NH}_3$)
• Neptune's atmosphere is similar in composition to Uranus', except that there is more methane (3% compared to 2% on Uranus), giving it a more blue appearance.
• Despite being farther from the Sun, Neptune's upper atmosphere is slightly warmer than Uranus'.
• Neptune has an internal heat source that is responsible for pronounced weather patterns.
  • High-level clouds are observed, and several storm systems are clearly visible from space.
  • The most prominent storm was the Great Dark Spot, observed by Voyager 2.
• The Great Dark Spot was similar to Jupiter's storms.
  • Wind speeds exceeded 1500 km/h.
  • It was roughly the size of Earth.
  • By the time Hubble images were taken in 2011, the Great Dark Spot had disappeared for unknown reasons.
• Other large storms have appeared and disappeared on Neptune since Voyager 2.
• These storms are much more short-lived than those on Jupiter.

Magnetospheres and Internal Structure

• Uranus and Neptune have strong magnetic fields, about 100 times stronger than Earth's.
• Unlike other planets, their magnetic fields are inclined at large angles with respect to their rotation axes.
  • Uranus: 60°
  • Neptune: 40°
• Unlike other planets, the magnetic fields of Uranus and Neptune are significantly off-center.
  • This suggests different physics are responsible for their magnetic fields.
  • Their magnetic fields must not be produced by dynamos, as other planets' fields are.
• Theoretical models suggest that Uranus and Neptune have rocky cores similar to Jupiter and Saturn (about 10 Earth masses).
• Uranus and Neptune are smaller than Jupiter and Saturn.
  • The rocky cores of Uranus and Neptune make up a larger fraction of the planet compared to Jupiter and Saturn.
• Pressure outside the cores of Uranus and Neptune is too low to form metallic hydrogen.
  • The origin of the magnetic field is therefore probably very different than Jupiter and Saturn.
• A possible