Inner Solar System

The Earth

Earth Structure

earth-intererior-structure — A schematic drawing of the major sections inside the earth

Region	Thickness	Constituents
Inner core	1300 km	Solid Iron & Nickel
Outer core	2250 km	Liquid Iron & Nickel
Mantle	2900 km	Rocky (heavy elements)
Crust	8-40 km	Rocky (lighter elements)
Atmosphere	16 - 480 km	Gasses

Earth Atmosphere

Fraction (by mass)	Fraction (by number)	Species
75.5 %	78.1 %	N₂
23.1 %	20.9 %	O₂
1.3 %	0.93 %	Ar
0.05 %	0.04 %	CO₂
trace	trace	Ne, He, CH₄, Neon, He, Methane, Krypton

atmosphere-layers — The Atmosphere of the Earth

Earth Magnetosphere

Origins of the Magnetosphere

geo-dynamo-Glatzmaier-Roberts — Simulation of the geo-dynamo fields

Contemporary Physics, 1997, 38 4, Glatzmaier, G. and Roberts, P. http://dx.doi.org/10.1080/001075197182351

The Dynamo Theory: Moving charges.

Why is the Earth magnetic?
Why has its magnetic field existed over at least 70% of geological time?
Why is it predominantly dipolar?
What determines its strength?
Why does its strength vary, but by so little?
Why does the magnetic compass needle point approximately North?
Why does the averaged geomagnetic axis coincide with the geographical axis?
Why does the polarity of the Earth’s field reverse?
What happens to the geomagnetic field during a reversal and why?
Why does the frequency of reversals vary so greatly over geological time?
Why is neither polarity of field favored over the other?
What causes the slow secular change of the field?
What is the significance of the westward drift?
Can a single mechanism explain why other planets and satellites are magnetic too?

The Earth's Magnetic field

Strength: 25 to 65 microteslas (0.25 to 0.65 gauss).

The north magnetic pole is in Greenland

It flips sometimes. (Last time was about 780,000 years ago.)

What does it do?

magnetosphere-solar-wind — Illustration of Earth's magnetic field

ESA/C. T. Russel

Van Allen Radiation Belts

Van Allen Probes

Johns Hopkins University Applied Physics Laboratory

Van Allen Probe - Science Overview

NASA

Van Allen Probe - Instruments

NASA

Earth's shape

Precession

torque-on-bulge — The spheroid allows for a torque, which leads to a precession.

Precession

The North Pole Star changes! Just very slowly.

The Moon

Moon Structure

moon-intererior-structure — Lunar internal structure

Formation

Artist's_concept_of_collision_at_HD_172555 — Moon Formation

By NASA/JPL-Caltech - http://www.nasa.gov/multimedia/imagegallery/image_feature_1454.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=8626942

Giant-impact hypothesis

Earth's spin and moon's orbit have similar orientations
Moon samples indicate that the Moon's surface was once molten.
The Moon has a relatively small iron core.
The Moon has a lower density than Earth.
Evidence exists of similar collisions in other star systems (that result in debris disks).
The stable-isotope ratios of lunar and terrestrial rock are identical, implying a common origin.

Explorations

First Touch

Luna_2_Soviet_moon_probe — Luna 2: Soviet Moon Probe, September 12, 1959

By NASA - http://nssdc.gsfc.nasa.gov/database/MasterCatalog?sc=1959-014A, Public Domain, https://commons.wikimedia.org/w/index.php?curid=16509292

Apollo Program

apollo11-1 — On the lunar surface

NASA: flickr album

1961 to 1972
First manned flight: 1968
First landing: Apollo 11, July 1969
Last landing: Apollo 17, Dec 1972
Missions brought back 842 lbs of rocks
Left several science experiments
Installed Retro-Reflectors

Earth Moon System

Tides

Tidal Locking

tidal-bulge-locked — A torque will arise if the two angular velocities are different, due to the tidal bulge.

Moon is leaving

Lunar Laser Ranging Experiment with the stereo camera in the background (NASA image number AS11-40-5952). This Retroreflector was left on the Moon by astronauts on the Apollo 11 mission. Astronomers all over the world have reflected laser light off the reflectors to measure precisely the Earth-Moon distance.

NASA https://www.hq.nasa.gov/office/pao/History/alsj/a11/AS11-40-5952.jpg

3.8 cm/year

Tidal Braking

Over time, the tidal bulge will create a counter-torque to the rotation. This will cause the central object to rotate just a little bit slower. We can measure this: $$\begin{equation} \frac{dP_\textrm{rot}}{dt} = 0.0016 \; \textrm{s} / \; \textrm{century} \end{equation}$$ But this implies a change in $L$! Where does it go?

Let's start with the angular momentum $L$ of the moon in orbit around the earth. It depends on the mass of the moon, its speed and its distance from the center of rotation. $$\begin{equation} L_\textrm{orbit} = M_\textrm{moon} v r = M_\textrm{moon}\left( \frac{G M_\textrm{E} }{r}\right)^{(1/2)}r = \left( G M_\textrm{E} M_\textrm{moon}^2 r\right)^{(1/2)} \end{equation}$$ Consider the change in angular momentum as a function of time: $$\begin{equation} \frac{dL_\textrm{orbit}}{dt} = \left(G M_\textrm{E} M_\textrm{moon}^2\right)^{(1/2)}\frac{1}{2}r^{-1/2}\frac{dr}{dt} \label{eq:moondLdt} \end{equation}$$ If the earth and moon are considered the only two bodies in the system, then any change in ang. momentum of the moon will have to be balanced by a change in angular momentum of the earth, i.e. the earth's rotation speed. $$\begin{equation} \frac{dL_\textrm{orbit}}{dt} = -\frac{dL_\textrm{rot}}{dt} \end{equation}$$

For a rotating body, the angular momentum is a product of the moment of inertia, $I$, and the angular velocity, $\omega$: $$\begin{equation} L_\textrm{rot} = I \omega \end{equation}$$ Considering the earth a sphere: $$\begin{equation} I = \frac{2}{5}M_\textrm{E} R_\textrm{E}^2 \end{equation}$$ which leads to: $$\begin{equation} L_\textrm{rot} = \frac{2}{5}M_\textrm{E} R_\textrm{E}^2 \left( \frac{2 \pi }{P_\textrm{rot}}\right) \end{equation}$$ where $P_\textrm{rot}$ is the rotational period. Considering the first time derivative: $$\begin{equation} \frac{d L_\textrm{rot}}{dt} = \frac{4 \pi M_\textrm{E} R_\textrm{E}^2}{5} \left(- \frac{1}{P_\textrm{rot}^2} \frac{dP_\textrm{rot}}{dt} \right) \end{equation}$$

Using \eqref{eq:moondLdt}, and the conservation of angular momentum, we obtain: $$\begin{equation} \frac{\left(G M_\textrm{E} M_\textrm{moon}^2\right)^{1/2}}{2r^{1/2}}\frac{dr}{dt} = \frac{4 \pi M_\textrm{E} R_\textrm{E}^2}{5 P_\textrm{rot}^2} \frac{dP_\textrm{rot}}{dt} \end{equation}$$

Rearranging for $dr/dt$: $$\begin{equation} \frac{dr}{dt}= \frac{8 \pi}{5} \left(\frac{M_\textrm{E} r}{G} \right)^{1/2}\frac{R_\textrm{E}^2}{M_\textrm{moon} P_\textrm{rot}^2} \frac{dP_\textrm{rot}}{dt} \label{eq:drdtmoon} \end{equation}$$ $dP/dt$ is measurable: $$\begin{equation} \frac{dP_\textrm{rot}}{dt} = 0.0016 \; \textrm{s} / \; \textrm{century} \end{equation}$$ Putting this into \eqref{eq:drdtmoon} yields a rate of motion as: $$\begin{equation} \frac{dr}{dt} \approx 4 \; \textrm{cm} / \; \textrm{yr} \end{equation}$$

Moon Phases

moon-orbit-phases — The moon in orbit showing its phases.

The phases of the moon in 2024

https://science.nasa.gov/moon/

Mercury

mariner 10 diagram — Mariner 10 spacecraft - launched November 3, 1973, Mercury 1st flyby March 1974

By NASA / Jet Propulsion Laboratory - http://solarsystem.nasa.gov/multimedia/display.cfm?IM_ID=1563http://www.nasa.gov/multimedia/imagegallery/image_feature_1483.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1182348

The Messenger Mission

messenger trajectory — The complicated trajectory to get to Mercury.

MercuryOrbitInsertionDirectionofSunFull — The 1st science orbit

By NASA, Jet Propulsion Laboratory, Applied Physics Laboratory - MESSENGER Website, Public Domain, https://commons.wikimedia.org/w/index.php?curid=15235525

MESSENGER has provided multiple lines of evidence that Mercury’s polar regions host water ice. The permanently shadowed craters near Mercury’s north pole have thermal environments that allow water ice to be stable in these craters either at the surface or a few tens of centimeters below the surface.

NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington

Mercury - stats

Atmosphere: None!
Temperature

Daytime: 700 K at equatorial noon
Nighttime: 100K at polar regions

Interior:

Little is known (hard to get to)
Probably has iron-rich interior
Probably has very thin silicate crust
Probably has some molten material in core – observed magnetic field is weak

mercury-3-2-spin-orbit — Mercury rotates 3 times during 2 orbits.

Orbital and Rotational Periods
Orbital Period	87.969 Earth Days
Rotation Period	58.646 Earth Days

Venus

Physical Parameters
Mass	$4.867 \times 10^{24} \; \textrm{kg}$	$0.815 M_\textrm{E}$
Radius	$6,051.8 \; \textrm{km}$	$0.9499 M_\textrm{E}$
Year	224.701 days	0.615 years
Rotation	once every 243 Earth days	Clockwise!
Eccentricity	0.006772	(nearly circular)
Magnetic Field	None	(due to slow rotation)

Greenhouse Effect

A planet is located a distance $D$ away from an energy source.

How hot would a planet be, if it didn't have an atmosphere?

$a$ is the albedo, or how much energy is reflected.
(1 = all of it, 0 = none of it.)

The Luminosity of the sun is: $$\begin{equation} L_\textrm{Sun} = 4 \pi R_\textrm{Sun} \sigma_\textrm{SB} T_\textrm{Sun}^4 \end{equation}$$ Now consider a planet a distance $D$ away from the sun. The power received by the planet would just be the ratio of its cross section to a sphere of radius $D$. The energy received per second will be $$\begin{equation} P_\textrm{in} = L_\textrm{Sun} (1-a)\left(\frac{\pi R_p^2}{4 \pi D^2} \right) \end{equation}$$ If the planet radiates as a blackbody, then: $$\begin{equation} P_\textrm{out} = 4 \pi R_p^2 \sigma_\textrm{SB} T_p^4 \end{equation}$$ In thermodynamic equilibrium: $P_\textrm{out} = P_\textrm{in}$

Thus, we can say: $$\begin{equation} L_\textrm{Sun} (1-a)\left(\frac{\pi R_p^2}{4 \pi D^2} \right) = 4 \pi R_p^2 \sigma_\textrm{SB} T_p^4 \end{equation}$$ Solving for $T_p$ $$\begin{equation} T_p = T_\textrm{Sun}(1-a)^{1/4} \sqrt{\frac{R_\textrm{Sun}}{2 D}} \end{equation}$$ Putting number relevant to the Earth and Sun in to this equation, yields a temperature for the earth equal to 255K = -19° C=-1° F. Obviously, we're missing something from this analysis: the greenhouse effect. Take away: the greenhouse effect is real.

https://www.weather.gov/jetstream/absorb

Venus' Atmosphere

Top of clouds is 250 K, however, at the surface the temperature is 750 K, above the melting point of Lead.
Atmospheric Carbon Dioxide prevents outgoing infrared radiation.
Pressure at the surface is about 90 atm.

The Soviet Union's Venera 14 probe captured two color panoramas of Venus's surface in 1982. This panorama came from the rear camera. Russian Academy of Sciences / Ted Stryk

https://www.planetary.org/space-images/venus-surface-panorama-from-venera-14-camera-2

Venus' Volcanos

More volcanos than any other object in the solar system. (>1500 major)
Unclear if they are active or not.

Venera Mission

Mars

Mars, from space. Mosaic of the Valles Marineris hemisphere of Mars projected into point perspective, a view similar to that which one would see from a spacecraft. The distance is 2500 kilometers from the surface of the planet, with the scale being .6km/pixel.

Credit: NASA/JPL-Caltech

Physical Parameters
Mass	$6.42 \times 10^{23} \; \textrm{kg}$	$0.107 M_\textrm{E}$
Radius	$3397 \; \textrm{km}$	$0.533 M_\textrm{E}$
Year	686.9 days	1.8807 years
Rotation	24 h 37 min 22.6 s
Eccentricity	0.0934
Magnetic Field	Weak	Probably larger in the past

Mars' Atmosphere

The atmosphere of Mars is mainly composed of carbon dioxide (95 %). It contains only 2 % nitrogen and 0.1–0.4 % oxygen.

The air pressure is only 5–8 mbar. Much has been lost. No greenhouse effect.

Mars' Surface

It's red: Iron Oxide aka rust.

Polar Caps: water ice and CO₂

mars-ocean — Mars may have had oceans

NASA's Goddard Space Flight Center

Indications are that water has flowed on Mars in the past. Geologic features like river beds and other erosion indicators suggest this. No liquid water has been found on the surface. Too cold and the pressure is too low.

Mars' Moons

Two relatively small moons: Phobos and Deimos