Geodesy of Terrestrial Planets

• 8 Planets and their satellites

• asteroids, comets, meteoroids

• sun

A planet is a celestial body that

• orbits around the sun

• has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equillibrium shape -> meaning its mass is large enough for it to become (nearly) spherical (if the mass is small, internal strength keeps it irregular) & the material behaves like a fluid over large timescales, allowing it to reshape

• has cleared the neighborhood around its orbit -> meaning there’s nothing of comparable size in its orbital path

  • if that’s not fulfilled but the other criteria are -> Dwarf Planet (like Pluto, which is part of the Kuiper Belt)

All planets, almost all asteroids & many comets orbit the sun in the same rotational sense (prograde; in the same direction as the sun rotates! This is counterclockwise viewed from the sun’s north pole). Most planets also rotate in the same rotational sense as they move around the sun (prograde) - exceptions are Venus (“upside down”, obliquity of 177°), Uranus (obliquity of 98°) & Pluto (obliquity of 120°) as well as some asteroids and comets.

The orbits are near-circular ellipses (low eccentricity) with an inclination of the ecliptic of almost zero (as if they were on a plate). Long-period comets like Hale-Bopp are an exception of this.

In general, all planetary motion follows the Kepler laws, which are:

• The orbit of a planet is an ellipse with the Sun at one of the two foci

• A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time (the closer the planet is to the sun, the faster it will travel)

• The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit (T² ~ a³) -> the bigger the distance is to the sun, the longer it takes the planet to travel around the sun

The Earth’s mean solar distance is 1 AU (around 149 million km).

Mercurys distance to the sun is 0.39 AU, while Pluto orbits at around 39.5 AU from the sun (Neptun: 30).

When a planet is between the Earth and the sun on the imaginary line that connects sun with earth, it’s in conjunction (inferior). When the planet is on the other side (sun is between Earth and planet) it’s also in conjunction (superior).

Opposition is referred to then the planet is on the opposite side of the Earth from the sun (Earth is in between planet and sun). That’s when the planet appears the brightest and clostest to earth.

Obliquity, also called axial tilt, is the angle between the planet’s rotational axis and the normal vector to the ecliptic.

For the Earth, this is 23°.

Rotation is the movement of the planet around the rotational axis.

Precession is when the rotational axis “wobbles” (change of orientation of the rot. axis, axis traces out a cone, Earth: ~25800 years) and nutation is when the rotational axis “nods” on top of the precession:

The rotation of planets is caused by a leftover “spin” from the early solar system (when planets form by gathering material around them, they started to spin similar to an ice skater pulling in their arms).

Both precession and nutation on Earth are caused by the gravitational forces of the sun and moon.

Precession is caused by the earth being a little flattened on the poles and a little bulged at the equator (due to its rotation). Gravity acts stronger on closer parts of the object. Equatorial bulge is closer, but due to Earth’s tilt, the bulge is not aligned with the line between Earth and the Sun/Moon. This misalignment causes twisting forces - the sun & moon pull more on one side than on the other. This causes the change of the direction of the rotational axis, similar to if you’d push a spinning top slightly. So, if a planet spins fast -> large bulge & has close moons, they will experience more precession.

Nutation is caused by the moon’s orbit being tilted slightly relative to the ecliptic (of the Earth). On top of that, the moons tilt is not fixed and the tilt direction changes due to precession. This causes the torque on the equatorial bulge to change slightly, causing nutation.

By the way: Other planets also have an effect on Earth’s precession! But minor.

• 3:2 Orbital Resonance between Neptune and Pluto: Pluto orbits the sun twice, whil Neptun orbits the sun three times in the same time

• 3:2 Spin/Orbit Resonance of mercury: Mercury orbits sun twice, and rotates three times

Mercury, Venus, Earth and Mars are considered Terrestrial Planets. They are composed mainly of iron and rock and are differentiated in a crust, mantle & core.

The Asteroid Belt is the region between Mars and Jupiter,a belt of millions of objects, including asteroids 200 > 100km, which is between the orbits of Mars and Jupiter. There are more asteroid belts like the Kuiper Belt, but this one is just called The Asteroid Belt.

The largest of the asteroids is called Ceres with a diameter of 950 km, now considered a dwarf planet.

A Theory is that the Asteroid Belt is the remains of a planet never formed due to the gravitational influence of Jupiter.

The Asteroid belt doesn’t include Jupiter’s Trojan clouds, which sit in his Lagrangian points L4 & L5 and are called “Greeks” and “Trojans”.

The Solar System formed 4.568 billion years ago when a large molecular cloud experienced gravitational collapse.

This contracting nebular began to spin -> formed protoplanetary disk. The center became hot due to spin -> protostar.

By accretion of material, the protoplanets were formed.

Inside the frost line, temperatures were too high to form ices, therefore only rock & metal could condense, forming terrestrial planets. Beyond the frost line, ices could form, leading to gas planets.

Beyond the soot line, there’s not enough heat to vaporize carbon -> stays solid, forms planets that are more carbon-rich -> my have to do with habitability

The protoplanets that didn’t manage to become planets congregated int the Asteroid belt, Kuiper belt & Oort cloud

• Sidereal period, the time required for a planet or a satellite, to return to the same state (rotation or position) relative to the stellar reference frame. For Earth: siderial day (stellar day): 23h 55m

• Synodic period, the time required for a planet or a satellite, to return to the same state (rotation or position) relative to some observer

  • synodic rotational period: time between successive recurrences of the same phase with respect to the Sun; e.g., for the Moon: the time between one and the next full moon. Earth synodic day: 24h (solar day)

  • synodic orbital period: time for the two planets to return to the same geometric configuration, as both go around the Sun, e.g. opposition or conjugation. Earth/Mars synodic period: 2.2 Earth years (for one opposition to the next)

For the synodic rotation period, some extra rotation is needed to complete the rotation, therefore synodic rotation periods are longer (for prograde orbits) but shorter (for retrograde orbits).

The Moon is the 5th largest natural satellite in the SOlar System, which is why Earth & Moon are sometimes called “double planet system”. Earth & Moon move around their common center of mass.

The mean Earth distance is ~ 385000km and the Moon orbits Earth with an orbital speed of around 1 km/s (comparison: Earth is around 30 km/s fast).

The orbit is slightly elliptic, which is why sometimes there’s a “Super moon”, where the Moon appears bigger in the sky.

The orbit is also nearly within the ecliptic plane (5° inclination), which means that the Moon does not orbit around Earth’s equator due to Earth’s obliquity. The Moons obliquity is 6.688°. The inclination to the ecliptic & the obliquity together result in a very small angle relative to the plane of its orbit around the sun and that the reason why the Moon does not have seasons.

An orbit takes 27.3 days, the synodic period is 29.5 days (from one full moon to the next), which is the reason why we see changing phases of the moon (full moon, crescent moon, new moon etc.).

Also, the Moon is tidally locked to Earth (although not completely), meaning it always shows Earth roughly the same side (nearside). The other side is called the farside.

There are more meteors at the morning.

In its path around the sun, Earth runs into more meteoroids on the leading edge. In the morning (before dawn), an observer looks towards the direction Earth is moving in its orbit and is therefore “standing on” the leading edge, which gets more meteoroids.

After sunset in the evening, an onbserver would look in the othher direction, on the trailing edge, where less meteoroids encounter the Earth.

This is also why the moon, as it’s tidally locked to Earth and therefore has a “fixed” leading edge (only considering the moons orbit and not Earth’s orbit), shows in studies that there are more craters on the leading edge of the moon.

The Moon was likely spinning faster a long time ago. However, as the moon orbits Earth, both bodies exert gravitational forces on each other, creating "tidal bulges”. Because Earth is spinning, the tidal bulges get pulled slightly ahead of time, so that they don’t sit exactly between Earth and Moon (additionally, friction on/inside the Earth causes a lag as well).

This creates a twisting force (torque) that gradually changes the rotation rates of both bodes and gradually changes their orbital distances and eccentricities as well.

That’s called tidal evolution. Over time, this process synchronizes rotations & orbits, leading to the Moon being (not completely) tidally locked. Additionally, this leads to a slowing of the rotation of the Earth, which in turn leads to the moon slowly spiralling away (3.8cm/year, as measured by LLR).

However, the moon is not completely tidally locked, it wobbles a bit in its orientation (called libration) -> we can see ~ 59% of the Moon’s surface! This is due to 3 reasons:

• its orbit eccentricity (while the rotation speed stays constant), causing a slight oscillation.

• the Moon’s axis is slightly tilted, causing libration in latitude

• the Moon isn’t a perfect sphere -> diurnal libration

Eclipses occur when the Earth, Moon & Sun are aligned - for this, the Moon needs to be on the ecliptic.

A solar eclipse looks like that because the apparent sizes of the moon and the sun, seen from Earth, are very similar (even though the apparent size of the Moon changes due to its orbit eccentricity).

The Moons surface consists of Maria (the dark patches) and Highlands (the lighter patches).

Maria (from latin: “seas”) are the lunar plains which are solidified pools of basaltic lava. Most of them are associated with impact basins (of meteroids and comets). They are found almost exclusively on the nearside of the Moon (maybe due to lower crustal thickness? More volcanism?).

Highlands (also Terrae) are the lighter-colored regions on the Moon, including mountain ranges like Montes Alpes.

The surface layer on the Moon’s crust is called Regolith and its thickness varies (3-5m in the (younger) maria, 10-20m in the (older) highlands. It was formed by impacts and mixing.

The surface is otherwise heavily cratered, and the impact craters accumulate at a early constant rate (with that, the age of the surface can be estimated). The craters are well reserved due to the lack of atmosphere & recent geological processes.

Some of the craters > 300km, called “basins”, sometimes filled with lava (“Mare basins”):

• Tycho

• Mare Imbrium

• Mare Crisium

The Lunar surface gravity is very low at 1.625 m/s².

The Gravity field is very irregular. It’s higher at mass concentratings associated with large impact basins.

The lunar interior is highly homogeneous with a mean density of 3.344 gr/cm³.

Chemistry data suggests that the Moon had a global Magma Ocean after formation and the crust has differentiated from it. The Moon has a small, partially molten deep interior, but the existence of a core is uncertain (a core needs to have a different composition than the mantle, typically metallic).

In Maria regions, the rocks common there are basalts, while in the highlands plutonic rocks are more common. The rocks brought back to Earth by missions were found to be very old at around 3.3 - 4.5 billion years.

The Moon has a magnetic field (1/100 from Earth in strength) from magnetized crustal rocks (therefore, it’s not active). This might be due to large impacts or maybe the early Moon did have a Dipole magnetic field (we don’t know).

From studies, we know that the composition of the Moon is similar to that of the Earth’s mantle.

Today, the most popular theory is that the Moon originated from an impact of a small planetary body with the early Earth (but Earth was already differentiated). Portions of the Earth’s crust and mantle were ejected into the Earth’s orbit, and the fragments re-accumulated to form the Moon.

A light year is the distance that light travels in a vacuum in one year. This equals 63240 AU.

• ITRS (International Terrestrial Reference System) with the Earth’s center of mass as origin

• ICRS (International Celestial Reference System)

Imagine the ecliptic of the Earth & the Earth’s equatorial plane as planes. Where they intersect, a line is formed (with the sun in the middle). The two points where Earth crosses the line are the Equinox points. There, day and night have the same lengths.

• Pioneer missions 0-5 (1958-60)

• Ranger missions in 3 blocks (1961-65), which produced images of the moon

• Surveyor missions (1966-68), which landed on the moon & performed ground tests as well as a laser test (for LLR)

• Lunar Orbiter missions (1966-67), which produced images of the moon with resolutions of up to 1m

• Apollo program (1968-72), manned missions which landed men on the moon. Missions 18-20 were cancelled, last men on the moon in 1972

• Luna 2 (1959), first spacecraft to reach the lunar surface

• Luna 3 (1959), returned first images of the farside of the moon

• Luna 9 (1966), first spacecraft to land succesfully on the moon

• Luna 13 (1966), returned images from the surface & studied luna soil

• sample missions: Luna 16, 20 & 24

• Lunokhod program, a robotic lunar rover program

• EM-1/2 (1990/1992), Galileo Earth Moon Flybys which analyzed the soil

• Clementine mission (1994), Laser Altimeter Experiment, was in a polar orbit and could therefore observe poles (ice at poles?)

• Smart-1 (2003), first European Lunar Mission

• Chang’e 1 (2007), Chinese mission

• SELENE (2007), japanese mission with a lot of instruments, for example spectrometers, altimeters, magnetometers etc.; searched for polar ice e.g. in Shackleton crater at the south pole

• Chandrayaan-1 (2008), indian mission

• Lunar Reconnaissance Orbiter LRO (2009), goals: produce a topographic model & image permanently shadowed polar regions of the moon

• Lunar Exploration Orbiter, never launched, from Germany

Mercury contains more iron relative to its total mass than any other planet in the solar system - its core is about 85% of its radius! (Earth: 55%). Therefore, Mercury has a high mean density and is nearly as dense as Earth (due to its core). This is unusual (from the terrestrial planets, Earth has the highest density, partly because the gravitational pressure is higher on Earth due to its size. This is why measuring the uncompressed density is more useful when you want to learn about the planets true composition).

Mercury has a 2:3 spin/orbit resonance; that means that Mercury rotates 3 times while it orbits the sun twice. This means that a synodic (solar) day on Marcury takes two Mercury years. It also means that the longitudes at 0° and 180° are aligned to face the sun at pericenter for every second orbit, absorbing a lot of solar energy and thus becoming the hottest spots on the planet over long timescales.

Also, Mercurys orbit has a relatively large eccentricity (e = 0.2), therefore it receives twice as much solar input at pericenter than at apocenter.

Together, these factors together produce an interesting phenomena on Mercury’s surface:

At pericenter, Mercury moves faster (2nd kepler law!), so fast that its orbital speed briefly overtakes its rotation speed. This leads to the sun rising, then stopping & moving backwards a bit before continuing “normally” on Mercurys surface.

Another fact is that Mercury orbits the sun at an elliptical path, therefore the points of closest approach (periphelion) slowly shifts over time. This is called periphelion precession and happens because of several factors, however, one that stayed a mystery for a long time was the shift due to General Relativity. Mercury is very close to the sun. General Relativity preditcs that spacetime is curved by mass, and this curvature alters the path of orbital objects, and thus the path of Mercury.

• Earth (dipole)

• Mercury (dipole)

Mars had a magnetic (dipole) field, but hasn’t anymore; we know this because the surface/crust is magnetized.

Venus doesn’t have a (dipole) magnetic field.

Max: 430°C

Min: -190°C

The strong differences are because Mercury doen’t have an atmosphere.

Some processes can lift surface atoms into the exosphere.

An example is Sputtering (mainly on Mercury), where high-energy particles (from the solar wind) strike the surface & knock atoms loose, which get ejected into the exosphere.

Mercury doesn’t have an atmosphere, therefore heat doesn’t persist on the sides of Mercury that are not exposed to the sun. Also, Mercury has a very low obliquity, leading to no seasons and permanently shadowed craters at the poles. At the poles, (water-) ice could occur.

It could be verified that there are deposits in the polar craters.

Mercury “wobbles” a bit because of Physical Longitudinal Libration, which are small oscillations in Mercurys rotation rate due to gravitational torques by the sun.

Measuring this provides clues about the internal structure of Mercury. If the core is molten, the mantle can oscillate independenttly, increasing the libration amplitude (similar to a raw vs cooked egg). This helps determining whether the core is solid or liquid. For this, the harmonic expansion coefficients C20 and C22 can be used. This is the so-called “Peale Experiment” from 1976.

It was found that Mercury has a molten core.

• Mariner 10 (1974/1975): 3 flybys

• MESSENGER (2011-2015, NASA): orbited Mercury, could only make altimeter measurements in the northern hemisphere

• BepiColombo (Mercury arrival December 2026, ESA/JAXA):

The MESSENGER mission to Mercury used a very elliptical orbit with an eccentricity of 0.74. Therefore, at periapsis, MESSENGER got very close to Mercury and got far away at apoapsis (& also farther away from the sun). This avoided excessive heat and lowered fuel comsumption as well. However, due to Mercurys mass distribution and solar activity, the periapsis was mostly over the northern hemisphere which is why only the northern hemisphere was mapped in high detail (as altimeters don’t work for high altitudes).

The Caloris Basin is a basin on Mercury and 1550 km in diameter (among the largest basins known in the Solar System).

It consists of the Central Basin, which is filled with smooth plains (possibly volcanic flows), the rings (multi-ring structure formed by shockwaves of the impact) and Carloris Montes, A mountain ring surrounding the basin, which was created by uplifted crustal blocks after impact.

It’s important for science because it procided evidence of volcanism after impact. It also excavated material from deep beneath Mercurys surface.

In the dissertation defense we also heard of a theory that the impact which created the Caloris basin may have changed the spin of Mercury.

• MDIS (Mercury Dual Imaging System): produced Stereo Images

• MLA (Mercury Laser Altimeter): produced topographic models

• MAG (Magnetometer): measured Mercurys magnetic field

Yes, there’s evidence for high tectonic activity in the past, e.g. km-thick deposits & volcanic events.

Mercurys “great valley” is the result of the global contraction & shrinking of Mercury. Mercury is a one-plate-planet, meaning when it cooled down, the whole crust is deformed (like a shriveling apple) by overlapping, cracking, etc., which forms giant valleys and ridges, such as the great valley. There are even some throughs that have been found on Mercury which can only survive meteroid bombardment if they’re fairly young - this means tectonic activity is still ongoing today!

This was confirmed by the MESSENGER mission.

The BepiColombo mission consists of the Mercury Transfer Module MTM , the Mercury Composite Spacecraft MCS, The MOSIF (a sunshield for MIO & also the connection between MPO and MIO), and two scientific modules:

The MMO or MIO (Mercury Magnetic Orbiter) from JAXA which focuses on the magnetic field & plasma, with 5 instruments, and

the MPO (Mercury Planetary Orbiter) from ESA which focuses on the surface & internal structure with 11 instruments, for example laser altimeter BELA (measures height & surface roughness), magnetometer, stereo camera.

When MIO and MPO get released, they will enter different orbits. MPO will have a low, stable polar orbit around Merucry to map the planet. MIO needs a wider orbit to cover more of Mercurys magnetic environment, using a orbit with higher eccentricity

Mercury orbits very close to the sun, therefore spacecrafts approaching gain a lot of speed due to the suns gravitational pull.

To slow down to be captured into Mercurys orbit, the spacecraft must lose a lot of energy to reduce its velocity, which would result in a high loss of fuel.

Therefore, BepiColombo must benefit from gravity; it does several flybys of Earth, Mercury and Venus to slow down the spacecraft and gradually lowers its orbit.

The Moment of Inertia MOI is a measure of how mass is distributed within a rotating body. It tells us how resistant a body is to rotational acceleration.

The general definition of MOI is (rho = density, r = radius, V = volume

For any sphere, MOI is defined as

Theta = I m R^2

where m is the mass, R is the radius and I is the Moment of Inertia coefficient. For homogenous spheres, I equals 0.4. If the planet has a dense core, I is lower, for spheres that are hollow the factor is higher. For example, for Earth, I = 0.3307, for the Moon 0.39 and for the sun 0.07.

Therefore, calculating the Moment of Inertia is important to understand a planet’s interior without drilling into it, which isn’t always possible.

The LRO is an orbiter which was launched by NASA to study the moon.

The Lunar Reconnaissance Orbiter LRO was launched in 2009 and still successfully returns data, even though the mission was initially planned to last only a year.

Its main goals are to produce a high-resultion global topographic model of the moon and to characterize the polar illumination environment including imaging permanently shadowed polar regions and their craters to identify possible locations of surface ice.

To archieve that, it has several instruments onboard, including LOLA (Lunar Orbiting Laser Altimeter) and the LROC (LRO Camera).

Since the LRO still works, it can now also monitor the surface to identify fresh craters.

The Gravity Recovery and Interior Laboratory (GRAIL) mission was a mission to the moon in 2012, which ended by impact on the lunar surface.

Its objectives were to map the structure of the lunar crust, determine subsurface structures of lunar basins, constrain the deep interior structure and place limits on the inner core size of the moon.

It consisted of two spacecrafts which performed range measurements between them (similar to GRACE on Earth), from which the gravity field can be determined.

It found that the Bouguer gravity anomalies of lunar basins reveal a bullseye pattern with a positive anomaly within the ring, surrounded by a gravity low. Further out, the gravity returns to normal. This positive anomaly is most likely caused by a mantle uplift after crater formation.

With the data, it was analyzed that the porosity is related to the formation age of a crater, meaning that the impacts modify the porosity of the upper lunar crust significantly.

• Chang’e program: 3 phases (orbital missions, landers/rovers, sample return)

  • 1: several Orbital missions (2007, 2010), goals were to produce 3D models of landforms, map the soil properties & study the lunar environment like the solar wind

  • 2: Landing missions (2013, 2018), which lead to the first soft lunar landing since 1976 & also the first landing on the farside. Deployed rovers.

  • 3: Sample return missions (2020, 2024): returned lunar soil including core probes from drilling

The principle of Laser Altimetry is to send and receive a laser pulse to a surface and measure its round-trip travel time.

For that to work, the spacecraft/satellite can’t have a too high altitude, therefore low orbiters (typical altitude of 100 - 1000km) are needed for the power of the returned laser pulse to be strong enough. Therefore, for global coverage they should have a polar orbit, meaning most of the data is in the polar regions and the tracks are further apart at the equator.

From the surface, the laser reflects diffusely, therefore less photons are returned to the transmitter.

There are Continous and Pulsed lasers - In geodetic mapping, pulsed lasers are used where each pulse if 10 - 100 ns long. Using laser shots of 20 ns, one can typically measure distances to typically within 3m.

In altimetry, e.g. a laser is used to measure the distance between a surface and a transmitter by measuring the round-trip travel time of the laser. The distance between the transmitter and the surface can’t be too big (typically 100-1000km)

In ranging, the distances are so big (typically 30000 - 400000km) that it needs a laser receiver or laser retroreflector to be able to do the range measurements (like in LLR).

• MOLA (Mars Orbiting Laser Altimeter), operated from 1997 - 2002

• Clementine mission, operated in 1994 on the moon

• SELENE Laser Altimeter, 2007 - 2009 on the moon (first global coverage of the moon at uniform resolution)

• LOLA (Lunar Orbiting Laser Altimeter) on LRO, launched in 2009 and still operating

• MLA (MESSENGER Laser Altimeter) on MESSENGER, mercury orbit insertion in 2011

• future: BELA (BepiColombo Laser Altimeter) to Mercury

The Artemis program is a deep space exploration program of NASA (in partnership with ESA, JAXA and others). The primary goal is to return humans to the moon (before the first manned chinese moon landing in 2030).

Additionally, a goal of the Artemis program is a new space station in moon orbit is planned, called Lunar Gateway. It is intended to serve as communication hub, science laboratory and habitation module for astronauts. It would be the first space station beyond low Earth orbit.

In 2022, there was the first (uncrewed) flight test of the Orion spacecraft, the Space Launch system (SLS) rocket and the ground systems.

The Orion Multipuropse Crew Vehicle (MPCV) sits atop the SLS rocket and includes the crew module which can support a crew of six.

The planet most similar to Earth is Mars, due to its similar obliquity (25.19°), day length (near-24h), tectonic activity (volcanoes), polar caps, etc.

Because of this Mars is the best known solar system planet and has had an extensive exploration program.

Mars has 38% of Earth’s gravity at its surface.

The atmospheric pressure is 1/150 of Earth’s atmospheric pressure, and the atmosphere contains 95% CO2, so much more than Earth’s atmosphere.

Mars orbital period is longer than Earth’s with 687 days (so around 22 months) at a mean distance to the sun of aboout 1.5 AU. But because the Mars orbit has a noticable eccentricity, the distance to the sun varies from 1.38 to 1.67 AU, which means that the seasons Mars experiences are different depending on the hemisphere.

The winters on the southern hemisphere are very long and cold (because that’s when Mars is farthest) but the summers are short and very hot (because that’s when Mars is closest). Meanwhile, on the northern hemisphere, the winters are shorter and the summers are longer and colder.

This also means that the distance between Earth and Mars when they’re in opposition can vary. Because Earth is moving faster, it passes Mars around every 26 months.

Mars has a pronounced dichotomy, meaning that topologically, the southern and northern hemipshere are very different. While the northern hemipshere is very low and flat and probably younger geologically, the southern hemisphere is higher (on average 6km higher) with lots of craters and a thicker crust.

A theory is that this dichotomy is due to an early large impact event.

Mars has several volcanic centers (for example Olympus Mons, 21 km elevation, no activity today) and graben systems (“Valles Marineris”, largest in known Solar Systems with 4000km length and up to 7km deep).

There are long-periodic oscillations in Mars obliquity and orbit eccentricity (predicted from numerical orbit analysis).

Mars obliquity varies between 15° and 35°, possibly up to 60°.

This is probably due to its proximity to Jupiter and due to no (bigger) moons (Earth’s Moon stabilizes the Earth rotation axis, the Martian moons are too small for that).

This can cause dramatic climate changes and caused the formation of the polar layers, which are different depending on the obliquity (low obliquity: stable ice cap growth at the poles, high obliquity: poles get more sunlight, polar ice moves). There has been evidence for a warm and wet climate on Mars in the past, for example outflow channels and fluvial deposits as well as the discovery of minerals like carbonates and salts that are known to form in water environments.

The polar ice caps of Mars consist of permanent water-ice caps with a CO2-ice cap on top.

During winter, the atmopshere partially condenses as CO2 ice onto the pole (as the Mars atmosphere consists almost entirely of CO2). This CO2 ice cap can grow up to 1km thick (nothern pole). In spring, the CO2 thaws again and sublimates back into the atmosphere.

On the southern pole, there is a permanent CO2 ice cap.

The atmopshere on Mars is thin and consists of 95% CO2. Still, it moderates the surface temperatures so that it varies from 20°C (equatorial summer) to -85° (southern winter).

Clouds are common, as seen from some rovers.

Since the atmospheric pressure is low, water evaporates quicker, therefore no liquid surface water is possible.

The atmosphere is dusty and near pericenter, dust storms are common which may reach global extent. This is because at pericenter, the solar heating is more intense but also uneven, creating a pressure gradient, leading to stronger winds. Dust devils and tornado tracks are frequently observed.

Mars has no dipole field, but a magnetized crust, therefore probably had a dipole in the past. There are patterns of magnetic anomalies, similar to Earth’s mid-ocean magnetic anomalies, so maybe there were early plate tectonics on Mars?

The Martian moons are Phobos and Deimos. They are very small and in irregular shape (Phobos, which is the bigger one, is only 26x23x18km in size) and have a low albedo, meaning they are very hard to see, which is why they were discovered very late.

They are relatively close to Mars, meaning the apparent size of Mars is very big seen from the moons. Phobos has a semimajor maxis of ~9400km, Deimos of ~23500km. However, Phobos orbit is decaying, and in 30-50 million years, it will be destroyed by tidal forces. Deimos on the other hand is moving outward and will eventually leave Mars.

Both are tidally locked to Mars.

Both Phobos and Deimos have a prograde orbit which is almost equatorial, but since the orbital period of Phobos is shorter than one Mars rotation, it rises in the West and sets in the East, twice a day.

The Roche limit is the distance in which a celestial body (for example a moon) disintegrates due to tidal forces exerted by a second body (for example its planet).

It depends on the density of the planet and the density of the moon. When the planet is dense and the moon has a low density (e.g. is fluid), the Roche limit is large, meaning the moon must stay farther away to “survive”.

For example, Phobos, one of the Martian moons, is inside the Roche limit for fluids, meaning it would break apart if it were not rigid. However, Phobos is rigid, and for rigid bodies it’s outside the Roche limit.

There are several theories on where Phobos and Deimos come from.

On theory is that they formed close to Mars, however, this does not account for a density differing so much from Mars.

They could also be captured asteroids, as they are of low density and are irregular in shape. However, asteroid orbits are usually ecliptic and have all kinds of inclinations, and Phobos and Deimos have nearly circular orbits in the equatorial plane of Mars. Therefore, Mars must have forced the asteroids onto the elliptic orbits of Phobos and Deimos, which could happen by atmospheric drag and tidal forces, however, the current Martian atmosphere is too thin for that.

Therefore, another theory is that there was an asteroid impact onto Mars which formed rings who accumulated again into moons which were then again destroyed by tidal forces and the new cycle began again so that there were several generations of moons. This is believed to have happened 5-6 times.

• CCD (Charge-Coupled Devices): widely used because of sensitivity and geometric stability, but can overflow

• APS (Active Pixel Sensors): every pixel has its own amplifier, is cheaper than CCD and radiation-tolerant, is therefore increasingly competetive

The HRSC is the High Resolution Stereo Camera on Mars Express, an ESA mission (the first European planetary mission) which arrived 2003 on Mars and is still ongoing.

The HRSC was the first camera in Mars orbit that was designed for precision mapping in 3D. It has 5 stereo viewing angles.

Today, the HRSC and MOLA compliment each other nicely as HRSC can fill gaps between MOLA tracks and MOLA data can be used to calibrate absolute heights of the HRSC Digital Terrain Models (DTMs).

• sensor type: CCD or APS

• pixel size: ~ 7 µm (e.g., HRSC camera)

• image resolution: 1000-1500 pixels per line (varies by mission)

• focal length: 100-1000mm (HRSC: 175mm)

• aperture diameter: varies

• f-number: common f/5.6, f/8, f/11

• field of view: narrow to medium which is optimized for mapping, no wide-angle imaging

• ground resolution: depends on altitude

• orbit altitude: typically 200-500 km

An Asteroid is a small rocky body orbiting the sun, mostly found in the “asteroid main belt” between Mars and Jupiter.

A Meteoroid is a small piece of asteroid or comet in space.

Meteors are then Meteoroids in the atmosphere and meteorites are meteors that landed on Earth.

Fireballs is a term for a very bright meteor.

A comet comes from the outer solar system and contains ice, leaving a trail when near the sun due to sublimation.

The biggest object in the Asteroid Main Belt is Ceres, a dwarf planet of 950km diameter that has low craters and with a possible cryovulcano. The largest asteroids are Vesta (which has one of the highest mointains in the solar system), Pallas and Hygia which are over 400km in diameter.

The total mass of the Asteroid Main Belt is 4% of Earth’s Moon, where Ceres accounts for 1/3.

The rotation of an asteroid can be determined from light observations. As the asteroid rotates, different parts of its surface face the observer, varying the observed brightness of the asteroid (since they are not spherical). The changes in brightness are regular and periodic, forming a pattern. The period of that pattern is then the rotation period of the object.

Large asteroids rotate similar to planets with an axis (more or less) perpendicular to the ecliptic, but smaller asteroids have larger variations. Smaller Asteroids also rotate faster and some tumble.

A rubble pile is an asteroid created by the reassembling on the fragments that resulted from a collision.

Asteroids are seperated into classes based on spectroscopy (how light interacts with matter).

• C-type: 75% of all asteroids, are carbonaceous, mostly found in outer belt

• S-Type: silicate, mostly found in inner belt

• M-type: metallic, mostly found in inner belt

• others

Collisions can completely shatter asteroids which can result in “asteroid families” which have simmilar orbital characteristics and compositions. 1/§ of asteroids belong to families.

Kirkwood Gaps are Gaps in the distribution of the asteroid belt, so, very few asteroids are found. These gaps correspond to orbital resonances with Jupiter, where the gravitational influence of Jupiter regularily perturbs asteroid objects.

For example, there are only few asteroids with a semimajor axis of 2.5 AU, which corresponds to a 3:1 orbital resonance (3 orbits around the sun for every 1 orbit of Jupiter). Jupiters gravitation destabilizes the orbit until they are ejected or collide.

Some resonances can send asteroids toward earth, these are called “source regions” for Near-Earth Objects (NEOs).

• Atens: average orbital radii closer than 1 AU & aphelia greater than Earth’s periphelion (see picture), which is why they are inside of the Earth orbit

• Apollos: average orbital radii greater than Earths

• Amors:avergae orbital radii in between the orbits of Earth and Mars, often cross the orbit of Mars, but not the orbit of Earth

• cretaceous-tertiary extinction event 66 million years ago, result of a large (10km) asteroid or comet impact event

• Tunguska Explosion (1908), caused by an >= 20m object. Explosion was recorded by seismograph stations as far as Potsdam. 1000 times stronger than “Little Boy” Hiroshima bomb

• Chelyabinsk Meteor Explosion (2013), meteor around 17m in diameter, 1500 people injured

500m-asteroid: One hit every 100000 years

1m asteroids: 20 hits per year

Venus has an obliquity of 177°, meaning it has a retrograde rotation, therefore, the sun rises in the west and sets in the east.

Venus’ rotation is also extremely slow, a sidereal day is 243 days, while the shorter (shorter bc rotation is retrograde!) synodic period is 116.7 days. A Venus year has only 224.7 days.

Since Venus is faster than Earth (because with 0.72 AU its closer to the sun), it “overtakes” Earth every 584 days, turning from an evening star to a morning star. It can only be seen in the morning/evening because Venus is (as seen from Earth) in the direction of the sun.

Venus has a very thick CO2 atmosphere which prevents observations of the surface with cameras. Therefore, observations are only possible with radar.

• Venera-5 to Venera-14, soviet mission: first landing & radar mapping in the 780s/80s

• Magellan mission: launch 89: global gravity field map & high resolution radar mapping

• Venus Express 2005-2014 (ESA): observe atmosphere

• three new missions: DAVINCI+ (launch 2030, NASA), VERITAS (launch 2028-2030), EnVision (launch 2032, ESA)

On Venus, there are 2 distinct highland “continents” that stand above smooth volcanic plains: Ishtar Terra (northern continent) and Aphrodite Terra (southern continent).

There are a lot of volcanic features, including volcanic domes and lava flows. However, since there is a lack of small craters, it is suggested that Venus had global volcanism (massive, planet-wide volcanic eruptions) and that the surface is young, likely younger than 500 million years.

The surface is also very hot due to the thick atmosphere (extreme greenhouse effect).

The Barometric Equation expresses how atmospheric pressure or density change with altitude. For example, if we want to know the atmoshperhic density of Earth at 10km height h, we can use this equation:

p(h) = p0 * e^(-h/H)

Where p0 is the atmospheric density on the ground and H is the scale height 7.8km.

At 10km, on Earth the atmsopheric denisty is 0.334 kg/m³, which is 27.7% of the density at the ground.

M = 5.3 x 10^15 tons (From more exact models: 5.13 x 10^15 tons)

Earth has the “Earth atmosphere” with mainly nitrogen (78%), oxygen (21%) as well as some CO2, water and argon.

Mars has a thin atmopshere which consist mainly of CO2 (95%), a little nitrogen and even less argon and oxygen.

Mercury has so significant atmosphere.

Venus has a CO2 atmpsphere which consists iof 96.5% CO2 and 3.5% nitrogen.

The atmopsheres of the gas giants mainly consist of hydrogen (around 90%), helium and CH4 (methane).

For two satellites with identical shape, the satellite with the smaller mass will experience more drag. For two satellites with identical mass, the satellite with the larger cross section will experience more drag. The drag/friction will slow down the spacecraft and at some point, the orbiting satellite will enter the planet’s atmopshere. This can be useful for orbit insertions!

Since the atmopshere on Mars is thin, aircrafts on Mars would encounter similar conditions to those at 30km altitude on Earth where conventional aircrafts can’t fly because the air is too thin.

It is much harder to generate lift in thin air. To maintain flight, aircrafts require large-area wings and/or high speed to provide the required lift.

The challenge is therefore to get the airplane off the ground.

1. Body Waves (travel through planet)

   1. P-Waves (Primary Waves): arrive first, can pass through solids, liquids and gases

   2. S-Waves (Secondary Waves): arrive after P-waves, can only pass thorugh solids; absence on other side of planet: hints at a liquid core

2. Surface Waves (travel along the planet’s surface)

   1. Love waves: horizontal side-to-side motion, cause strong shaking

   2. Rayleigh waves: rolling motion like ocean waves

The seismic network is sparse and they are relatively close together, so they can’t triangulate deep refractions globally.

Also, most Moonquakes are weak, as there are no plate tectonics, therefore fewer usable seismic waves penetrate the deep interior (although there are some deep moonquakes which correlate in time with lunar tides).

An additional problem is that the lunar crust is fractured and dry, leading to a strong scattering of the waves, which makes it hard to identify wave types and their arrival times.

Therefore, there is no data available for depths greater than 1100km.