The Earth – Moon System

THE EARTH – MOON SYSTEM

Martin Crow Crayford Manor House Astronomical Society

The Solar System


The Solar System : Earth Moon system

Last time:

The formation of the Sun (and Solar system).

About the Sun

The Sun’s effect on the Earth.


The Solar System : Earth Moon system

This week:The formation of the Earth and Moon

Consequences of a gravitationally bound system.The local gravitational environment

Phases of the Moon and its orbital characteristics.

Solar and Lunar eclipses.


Some Physical data

Earth

Mean Earth Sun distance = 149.6 x 10⁶ km (1 A.U.)

Inclination to the Sun’s equator = 7.16°

Mean diameter = 12,742 km

Mass = 5.97 x 10²⁴ kg

Mean density = 5.52 x 10³ kg/m³ (water = 1 x 10³ kg/m³)

Axial tilt = 23° 26’ 21”

Albedo = 0.3 (Bond)


Moon

Mean Earth Moon distance = 384.4 x 10³ km

Sidereal month = 27.321582 days (27 d 7 h 43.1 min) relative to fixed frameof reference.

Mean diameter = 3,474 km

Mass = 7.35 × 1022 kg

Mean density = 3.35 x 10³ kg/m³

Synodic period = 29.530589 d (29 d 12 h 44 min 2.9 s) New Moon to new Moon andis commonly called a Lunar month.

Albedo = 0.12 (Bond)

Draconic month = 27.2122 days (the nodes precess over a period of 18.6 years)

Anomalistic month = 27.5546 days (the line of Apsides connecting Perigee and Apogee precesses over a period of 8.85 years.


Formation of the Earth – Moon system

The Earth formed 4.567 x 10⁹ years ago from the disk of material orbiting the newly forming Sun.


The Moon is now thought to have formed during an impact with a Mars sized object the so called ‘giant impact hypothesis’. This would have been within the first 50 x 10⁶ years of the formation of the solar system.



Computer simulations are consistent with observations such as:

The measured angular momentum of the Earth- Moon system.

The small size of the Moon’s core.

The composition of the Moon.


A. Initial Accretion of the Moon, probably from debris launched into Earth orbit by a mega-impact.

B. In the last stages of accretion, so much heat accumulates that the outermost 100 km of the lunar crust melts to form a magma ocean. C. Late impacts excavate giant basins.

D. Mare Nectaris and other basins form.

E. Mare Imbrium forms.

F. Mare Orientale forms

G. Mare basalts erupt and flood many of the impact basins.

H. Since 3000 Ma, only a few large rayed craters like Tycho and Copernicus have formed.


The Lunar surface

Near side Far side





Structure

Earth

Moon


Life on Earth


Consequences of a gravitationally bound system.

Due to tidal drag the Moon’s rotation has become locked into its rotationaround the Earth.The effect of this is that the Moon rotates only once for every orbit. Whichis why we only see one face.The Moon raises tides on Earth with the effect that the Earth spin is slowed.This loss of energy is transferred to the Moon thereby increasing its speed. This causes the Moon to move away from the Earth by 38mm every year.Although the Earth’s spin rate reduces by only 2.3 ms per year (not constantover time and depends on the configuration of the continents) this adds up over time. During the Devonian period 400 x 10⁶ years ago the year was 400days long with each day approx. 21.9 hrs.


The local gravitational environment.

The Lagrangian points.


The Phases of the Moon

Syzygy – When the Earth, Moon and Sun are aligned.

Quadrature – When the Moon’s elongation is either 90° or 180°

Orbital period = 27.321582 days Synodic period = 29.530589 d


The Moons orbit

The line of Apsides joins the points of Perigee and Apogee and precesses over8.85 years.

The Moons orbit is an ellipse.

The Moon crosses the same node every27.2122 days (the Draconic month)The Nodes precess in a retrogrademotion over a period of 18.6 years.

The Moons orbit is inclined at an angleof 5° 8´ to the Ecliptic.

Lunar and Solar eclipses can only occurwhen the line of the nodes point towards the Sun, roughly every 5.4 months.The type of eclipse will depend on the Moon’s orbital circumstance.


Images showing the apparent size difference due to the Moon’s non circular orbit and alsoLibration.


Eclipses

How does a solar eclipse occur.


Solar eclipses occur in cycles called Saros cycles. The Saros cycle is based on the recognition that 223 synodic months approximately equal to 242 draconic months and 239 anomalistic months.

At this time there are 41 different Saros series in progress.

Each Saros series is given a number. Odd numbers are used for solar eclipses occurring at the ascending node and evens for the descending node. The opposite is true for Lunar eclipses.

Each series lasts for between 1226 and 1550 years depending on the geometry.

During the life time of a series of eclipses the path for odd numbered Saros serieswill travel from south to north and visa versa.




Total eclipse showing the solar coronaAnnular eclipse

The totally eclipsed Sun is safe to look directly at. Bright stars and any visible planets will be seen in the sky.

A Solar eclipse will only last a few minutes and depends on the geometry of the Earth, Sun, Moon alignment.


The 1919 Solar eclipse observed by Sir Arthur Eddington gave observationalevidence that proved the Einstein’s theory of general relativity was correct.

Martin Crow Crayford Manor House Astronomical SocietyCornwall 1999 Aug 11 MVCrow



The 2006 Turkey eclipse as seen from the ISS.


Diamond ring

China 2008 Aug 01 MV Crow



Eclipses

How does a lunar eclipse occur.





The Planets


Mercury

Average distance from Sun = 57.9 x 10⁶ km

Diameter = 4,878 km

Has quite an eccentric orbit

Has a 3:2 resonance so it rotates threetimes for every two orbits.Takes 88 days to complete one orbit.(Sidereal period)The synodic period is 115.9 days.

Albedo = 0.068 (Bond)


Venus


Diameter = 12,102 km

Albedo = 0.9 (Bond)Takes 224.7 days to complete one orbit.(Sidereal period)The synodic period is 583.9 days.

Very dense atmosphere of CO₂ with a surfacepressure of 93 bar (Earth = 1 bar)

Surface temperature of 460° C


Mars


Diameter = 6,792 km

Albedo = 0.25 (Bond)Takes 687 days to complete one orbit.(Sidereal period)The synodic period is 780 days.

Very thin atmosphere of CO₂ with a surfacepressure of 0.006 bar (Earth = 1 bar)Surface temperature of -87° C to 20°C.

Mars has two moons – Phobos and Deimos both probably captured asteroids.


Jupiter


Diameter = 142,984 km at equator

Albedo = 0.34 (Bond)Takes 11.9 years to complete one orbit.(Sidereal period)The synodic period is 399 days.

Atmosphere of Hydrogen with a rocky core overlaid by a deep layer of metallic hydrogen.


Moons of Jupiter – the Galilean moons.

Io Europa

Ganymede Callisto

Jupiter has in total 65 confirmed moons.


Saturn

Average distance from Sun = 1,422 x 10⁶ km



Atmosphere of Hydrogen with a small rocky core.


Moons of Saturn

Saturn has at least 62 moons.


Saturn’s rings

The rings are 93% water ice and very thin – 20 m !!!

They are composed of objects ranging in size from mm to meters.


Uranus




Atmosphere of Hydrogen with a small rocky core.

Rotates on its side relative to the plane of the solar system.Discovered 1781 March 13 by William Herschel.


Moons of Uranus

Uranus has 27 known moons and a ring system.


Neptune



Albedo = 0.29 (Bond)Takes 164.8 years to complete one orbit.(Sidereal period)The synodic period is 367.5 days.

Atmosphere of Hydrogen, Helium and Methane with a small rocky core.

Discovered 1846 September 23 by Urbain Le Verrier, John Couch Adams and Johann Galle.


Moons of Neptune

Neptune imaged in Methane light andShowing Proteus, Larissa, Galatea andDespina.

Neptune also possesses a ring.


Trans-Neptunian objects

A trans-Neptunian object in 2:3 mean motion resonance with Neptune. For every 2 orbits that a plutino makes, Neptune orbits 3 times. Plutinos are namedafter Pluto, which follows an orbit trapped in the same resonance

Plutinos form the inner part of the Kuiper belt and represent about a quarter of the known Kuiper belt objects (KBOs).


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The Earth – Moon System