Orbiter 2010 Telescope Manual

Not to be confused with in the sense of a selenocentric orbit, that is, an orbit around the MoonThe completes its around the in approximately 27.32 days (a ). The Earth and Moon orbit about their (common centre of mass), which lies about 4 600 km from Earth's centre (about three quarters of the Earth's radius). On average, the Moon is at a distance of about 385 000 km from the centre of the Earth, which corresponds to about 60 Earth radii. With a mean orbital velocity of 1.023 km/s, the Moon moves relative to the each hour by an amount roughly equal to its, or by about 0.5°. The Moon differs from most of other in that its orbit is close to the plane of the, and not to the Earth's. The lunar orbit plane is inclined to the ecliptic by about 5.1°, whereas the Moon's is inclined by only 1.5°.PropertyValue384 748 kmmean distance385 000 kminverse sine parallax384 400 kmDistance at perigee 362 600 km( 356 400– 370 400 km)Distance at apogee 405 400 km( 404 000– 406 700 km)Mean0.054 9006(0.026–0.077)Mean of orbit to ecliptic5.14°(4.99–5.30)Mean6.58°Mean inclination of lunar equator to ecliptic1.543°Period of18.5996 yearsPeriod of recession of line of apsides8.8504 years.

With the Earth scaled to the size of a basketball, the Moon is the sizeof a tennis ball and orbits at the distance of the 3-point line. Andwith the court as the ecliptic plane, the Moon's orbit extends out ofthat plane by the distance of a tennis racket (10.46 Moon diameters).The properties of the orbit described in this section areapproximations. The Moon's orbit around the Earth has manyirregularities , whose study has a long history.Elliptic shapeThe orbit of the Moon is distinctly elliptical, with an averageof 0.0549. The non-circular form of the lunar orbit causes variationsin the Moon's angular speed and apparent size as it moves towards andaway from an observer on Earth. The mean angular movement relative to animaginary observer at the barycentre is 13.176° to the east (Julian Day 2000.0 rate).Line of apsidesThe orientation of the orbit is not fixed in space, but over time. The nearest and farthest points in the orbit are the and respectively. The line joining these two points (the ) rotates slowly in the same direction as the Moon itself (direct motion), making one complete revolution in 3 232.6054 days or about 8.85 earth years.ElongationThe Moon's is its angular distance east of the Sun at any time.

At new moon, it is zero and the Moon is said to be in. At full moon, the elongation is 180° and it is said to be in. In both cases, the Moon is in, that is, the Sun, Moon and Earth are nearly aligned.

When elongation is either 90° or 270° the Moon is said to be in.NodesThe nodes are points at which the Moon's orbit crosses the ecliptic.The Moon crosses the same node every 27.2122 days, an interval calledthe or draconitic month. The line of nodes, the intersection between the two respective planes, has a:for an observer on Earth it rotates westward along the ecliptic with aperiod of 18.60 years, or 19.3549° per year.

Orbiter 2010 Manual

When viewed from celestialnorth, the nodes move clockwise around the Earth, opposite the Earth'sown spin and its revolution around the Sun. Lunar and solar eclipses canoccur when the nodes align with the Sun, roughly every 173.3 days.Lunar orbit inclination also determines eclipses; shadows cross whennodes coincide with full and new moon, when the sun, earth, and moonalign in three dimensions.InclinationThe mean inclination of the lunar orbit to theis 5.145°. The rotation axis of the Moon is also not perpendicular toits orbital plane, so the lunar equator is not in the plane of itsorbit, but is inclined to it by a constant value of 6.688° (this is the ).One might be tempted to think that, as a result of the precession ofthe Moon's orbital plane, the angle between the lunar equator and theecliptic would vary between the sum (11.833°) and difference (1.543°) ofthese two angles. The Moon orbiting Earth with sizes and distances to scale. Each pixel represents 500 km.History of observations and measurementsAbout 3,000 years ago, thewere the first human civilization to keep a consistent record of lunarobservations.

Clay tablets from that period, which have been found overthe territory of present-day Iraq, are inscribed withwriting recording the times and dates of moonrises and moonsets, thestars that the Moon passed close by, and the time differences betweenrising and setting of both the Sun and the Moon around the time of the. Discovered the three main periods of the Moon's motion and used to build lunar calendars that extended well into the future. This use of detailed, systematic observations to make predictions based on experimental data may be classified as the firstin human history.

However, the Babylonians seem to have lacked anygeometrical or physical interpretation of their data, and they could notpredict future lunar eclipses (although 'warnings' were issued beforelikely eclipse times).astronomers were the first to introduce and analyze of the motion of objects in the sky. Described lunar motion by using a well-defined geometric model of and.was the first to develop a complete theory of motion, mechanics. Thesheer wealth of humanity's observations of the lunar motion was the maintestbed of his theory.Lunar periods. See also:NameValue (days)Definitionsidereal month27.321 661 55with respect to the distant stars (4 passes per solar orbit)synodic month29.530 588 86with respect to the Sun (phases of the Moon, 4 passes per solar orbit)tropical month27.321 582with respect to the (precesses in 26,000 years)anomalistic month27.554 550with respect to the perigee (recesses in 3 232.6054 days = 8.850578years)draconic (nodical) month27.212 220 815with respect to the ascending node (precesses in 6 793.4765 days = 18.5996 years)There are several different periods associated with the lunar orbit.

The is the time it takes to make one complete orbit of the earth with respect to the fixed stars, it is about 27.32 days. The is the time it takes the Moon to reach the same visual.This varies notably throughout the year. But averages around 29.53days.

The synodic period is longer than the sidereal period because theEarth–Moon system moves in its orbit around the during each sidereal month, hence a longer period is required to achieve a similar alignment of the earth, sun and moon. The is the time it takes to go fromto perigee, the points of closest approach to the earth. The earth-moonseparation determines the strength of the lunar tide raising force.This period is around 27.55 days.The is the time from to ascending node. The time between two successive passes of the same ecliptic longitude is called (the ).

The latter three periods are slightly different from the sidereal month.The average length of a calendar month (a twelfth of a year) is about30.4 days. This is not a lunar period, though the calendar month ishistorically related to the visible lunar phase. See also:, andThe attraction that the Moon exerts on Earth is the major cause ofin the sea; the Sun has a lesser tidal influence. If the Earthpossessed a global ocean of uniform depth, the Moon would act to deformboth the solid earth (by a small amount) and the ocean in the shape ofan ellipsoid with high points roughly beneath the Moon and on theopposite side of the Earth. However, because of the presence of thecontinents, the much faster rotation of the earth and varying depths, this simplistic visualisation does not happen. While theperiod is generally synchronized to the Moon's orbit around Earth, itsrelative timing varies greatly. In some places on Earth, there is onlyone high tide per day while others have four, though this is somewhatrare.The notional tidal bulges are carried ahead of the Earth–Moon axis bythe continents as a result of the Earth's rotation.

Orbitor 2010 Telescope Manual

The eccentric massof each bulge exerts a small amount of gravitational attraction on theMoon, with the bulge on the side of the Earth closest to the Moonpulling in a direction slightly forward along the Moon's orbit (becausethe Earth's rotation has carried the bulge forward). The bulge on theside furthest from the Moon has the opposite effect, but because thegravitational attraction varies inversely with the square of distance,the effect is stronger for the near-side bulge. As a result, some of theEarth's angular (or rotational) momentum is gradually being transferredto the rotation of the Earth-Moon couple about their mutual centre ofmass, called the.This slightly faster rotation causes the Earth-Moon distance toincrease at approximately 38 millimetres per year.

In keeping with the,the Earth's axial rotation is gradually slowing, and the Earth's daythus lengthens by about 23 microseconds every year (excluding ). Both figures are valid only for the current configuration of the continents.from 620 million years ago show that, over hundreds of millions ofyears, the Moon receded at an average rate of 22 millimetres per yearand the day lengthened at an average rate of 12 microseconds per year,both about half of their current values. See for a more detailed description and references.The Moon is gradually receding from the Earth into a higher orbit, and calculationssuggest that this would continue for about fifty billion years. By thattime, the Earth and Moon would become caught up in what is called a'spin–orbit resonance' or 'in which the Moon will circle the Earth in about 47 days (currently 27days), and both Moon and Earth would rotate around their axes in thesame time, always facing each other with the same side. (This hasalready happened to the Moon—the same side always faces Earth. This isslowly happening to the Earth as well.) However, the slowdown of theEarth's rotation is not occurring fast enough for the rotation tolengthen to a month before other effects change the situation: about 2.3billion years from now, the increase of the Sun's will have caused the Earth's oceans to vaporize, removing the bulk of the tidal friction and acceleration.Libration. Animation of the Moon as it cycles through its phases.

The apparent wobbling of the Moon is known as libration.The Moon is in,meaning that it keeps the same face turned toward the Earth at alltimes. This synchronous rotation is only true on average, because theMoon's orbit has a definite.As a result, the angular velocity of the Moon varies as it moves aroundthe Earth and hence is not always equal to the Moon's rotationalvelocity. When the Moon is at its,its rotation is slower than its orbital motion, and this allows us tosee up to eight degrees of longitude of its eastern (right). Conversely, when the Moon reaches its,its rotation is faster than its orbital motion and this reveals eightdegrees of longitude of its western (left) far side. This is referred toas longitudinal.Because the lunar orbit is also inclined to the Earth's eclipticplane by 5.1°, the rotation axis of the Moon seems to rotate towards andaway from us during one complete orbit. This is referred to as latitudinal libration,which allows one to see almost 7° of latitude beyond the pole on thefar side. Finally, because the Moon is only about 60 Earth radii awayfrom the Earth's centre of mass, an observer at the equator who observesthe Moon throughout the night moves laterally by one Earth diameter.This gives rise to a diurnal libration, which allows one to view an additional one degree's worth of lunar longitude.

For the same reason, observers at both of the Earth would be able to see one additional degree's worth of libration in latitude.Path of Earth and Moon around Sun. The Moon's orbital path around the Sun (gray) as it accompanies theEarth in its own path around the Sun (blue) is always convex outwards. (In this diagram, the Sun is below and to the left of the frame.)When viewed from the north, i.e.

From the star, the Moon orbits the Earth, the Earth orbits the Sun anticlockwise, and the Moon and Earth rotate on their own axes anticlockwise.Thecan be used to indicate the direction of the angular velocity. If thethumb of the right hand points to the north celestial pole, its fingerscurl in the direction that the Moon orbits the Earth, the Earth orbitsthe Sun, and the direction the Moon and Earth rotate on their own axes.In representations of the,it is common to draw the trajectory of the Earth from the point of viewof the Sun, and the trajectory of the Moon from the point of view ofthe Earth. This could give the impression that the Moon circles aroundthe Earth in such a way that sometimes it goes backwards when viewedfrom the Sun's perspective. Since the orbital velocity of the Moon aboutthe Earth (1 km/s) is small compared to the orbital velocity of theEarth about the Sun (30 km/s), this never occurs. There are no rearwardloops in the Moon's solar orbit.Considering the Earth–Moon system as a binary planet, its centre ofgravity is within the Earth, about 4,624 km from its centre or 72.6% ofits radius. This centre of gravity remains in-line towards the Moon asthe Earth completes its diurnal rotation. It is this mutual centre ofgravity that defines the path of the Earth–Moon system in solar orbit.Consequently the Earth's centre veers inside and outside the orbitalpath during each synodic month as the Moon moves in the oppositedirection.Unlike most moons in the Solar System, the trajectory of the Moonaround the Sun is very similar to that of Earth.

The Sun's gravitationaleffect on the Moon is more than twice that of the Earth's on the Moon;consequently, the Moon's trajectory is always convex(as seen when looking Sunward at the entire Sun–Earth–Moon system from agreat distance outside the Earth/Moon solar orbit), and is nowhereconcave (from the same perspective) or looped.