Orbit of the Moon
synodic) 29.530 days | | |
precession of nodes | 18.5996 years | |
---|---|---|
precession of line of apsides | 8.8504 years |
The
With a mean
Properties
The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations (perturbations) due to the gravitational attraction of the Sun and planets, the study of which (lunar theory) has a long history.[7]
Elliptic shape
The orbit of the Moon is a nearly circular ellipse about the Earth (the semimajor and semiminor axes are 384,400 km and 383,800 km, respectively: a difference of only 0.16%). The equation of the ellipse yields an eccentricity of 0.0549 and perigee and apogee distances of 362,600 km (225,300 mi) and 405,400 km (251,900 mi) respectively (a difference of 12%).
Since nearer objects appear larger, the Moon's apparent size changes as it moves toward and away from an observer on Earth. An event referred to as a "supermoon" occurs when the full Moon is at its closest to Earth (perigee). The largest possible apparent diameter of the Moon is the same 12% larger (as perigee versus apogee distances) than the smallest; the apparent area is 25% more and so is the amount of light it reflects toward Earth.
The variance in the Moon's orbital distance corresponds with changes in its tangential and angular speeds, as stated in
Elongation
The Moon's
Precession
The orientation of the orbit is not fixed in space but rotates over time. This orbital precession is called
Inclination
The mean inclination of the lunar orbit to the
The rotational axis of the Moon is not perpendicular to its orbital plane, so the lunar equator is not in the plane of its orbit, but is inclined to it by a constant value of 6.688° (this is the
Nodes
The nodes are points at which the Moon's orbit crosses the ecliptic. The Moon crosses the same node every 27.2122 days, an interval called the
In effect, this means that the "
The solar eclipse of September 1 of the same year, the Moon was near its ascending node, and the Sun was near the point in the sky where the equator of the Moon crosses the ecliptic. When the Sun reaches that point, the centre of the Sun rises at the lunar north pole and sets at the lunar south pole.
Inclination to the equator and lunar standstill
Every 18.6 years, the angle between the Moon's orbit and Earth's equator reaches a maximum of 28°36′, the sum of Earth's equatorial tilt (23°27′) and the Moon's orbital inclination (5°09′) to the ecliptic. This is called major lunar standstill. Around this time, the Moon's declination will vary from −28°36′ to +28°36′. Conversely, 9.3 years later, the angle between the Moon's orbit and Earth's equator reaches its minimum of 18°20′. This is called a minor lunar standstill. The last lunar standstill was a minor standstill in October 2015. At that time the descending node was lined up with the equinox (the point in the sky having right ascension zero and declination zero). The nodes are moving west by about 19° per year. The Sun crosses a given node about 20 days earlier each year.
When the inclination of the Moon's orbit to the Earth's equator is at its minimum of 18°20′, the centre of the Moon's disk will be above the horizon every day from latitudes less than 70°43' (90° − 18°20' – 57' parallax) north or south. When the inclination is at its maximum of 28°36', the centre of the Moon's disk will be above the horizon every day only from latitudes less than 60°27' (90° − 28°36' – 57' parallax) north or south.
At higher latitudes, there will be a period of at least one day each month when the Moon does not rise, but there will also be a period of at least one day each month when the Moon does not set. This is similar to the seasonal behaviour of the Sun, but with a period of 27.2 days instead of 365 days. Note that a point on the Moon can actually be visible when it is about 34 arc minutes below the horizon, due to atmospheric refraction.
Because of the inclination of the Moon's orbit with respect to the Earth's equator, the Moon is above the horizon at the
The Moon's light is used by zooplankton in the Arctic when the Sun is below the horizon for months[13] and must have been helpful to the animals that lived in Arctic and Antarctic regions when the climate was warmer.
Scale model
History of observations and measurements
About 1000 BC, the Babylonians were the first human civilization known to have kept a consistent record of lunar observations. Clay tablets from that period, which have been found over the territory of present-day Iraq, are inscribed with cuneiform writing recording the times and dates of moonrises and moonsets, the stars that the Moon passed close by, and the time differences between rising and setting of both the Sun and the Moon around the time of the full moon. Babylonian astronomy discovered the three main periods of the Moon's motion and used data analysis to build lunar calendars that extended well into the future.[7] This use of detailed, systematic observations to make predictions based on experimental data may be classified as the first scientific study in human history. However, the Babylonians seem to have lacked any geometrical or physical interpretation of their data, and they could not predict future lunar eclipses (although "warnings" were issued before likely eclipse times).
Sir Isaac Newton was the first to develop a complete theory of motion, mechanics. The observations of the lunar motion were the main test of his theory.[7]
Lunar periods
Name | Value (days) | Definition |
---|---|---|
Sidereal month |
27.321662 | with respect to the distant stars (13.36874634 passes per solar orbit) |
Synodic month |
29.530589 | with respect to the Sun (phases of the Moon, 12.36874634 passes per solar orbit) |
Tropical month |
27.321582 | with respect to the vernal point (precesses in ~26,000 years)
|
Anomalistic month |
27.554550 | with respect to the perigee (precesses in 3232.6054 days = 8.850578 years) |
Draconic month |
27.212221 | with respect to the ascending node (precesses in 6793.4765 days = 18.5996 years)[citation needed] |
There are several different periods associated with the lunar orbit.
The
The average length of a calendar month (a twelfth of a year) is about 30.4 days. This is not a lunar period, though the calendar month is historically related to the visible lunar phase.
Tidal evolution
The
However the speed of seismic waves is not infinite and, together with the effect of energy loss within the Earth, this causes a slight delay between the passage of the maximum forcing due to the Moon across and the maximum Earth tide. As the Earth rotates faster than the Moon travels around its orbit, this small angle produces a gravitational torque which slows the Earth and accelerates the Moon in its orbit.
In the case of the ocean tides, the speed of tidal waves in the ocean[16] is far slower than the speed of the Moon's tidal forcing. As a result, the ocean is never in near equilibrium with the tidal forcing. Instead, the forcing generates the long ocean waves which propagate around the ocean basins until eventually losing their energy through turbulence, either in the deep ocean or on shallow continental shelves.
Although the ocean's response is the more complex of the two, it is possible to split the ocean tides into a small ellipsoid term which affects the Moon plus a second term which has no effect. The ocean's ellipsoid term also slows the Earth and accelerates the Moon, but because the ocean dissipates so much tidal energy, the present ocean tides have an order of magnitude greater effect than the solid Earth tides.
Because of the tidal torque, caused by the ellipsoids, some of Earth's angular (or rotational) momentum is gradually being transferred to the rotation of the Earth–Moon pair around their mutual centre of mass, called the barycentre. See tidal acceleration for a more detailed description.
This slightly greater orbital angular momentum causes the Earth–Moon distance to increase at approximately 38 millimetres per year.
The present high rate may be due to near resonance between natural ocean frequencies and tidal frequencies.[18] Another explanation is that in the past the Earth rotated much faster, a day possibly lasting only 9 hours on the early Earth. The resulting tidal waves in the ocean would have then been much shorter and it would have been more difficult for the long wavelength tidal forcing to excite the short wavelength tides.[19]
The Moon is gradually receding from Earth into a higher orbit, and calculations suggest that this would continue for about 50 billion years.[20][21] By that time, Earth and the Moon would be in a mutual spin–orbit resonance or tidal locking, in which the Moon will orbit Earth in about 47 days (currently 27 days), and both the Moon and Earth would rotate around their axes in the same time, always facing each other with the same side. This has already happened to the Moon—the same side always faces Earth—and is also slowly happening to the Earth. However, the slowdown of Earth's rotation is not occurring fast enough for the rotation to lengthen to a month before other effects change the situation: approximately 2.3 billion years from now, the increase of the Sun's radiation will have caused Earth's oceans to evaporate,[22] removing the bulk of the tidal friction and acceleration.
Libration
The Moon is in
The Moon's axis of rotation is inclined by in total 6.7° relative to the normal to the plane of the ecliptic. This leads to a similar perspective effect in the north–south direction that is referred to as optical libration in latitude, which allows one to see almost 7° of latitude beyond the pole on the far side. Finally, because the Moon is only about 60 Earth radii away from Earth's centre of mass, an observer at the equator who observes the 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 Earth's geographical poles would be able to see one additional degree's worth of libration in latitude.
Besides these "optical librations" caused by the change in perspective for an observer on Earth, there are also "physical librations" which are actual nutations of the direction of the pole of rotation of the Moon in space: but these are very small.
Path of Earth and Moon around Sun
When viewed from the north
The
In representations of the Solar System, it is common to draw the trajectory of Earth from the point of view of the Sun, and the trajectory of the Moon from the point of view of Earth. This could give the impression that the Moon orbits Earth in such a way that sometimes it goes backwards when viewed from the Sun's perspective. However, because the orbital velocity of the Moon around Earth (1 km/s) is small compared to the orbital velocity of Earth about the Sun (30 km/s), this never happens. There are no rearward loops in the Moon's solar orbit.
Considering the
The Sun's gravitational effect on the Moon is more than twice that of Earth's on the Moon; consequently, the Moon's trajectory is always convex[25][26] (as seen when looking Sunward at the entire Sun–Earth–Moon system from a great distance outside Earth–Moon solar orbit), and is nowhere concave (from the same perspective) or looped.[23][25] That is, the region enclosed by the Moon's orbit of the Sun is a convex set.
See also
- Ernest William Brown
- Double planet
- List of orbits
- ELP2000
- Ephemeris
- Jet Propulsion Laboratory Development Ephemeris
- Lunar Laser Ranging experiment
- Milankovitch cycles
- Orbital elements
Notes
- Kepler's laws.
- ^ The constant in the ELP expressions for the distance, which is the mean distance averaged over time.
- IAU 1976 Astronomical Constants were "mean distance of Moon from Earth" 384,400 km, "equatorial horizontal parallax at mean distance" 3422.608″, and "equatorial radius for Earth" 6,378.14 km.[4]
References
- Bibcode:1983A&A...124...50C.
- Bibcode:1988A&A...190..342C.
- ^ ISBN 0-943396-51-4
- ISBN 0-935702-68-7
- ^ Lang, Kenneth R. (2011), The Cambridge Guide to the Solar System, 2nd ed., Cambridge University Press.
- ^ "Moon Fact Sheet". NASA. Retrieved 2014-01-08.
- ^ .
- doi:10.1086/117209.
- S2CID 4456736.
- ^ Jacob Aron (Nov 28, 2015). "Flying gold knocked the moon off course and ruined eclipses". New Scientist.
- ^ "View of the Moon". U. of Arkansas at Little Rock. Retrieved May 9, 2016.
- ^ Calculated from arcsin(0.25°/1.543°)/90° times 173 days, since the angular radius of the Sun is about 0.25°.
- ^ "Moonlight helps plankton escape predators during Arctic winters". New Scientist. Jan 16, 2016.
- ^ The periods are calculated from orbital elements, using the rate of change of quantities at the instant J2000. The J2000 rate of change equals the coefficient of the first-degree term of VSOP polynomials. In the original VSOP87 elements, the units are arcseconds(”) and Julian centuries. There are 1,296,000” in a circle, 36525 days in a Julian century. The sidereal month is the time of a revolution of longitude λ with respect to the fixed J2000 equinox. VSOP87 gives 1732559343.7306” or 1336.8513455 revolutions in 36525 days–27.321661547 days per revolution. The tropical month is similar, but the longitude for the equinox of date is used. For the anomalistic year, the mean anomaly (λ−ω) is used (equinox does not matter). For the draconic month, (λ−Ω) is used. For the synodic month, the sidereal period of the mean Sun (or Earth) and the Moon. The period would be 1/(1/m−1/e). VSOP elements from
Simon, J.L.; Bretagnon, P.; Chapront, J.; Chapront-Touzé, M.; Francou, G.; Laskar, J. (February 1994). "Numerical expressions for precession formulae and mean elements for the Moon and planets". Astronomy and Astrophysics. 282 (2): 669. Bibcode:1994A&A...282..663S.
- ^ Jean Meeus, Astronomical Algorithms (Richmond, VA: Willmann-Bell, 1998) p 354. From 1900–2100, the shortest time from one new moon to the next is 29 days, 6 hours, and 35 min, and the longest 29 days, 19 hours, and 55 min.
- ISBN 9781421410784.
- S2CID 124256137.
- S2CID 51948507.
- .
- ^ C.D. Murray; S.F. Dermott (1999). Solar System Dynamics. Cambridge University Press. p. 184.
- ISBN 0-921820-71-2.
- ^ Caltech Scientists Predict Greater Longevity for Planets with Life Archived 2012-03-30 at the Wayback Machine
- ^ a b The reference by H. L. Vacher (2001) (details separately cited in this list) describes this as 'convex outward', whereas older references such as "The Moon's Orbit Around the Sun, Turner, A. B. Journal of the Royal Astronomical Society of Canada, Vol. 6, p. 117, 1912JRASC...6..117T"; and "H Godfray, Elementary Treatise on the Lunar Theory" describe the same geometry by the words concave to the sun.
- ISBN 0-935702-68-7
- ^ a b c "The Orbit of the Moon around the Sun is Convex!". Archived from the original on 31 March 2004. Retrieved 2022-04-14.
- ^ The Moon Always Veers Toward the Sun at MathPages
External links
- View of the Moon Good diagrams of Moon, Earth, tilts of orbits and axes, courtesy of U. of Arkansas