Showing posts with label orbital mechanics. Show all posts
Showing posts with label orbital mechanics. Show all posts

Wednesday, June 26, 2013

Earth's Nightlight

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Full Moon in natural color, January 2, 2007
Paul D. Spudis
The Once and Future Moon
Smithsonian Air & Space


As a naturally orbiting object, the Moon orbits Earth in an elliptical path, with the center of the Earth at one focus – more precisely, both Earth and Moon orbit each other around what it called the barycenter, the imaginary point about 1800 km below the surface of the Earth that constitutes their mutual center of gravity.  Since the Moon is only about one percent the mass of Earth, the barycenter is much closer to the center of Earth than it is to the center of the Moon.

When the Moon comes closest to Earth in its elliptical orbit it is said to be at perigee.  If the Sun, Earth and Moon come into alignment along a straight-line, a condition occurs that astronomers perversely have named syzygy (a great word to keep in your hip pocket the next time you play Scrabble, though you’ll need a blank to get there).  Syzygy (alignment) is not the same as perigee (the closest approach of Moon to Earth) but on the occasion when syzygy and perigee coincide, we have what’s called a “Super Moon.”

During perigee, the Moon’s elliptical orbit causes it to be about 45,000 km closer to Earth than at farthest point (apogee).  As the average distance between the two is about ten times that distance, the visual effects of this variation, though not large, is measurable.  I’ve been skeptical about noticing this size difference by “eyeballing” the Moon at perigee (closest) and apogee (farthest).  However, during an early morning walk with the dog this last weekend, I was somewhat startled to see the full Moon low in the sky, definitely appearing larger than usual.

In part, this appearance results because of the “Moon illusion,” whereby the Moon appears much larger on or near the horizon than when it is overhead, near zenith.  The traditional explanation for this illusion is that when the Moon is near the horizon, we can compare the size of the Moon’s apparent disk to known objects on the Earth (such as a house, distant tree or hill).  When the Moon is directly overhead, there is no nearby object with which to compare it.  Many depictions in art show the Moon as an enormous lunar disc, glowing the night sky; it is to this optical illusion that such portrayals refer.

The Moon’s apparent diameter is about one-half of a degree of arc (same as the Sun), or roughly the dimensions of a small pea held at arm’s length.  Although the biggest object in our sky, that size is much too small for the naked eye to resolve most surface features (except for the vague markings of light and dark that comprise the lunar maria, the “Man in the Moon”).  In full phase, the Moon can be quite bright, illuminating the landscape at about -12 visual magnitude.  While no one would mistake such conditions with daylight (the Sun is about -26 visual magnitude, about 400,000 times brighter than the full Moon), full moonlight is bright enough to cast strong shadows and to read by.  This is one of the reasons astronomers “hate” the Moon – during full phase, the sky is typically too bright to reveal any but the very brightest stars and it interrupts their views of coinciding meteor showers.   However, they’ll “love” the views that await them from the far side of the Moon, the only place in our Solar System where radio noise from Earth is silent and at times, when Earth blocks the Sun, the sky-viewing would be unsurpassed.

The most important effect of a “Super Moon” is on tides, which can be extraordinarily high during perigee.  This effect can be especially significant in coastal areas that experience high tides, such as the famous Bay of Fundy in Canada.  In this area, the combination of shore depth and geometry, prevailing winds and position create tidal height variations as high as 16 meters (over 52 feet) in the course of a day.  At Super Moon, tidal variations are at their largest; during the passage of Hurricane Sandy up the East Coast last year, landfall occurred during full Moon (syzygy), resulting in both a storm surge (i.e., a large dome of water caused by low atmospheric pressure and wind) and high gravitational tides.  As witnessed with Hurricane Sandy, the combination of both occurring together can be devastating.

Contrary to an illusion of our Earth-bound perspective, the Moon does not orbit Earth's center, rather both Earth and Moon revolve around their common center of gravity, the barycenter of the Earth-Moon system. That moment of inertia, at any given time, is about one-third the distance from Earth's surface and its center GravitySimulator.com
Tidal effects are most notable in large bodies of water, but the solid Earth also deforms in response to the pull of the Moon’s gravity.  On both objects, a tidal bulge extends slightly above the mean radius of both Earth and Moon.  This bulge is not perfectly aligned with the geometric line that connects the centers of the two objects because both Earth and Moon are rotating, and it takes time for the solid bodies to deform plastically.  Thus, the tidal bulge of the rapidly spinning Earth slightly leads the Earth-Moon line, resulting in a constant increased tug at the Earth by the Moon, slightly slowing the rate of Earth’s rotation down.  At the same time, this leading tidal bulge attracts the Moon more, making it speed up in its orbital path slightly and thus, move outward, away from the Earth.  So over time, as the Earth spin rate slows, the Moon gradually recedes away from its grip; this rate of recession is about 4 cm per year.  The Moon is currently about 60 Earth radii away; it was once much closer, possibly as close as a few Earth radii.  It could not be closer than about 3 radii (the Roche limit) because at distances closer than the Roche limit, tidal forces would tear the Moon apart.  In a few hundred million years, the Moon will be too far away to permit a total solar eclipse to be seen from Earth.  A timely and good thing that we came along when we did!

Using information from a lunar seismic network deployed on the Moon during the Apollo missions, we know that “moonquakes” often correlate with the tidal flexing of the solid Moon induced by the Earth (which is much larger than the terrestrial bulge because Earth is much more massive).  In fact, although there is a slight suggestion that the Moon might induce the initiation of an earthquake, in most cases there is no obvious connection.  The Earth is an active, dynamic body and its great internal heat and complexity of configuration appear to be more important in determining when and where an earthquake occurs than by tidal effects caused by the Moon.  But if the proper tidal conditions and the alignment of stress and magnitude of effect coincided, there is no reason that either syzygy or Super Moon could not induce an earthquake.

Our Moon is much more than the familiar, comforting nightlight orbiting Earth.  Beyond touching us emotionally and affecting our planet physically, the Moon is also an orbiting treasure trove of, as yet unrealized (some imagined but mostly yet unimagined) scientific discoveries and technological breakthroughs.  But before we make it our goal to settle the Moon, we must make it our goal to sail beyond it.

Originally published June 26, 2013 at his Smithsonian Air & Space blog The Once and Future Moon, Dr. Spudis is a senior staff scientist at the Lunar and Planetary Institute. The opinions expressed are those of the author but are better informed than average

Wednesday, October 20, 2010

A first lunar transit for SDO


Close up on a solar prominence, with startling clarity, the New Moon's disk slides between the new Solar Dynamics Observatory in geosynchronous orbit and it's constant view of the Sun. The inconstant Moon is our humbling reminder how comparatively little things often obscure our view of a much bigger picture [NASA/GSFC/SDO].

Sun and Moon - A first for the Solar Dynamics Observatory (SDO), and it was visually engaging too. On October 7, 2010, SDO observed its first lunar transit when the new Moon passed directly between the spacecraft (in its geosynchronous orbit) and the Sun. With SDO watching the Sun in a wavelength of extreme ultraviolet light, the dark Moon created a partial eclipse of the Sun.

These images, while unusual and cool to see, have practical value to the SDO science team. Karel Schrijver of Lockheed-Martin's Solar and Astrophysics Lab explains: "The very sharp edge of the lunar limb allows us to measure the in-orbit characteristics of the telescope e.g., light diffraction on optics and filter support grids. Once these are characterized, we can use that information to correct our data for instrumental effects and sharpen up the images to even more detail."

The image below shows a full disk version, view the larger story here.

Friday, September 3, 2010

Chang'e-2 sets stage for future Moon missions


China's second lunar orbiter Chang'e-2 began as back up for Chang'e-1 (2007-2009). Scheduled for a possible October launch, Chang'e-2 should arrive sooner, orbit the Moon closer and gather better data. If all goes well the vehicle should allow rehearsal opportunities for China's first soft landing on the Moon in 2013, and a better camera on Chang'e-2 may gather 1 meter resolution photographs of preferred landing sites.

China's unmanned space program has only one deep space target: the Moon. The United States may be preparing to abandon manned exploration of the lunar surface but the new era of international lunar exploration, a 'second moon race,' continues. India, Russia and China may each have achieved soft landings there before the U.S. deploys the first, if any, of planned nodes for an International Lunar Network (ILN). After Chandrayaan-2 and Chang'e-3, Chang'e-4 may return the first lunar samples to Earth since the Soviet's Luna 24 in 1976.

From Xinhua -- China's second lunar probe, Chang'e-2, will transition much faster than its predecessor, reaching lunar orbit in a shorter period of time, a top Chinese space scientist told Xinhua Friday.

China launched Chang'e-1 from Sichuan October 24, 2007. The first of China's planned unmanned lunar missions ended a 16-month mission March 1, 2009 when it was intentionally de-orbited into Mare Fecunditatis.

"It is estimated Chang'e-2 can reach lunar orbit within five days, compared to 13 days, 14 hours and 19 minutes for Chang'e-1," Ouyang Ziyuan, chief scientist at the China Lunar Exploration Project, told Xinhua.

"China had not been to Moon before Chang'e-1 so we were very prudent and adjusted its transfer orbit in a very slow manner. It traveled 2.06 million kilometers before lunar orbit insertion," Ouyang said. "It's different now. We are more certain about the launch and can send Chang'e-2 directly to the moon, and we have also planned the transfer orbit to reach the Moon within five days."

Plans call for Chang'e 2 to orbit 100 km closer to the moon with a higher resolution camera, he said.

According to China's three-phase lunar exploration 'road map,' the country will first launch the Chang'e-2 and afterward soft-land Chang'e-3 on the moon in 2013 and, in 2017, Chang'e-4 will return a lunar sample to Earth.

Experts have speculated the Chang'e-2 mission will allow China to begin mastering soft-landing techniques for Chang'e-3 and 4, short of terminal descent. Careful lowering of its orbit to rehearse everything short of terminal descent that otherwise might begin after passing perilune could allow low passes over an intended target and an opportunity to take high-resolution photography.


Public mock-up of the China Lunar Exploration Program (CLEP) Chang'e-4, in development for a soft landing on the Moon in 2013. China's methodical dual-track developmental plans, its manned and unmanned (lunar), space programs seem devoted more to engineering design capability over science [Xinhua].