Orbit and
Phases of the Moon

Nov 14, 2017 The moon travels around the Earth in an elliptical orbit, a slightly stretched-out circle. When the moon is closest to Earth, its rotation is slower than its journey through space, allowing. The orbit of PFS-2 rapidly changed shape and distance from the Moon. In 2-1/2 weeks the satellite was swooping to within a hair-raising 6 miles (10 km) of the lunar surface at closest approach. As the orbit kept changing, PFS-2 backed off again, until it seemed to be a safe 30 miles away.

Introduction

'Phase' refersto the fact that the moon shows differingamounts of lighted hemispheres as viewed from the earth during itsorbit around the earth.

'Cycle' refers to the repetition of these phases, as well as cyclesof eclipses. We will investigate these here.

Understanding the observed phases of the moon, requires understandinghow light and shadowing works in relation to the sun's light and theorbit of the moon and earth around the sun.

A superstition: It is sometimes believed that when the moon is bright and full, people act crazy. In fact, there is no statistical scientific evidence to support this. It is a myth.

Also: note that there are no monsters devouring the sun, as you mighthave been told if you were listening to a professor in 2000 BC.

One thing about studying moon phases: it begins to addressspecifically how what we see observe in astronomy has a very clear scientific explanation.

Motion of the Moon

First note that if you watch the moon night after night,you will see two key features which are fundamental cluesto understanding its motion:

1. It moves eastward against the background stars.
2. It shows same face toward Earth in all phases.

Given these facts, can you infer if the moon rotates around its own axis?(figure 3-2)

Other Key Points:

The moon orbits quite fast: it moves about 0.5 degrees per hour in the sky.In 24 hours it moves 13 degrees.

The moon's observed motion eastward results from its physical motion of the moon along its orbit around the Earth.

Lunar Orbital Period

The distance from the Earth to the moon is about 60 times the Earth'sradius, about 384,000 km.

The moon orbits counterclockwise around the Earth.Orbit is slightly elliptical and distance from Earth varies 6 %.Period of the orbit is about 27.3 days. This is called theSIDERIAL PERIOD or SIDEREAL MONTH.This is measured with respect to the background stars:the moon takes 1 sidereal period to cycle around once.

In its eastward motion, the moon stays near the ecliptic.(recall, this is the plane of the sun's motion on the sky).It is tipped by 5 degrees 9' (5 degrees 9 arc seconds) to the plane of the Earth's orbit around the sun and this tilted toecliptic by same amount.

This means that the moon also appears to trace the Zodiacalong the sky since its deviation from the ecliptic plane onthe sky as it orbits is so small.

Lunar Phases, Phase Cylce

Moon does not produce its own light, and so the light that we seefrom it is that which is merely reflected from the sun.

As the moon moves around the sky sun illuminates different amountsof its surface. The phase of the moon is thus entirely determined bylooking at the Earth's location relative to the sun. The best way to see the phases is to study figure (see also(figure 3-3) of text).

The Moon appears to go through a complete set of phases as viewed from theEarth because of its motion around the Earth, as illustrated below:

Phases of the Moon

In this figure, the various positions of the moon on its orbit are shown(the motion of the moon on its orbit is assumed to be counter-clockwise).The outer set of figures shows the corresponding phase as viewed fromEarth, and the common names for the phases.One can see the progression of phases:New, Waxing Crescent, First quarter, waxing gibbous, full,waning gibbous, 3rd quarter, waning crescent.

Note: the use of the word 'quarter' here does not refer to howmuch of the moon is visible, but the phase in the cycle.

Cycle of lunar phases takes 29.5 days this is the SYNODIC PERIOD.

Why is this longer than the SIDERIAL PERIOD which was 27.3 days?very simple: this is because the moon returns to the sameplace on the sky once every siderial period, but the sun isalso moving on the sky. When the moon returns to the samespot on the sky the sun has moved 27 degrees. Thus the moon now hasto take some extra time to catch up. (figure 3-4). The moon takes about 2 days to catch up.

(A good way to understand moonrise and moonset from thebook is to look at the picture on page 34 of the text)Imagine standing with the human figure on the globe Now the key point is that the horizon above which the moon isvisible, is the plane perpendicular to your body. The timeof the day is given by 'sunrise, sunset, noon, midnight.'Those times of day appear to us as the Earth rotates so that the USpasses through them. While the Earth rotates, the position of the moonin its orbit doesnt change much, so we can talk about moonrise and moonset.As you imagine the Earth turning and the various times of day passing you can see how the moonrise and moonset differs for different moon phases.)

Summary of Moon Motion and Phases

The moon appears to move completely around the celestial sphere once in about27.3 days as observed from the Earth (a siderealmonth) and reflects the corresponding orbital period of 27.3 days

The moon takes 29.5 days to return to the same point on the celestial sphereas referenced to the Sun because of the motion of the Earth around the Sun (synodicmonth)

Lunar phases as observed from the Earth are correlated with thesynodic month.

Since the Moon must move Eastward among the constellations enough togo completely around the sky (360 degrees) in 27.3 days, it must move Eastwardby 13.2 degrees each day (in contrast, remember that the Sun only appears tomove Eastward by about 1 degree per day). Thus, with respect to the backgroundconstellations the Moon will be about 13.2 degrees further East each day.Since the celestial sphere appears to turn 1 degree about every 4 minutes, theMoon crosses our celestial meridian about 13.2 x 4 = 52.8 minutes later eachday.

Perigee and Apogee

The largest separation between the Earth and Moon on its orbit is called

Lunar Orbit Speed

apogee and the smallest separation is called perigee.

Rotational Period and Tidal Locking

Lunar Orbiter 1

The Moon has a spin period of 27.3 days that (except for smallfluctuations) exactly coincides with its (sidereal) period for revolution about the Earth.This is equivalent to saying that we see the same faceof the moon all the time, as was mentioned above.

This is no coincidence; it is a consequence of tidal coupling between the Earth and Moon. This tidal locking of the periods for revolution and rotation, the Moon alwayskeeps the same face turned toward the Earth

Whether the world is celebrating the 50th anniversary of the lunar landing or looking forward to a return to the lunar surface with the NASA-led Gateway, there's a lot of focus on the moon these days. And that's a good thing, because, let's face it, going to the Moon is pretty exciting and is a necessary precursor to a human mission to Mars. We have a lot to learn along the way, and one place to start is with the orbit.

Maxar is a leader in designing and building communication satellites that reside in geosynchronous orbit (GEO) and imaging satellites that call Low Earth Orbit (LEO) home. But now it's time to take a look at a new neighborhood: Near Rectilinear Halo Orbit (NRHO).

Epicycle Orbit

The NRHO is a highly inclined orbit around the moon and is considered to be in cislunar space. Cislunar is Latin for 'on this side of the moon' and generally refers to the volume between Earth and the moon. Cislunar space includes LEO, Medium Earth Orbit, GEO, as well as other orbits, such as Low Lunar Orbit and NRHO, the intended orbit for the Gateway.

The NRHO is a seven-day cycle, taking the Gateway as close as approximately 1,600 km (1,000 miles) and as far away as about 68,260 km (42,415 miles) from the lunar surface. Consequently, roughly every seven days, the lunar lander can depart the Gateway to travel to the lunar surface. Because the Gateway can sit in this halo orbit, almost like it’s held in place by the gravity of Earth and the moon, it requires little energy for stationkeeping or to maneuver into other cislunar orbits. The orbit is called a 'halo' orbit because the tracked orbit looks like a halo around the moon.

The L2 family orbit (shown in green in the picture to the left) is the baseline orbit that the Gateway will use. The moon's south pole is the primary region of interest for initial future missions to the surface of the moon due to the presence of significant quantities of water ice in shaded craters. With a southern-oriented orbit, the spacecraft spends the vast majority of its time over the southern regions, allowing for more continuous communications with objects near the south pole, as well as allowing for the Gateway to act as a communications relay for the astronauts on the lunar surface to communicate with the Earth Mission Control. The Shackleton crater is in the southern region of the moon and is a strong candidate for future lander missions to the crater rim.

The Maxar-built Power and Propulsion Element of the Gateway, however, has the flexibility to maneuver between any of the orbits as the NASA mission changes. For example, if the lunar north pole becomes more attractive due to potential ice, minerals and science research, the orbit can be changed to make the north pole easily accessible. Maxar's highly efficient solar electric propulsion system allows multiple orbit changes because the amount of propellant used is minimal. Such an orbit change would be less feasible with a purely chemical propulsion system.

Moreover, learning how to leverage different orbits is critical to support a future human mission to Mars. Similar to early nautical explorers that had to learn how to use trade winds, we need to gain experience with using different orbits in cislunar space to carry America and all of humanity to the moon and Mars.

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