The Lunar Express

There is a posting on this blog titled "The Westbound Rule". This is an effort to make routine flight more efficient by parceling air corridors to take advantage of the earth's eastward rotation. I explained how it would be best if eastbound flights flew as low as is practical, because the earth's rotation is working with them, while westbound flights should fly as high as possible, to keep a distance from the rotation that is working against them.

Today, I would like to apply a similar concept to space flight between the earth and the moon.

The astronauts of the Apollo missions of around forty years ago obviously wanted to land on the moon where the sun was shining, not in the dark. The daylight on the moon made the mission much easier, particularly the taking of photographs, than it would been in the dark. But it is my observation that this may not be the best in the long run if lunar flight ever becomes routine.

Another factor in the lunar missions involved launches. The take-offs of the rockets during the afternoon was to accommodate the audiences and so that daylight would minimize the chances of errors and complications. But this meant that the spacecraft was launched eastward, along with the direction of the earth's rotation, and thus had to outpace the earth.

While this may have been good for public relations, it certainly was not the most efficient path.

Picture the moon orbiting the earth, as the earth orbits the sun. Of course, this is only an "apparent" orbit, as I described in the posting "The Earth, The Moon And, The Sun", simply because, at the moon, the gravity of the sun is more than twice as powerful as that of the earth. However, that is not very important for our purposes here.

Let's review the mechanics of the moon, as seen from our perspective on earth.

The moon orbits the earth every 29 days, in the same eastward direction that the earth rotates. This is why the moon rises 50 minutes later each day or night. 24 hours divided by 29 equals about 50 minutes. The same side of the moon always faces earth because the moon's rotation period, or day, is the same as it's orbital period.

The phases of the moon that we see are due to the changing angles between the earth, moon and, sun. Full moon is when the moon is on the opposite side of the sun from the earth, so that those on the night side of the earth see the moon fully illuminated by the sun. Unless, of course, there is a lunar eclipse. This happens when earth, moon and, sun are in the same lateral plane in a straight line so that the earth casts it's shadow on the moon.

New moon is when the moon is between the earth and the sun so that we cannot see the moon at all. A solar eclipse can happen at this point, if all three are in the same plane and in a straight line. Eclipses do not occur every month because there is a difference of about 5 degrees between the moon's path around the earth and the earth's orbit around the sun.

We see a half moon when the moon crosses the earth's path around the sun. A half moon when the moon's phase is waning, or getting less, between full and new moon, is when the moon crosses the earth's orbit in the direction from which the earth has already passed. A half moon when the phase is waxing, or increasing, is when the moon crosses the earth's path in the direction in which the earth is heading.

At sunrise, the direction overhead is the direction from which the earth has come in it's orbit around the sun. At sunset, the direction overhead is the direction in which the earth is heading. This means that a waxing half moon will be overhead at sunset, and a waning half moon will be overhead at sunrise, taking the observer's latitude into account.

Let's express the path of the moon around the earth, relative to the sun, in degrees and quadrants. Let 0 degrees be the new moon, 90 be waxing half moon, which is also called "first quarter". Let 180 be the full moon and 270 be the waning half moon, also known as "last quarter". This fits in with the posting on this blog, "New Trigonometric Functions", in which I proposed a function based on 180 degrees, "The Lunar Function", in addition to the standard 90 degree functions.

Here is a link to a diagram of the moon's phases: www.moonconnection.com/moon_phases.phtml

There are three gravitational zones that we will deal with in a trip between the earth and the moon. Simply that where the earth's gravity is the strongest influence on the spacecraft, that of the moon and, that of the sun. At the moon, the sun's gravity is more than twice as powerful as that of the earth so that the majority of the trip will be spent in the sun's gravitational zone.

The concept that I want to discuss today is my vision of optimum points of departure and return on opposite sides of the moon's path around the earth, about two weeks apart. The great advantage of this is that most of the flight will be simply letting gravity do the work for us. The spacecraft can be made to literally "fall" toward it's destination. First, to the moon, and then the return flight to the earth.

When a spacecraft is on the way to a destination toward the sun, such as Mercury or Venus, the sun's gravity can be put to work. At launch, the spacecraft is essentially a part of the earth orbiting the sun. If we point the engines of the spacecraft in the direction of the earth's orbital path, it will counteract the orbital momentum around the sun that the spacecraft has. This will cause it to lose orbital momentum and literally fall toward the sun, and it's destination.

My thought is that a launch early in the morning, some time after third quarter (waning half moon), would definitely bring about the best flight efficiency. Once the spacecraft left the earth's gravitational zone, the gravity of both the sun and the moon would be working for us, as well as the earth's rotational momentum. Assuming that the flight takes a few days, this would land the spacecraft on the moon with the new moon approaching, in which the side facing the earth is in the dark. Once we are more experienced at lunar landings, this should not be as much of a problem as it would have been in the days of the Apollo landings.

A first quadrant launch, between new moon and first quarter, is also a possibility. But this will make it necessary to speed up the spacecraft, to get ahead of earth in it's orbit around the sun. This would be less efficient than simply losing orbital momentum so that the spacecraft literally falls toward it's target.

I see the return flight back to earth as being best as we approach full moon, after first quarter. the gravity of both the earth and the sun would be working for us. Whereas if we went to the moon near full moon, this most powerful gravitational combination would be working against us. The return trip should be easier, simply because the gravity of the earth is much more powerful than that of the moon.

So, if we approach the moon between last quarter and new moon, and return between first quarter and full moon, all we need to do is to lose orbital momentum by pointing the rocket engines in the direction of the earth's orbit around the sun so that the rocket thrust counteracts this orbital momentum, and we will literally fall along either journey. Gravity will do most of the work for us. We must always consider the tremendous gravity of the sun so that we aim to hit the moon while it is toward the sun, and return to earth when it is toward the sun, relative to the moon.

There is another thing to consider for lunar flights. The Apollo lunar missions from Cape Canaveral in Florida first went into an equatorial orbit around the earth and then, upon arrival, and equatorial orbit around the moon. The landing sites were thus relatively close to the moon's equator.

Another possibility is using polar orbits. This would be more complex, in that we would have to calculate the trajectory in another dimension also, that of north-south. The moon would be approached so that the spacecraft would be to the north or south of the plane of the moon's path around the earth, and it would go into orbit over the moon's north and south poles rather than around it's equator. To accomplish this, we could make use of the 5 degree difference between the planes of the earth's orbit around the sun and the moon's path around the earth.

There are disadvantages to the polar orbit route. There is no rotational momentum to build on during launches, and the mission is simpler if all is kept in the same plane. But a polar approach would make it much easier to land on any specific site, both on the moon and the return to earth, instead of just in the zones around the equators.

One more thing to remember during spaceflights like these. The posting "The Effective Center Of Gravity" on my physics and astronomy blog, http://www.markmeekphysics.blogspot.com/ , explains why the commonly-held belief that the center of mass and the center of gravity for a moon or planet is the same thing, must be incorrect.

In that posting, I explained that while the center of mass will be constant, the effective center of gravity will vary with our distance from the moon or planet. The two will be the same only if we are an infinite distance from the moon or planet. This is because the near side of the planet is closer to us so that it must have a greater gravitational influence on us than the far side. The closer we are to the moon or planet, the closer is it's center of gravity to us and the more difference between the center of mass and the center of gravity.