scilogs SpaceTimeDreamer

Far Away From Home

from Gerhard Holtkamp, 06. June 2009, 22:13

Some people like to get away from home as far as possible. Just how far away can you get and who has been furthest?

Over the years I have travelled a lot and seen many countries. Twice I had the pleasure to visit New Zealand which on the globe is opposite Europe where I live. At those times my geometric distance from home was about one Earth diameter. That is about as far away as most of us will ever get. The residents of the International Space Station can add 360 km to that distance because this is the height of the ISS above the surface of the Earth. This amounts to barely 3% more than my greatest distance - not particularly impressive!

But some 40 years ago 24 individuals ventured much further than that: These were the Apollo astronauts who between December 1968 and December 1972 flew to the Moon. After arriving the Apollo flights would swing around the far side of the Moon and at a height of 111 km above the lunar surface and almost diametrically opposite to the Earth perform a Lunar Orbit Insertion Maneuver (LOI) to go into orbit around the Moon. Later on once again over the far side of the Moon a Trans Earth Insertion Maneuver (TEI) would get them back on a course toward our home planet. There was one exception to this routine: After suffering an explosion Apollo 13 would no longer attempt to orbit the Moon but rather swing around the Moon at a distance of 252 km to directly get back to Earth.

Having gone behind the Moon some 140 km further than the other Apollo spacecraft one might think that Apollo 13 must have been further away from Earth than anyone else. But that neglects an important fact: The distance between the Earth and the Moon can vary by as much as 50,000 km depending on whether the Moon is at perigee or at apogee. So you will have to calculate the actual Earth - Moon distance on a case by case basis. Also needed is some information about the individual Apollo orbits around the Moon which you can find on the Internet in the Apollo Mission Transcripts - once you 've figured out what all those cryptic numbers mean they are talking about on the Air-to-Ground voice loop.

I don't play video games so I have to keep my computer occupied with other useless tasks. A few years ago I actually went ahead to figure out who the distance-from-Earth record holders were. None of the Apollo flights was at the Moon with the Moon at apogee. Thus there are only two different cases to consider: Either the Moon had passed apogee and was closing in on Earth - in this case the Apollo spacecraft would be farthest from Earth at LOI - or the Moon was still heading toward apogee in which case the maximum distance of Apollo would be at TEI.
Apollo 13 - farthest from EarthIronically, it was Apollo 13 which flew past the Moon just a few hours before lunar apogee - the closest of all the Apollo missions. At 23:34 GMT on April 14, 1970 Apollo 13 was 400,020 km away from the surface of the Earth closely followed by Apollo 10 with just 200 km less at 20:45 GMT on May 21, 1969. Third placed is Apollo 15 trailing by another 1340 km.

Paradoxically, while Jim Lovel, Jack Swigert and Fred Haise hold the current world record of having been furthest from Earth, Apollo 10's Tom Stafford, John Young and Gene Cernan can claim to have been further from home than anybody else! Here's why: During the moment of maximum distance for both Apollo 13 and 10, Houston happened to be on the near side of the Earth (as viewed from the Moon) adding only some extra 800 km to the 'slant range' distance. Apollo 10 - farthest from homeBut while Apollo 13 was racing back to Earth after its brief lunar swingby Apollo 10 went into orbit around the Moon. Half a day later the Earth had turned  and Houston was now on the far side - almost an Earth diameter further away - while the Moon itself had closed in on Earth by a mere 1200 km. As a result at around 10:45 GMT on May 22, 1969 the Apollo astronauts found themselves some 408,950 km away from their Houston homes and families. That is 32 times as far as I have ever been!

To the Apollo astronauts themselves the actual Earth-Moon distance was of little importance. The maneuvers they had to perform remained the same. It was just a matter of entering slightly different numbers into the computer. It could even happen that the transfer time was faster while the Earth - Moon distance was larger due to the specifics of what mission planners had figured out was best.

Shouldn't I rather worry about more important things like say the state of the world ecconomy, global warming or who will be the next champion in Formula I auto racing? On his second voyage of discovery James Cook tried to sail as far south as possible.George Vancouver - farthest SouthOn January 31, 1774 at a latitude of 71°10' S the ice became too thick to continue and he ordered his ship, the HMS Resolution, to pull back and head north again. At this very moment a young man rushed to the ship's bow happily jumping up and down and shouting "I have been further south than anyone else!". I suppose it is things like this that distiguish us from robots and make us Human Beings.
By the way, the young man who in January 1774 had been furthest south was George Vancouver. He went on to become a famous explorer in his own right.

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  1. Michael Blume A beautiful text...
    07.06.2009 | 14:41

    ...inspiring longing for the "real" long travels...

    The first post, and I already love that Scilog!

    Welcome & warm greetings!

  2. arnost Subject
    07.06.2009 | 23:11

    Not bad, not bad at all. Why am I not surprised, Gerhard?
    Keep the good work.

  3. Michael Khan The Moon Orbit
    08.06.2009 | 11:01

    Your post reminded me of some analysis I did some time ago related to the lunar orbit and prompted me to dig it up again.

    Moon and Earth are akin to a binary system, although the barycentre (the common centre of mass of both bodies) still always remains inside the Earth, at about 4500 km from its centre.

    However, the fact that the Moon's mass is significant compared to that of the Earth (with more than 1% of the Earth's mass) together with the gravitational perturbations through the Sun lead to some interesting effects.

    (I will get to the point ... bear with me for just a few minutes)

    Here is the osculating semi-major axis (osculating means instantanoeus, as opposed to the mean value that is evened out over a time period, such as one orbital revolution.)

    This shows considerable varitaion, but that in itself doesn't mean very much in terms of actual distance.

    Let's look at the osculating eccentricity:

    Again, significant variations, but also the disclaimer that the osculkating eccentricuty doesn't give the full picture.

    Looking at the actual orbital radius with respect to the centre of the Earth, we get this:

    Now this is interesting.

    We see two things here, one expected and one perhaps somewhat less so. Firstly, there is a variation in the radius with a period of a sidereal lunar month, which is why you see 13 peaks) due to the fact that the Moon orbit is eccentric. This is to be expected.

    The unexpected thing appears when you look at the actual radii of apogee and perigee (the peaks and valleys. The apogee, i.e., the farthest point from the Earth, varies by several thousands of kilometers, the peigee by mor ethan 10,000 km!

    So what am I winding up to with this admittedly somewhat pedantic comment?

    For all the record-breakers out there, it's not enough to just reach the Moon at apogee, you also have to choose the right one.

    Even if you, one day, fly to the Moon and reach it at its apogee, and your friend flies there a few lunar months later and also reaches it at an apogee, you may still get a chance of telling him: "Hey, I was 2000 km farther from home than you! Nyah! Nyah! Nyah!" Or, alternatively, he might say that to you.

    So consider yourselves forewarned, and adjust your schedule accordingly.

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