Wednesday, January 16, 2008

Mercury looks like the Moon, nearly...

On Monday, the spacecraft Messenger visited Mercury, and shot this photo of the planet closest to the Sun:

Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington (Source)

The photo was taken at 20:25 UTC on January 14, 2008, about 80 minutes after Messenger's closest approach to Mercury, from a distance of about 27,000 kilometres (17,000 miles). Mercury had been visited 30 years ago by the space probe Mariner 10, but most details of the planet visible in this photo have never been seen before!

Here is another photo, taken about 56 minutes before the closest encounter from a distance of 18,000 kilometres (11,000 miles), showing a region roughly 480 kilometres (300 miles) across, including craters less than a mile wide:

Credit: NASA/Johns Hopkins University Applied Physics Laboratory/Carnegie Institution of Washington (Source)

The dark, eye-like structure close to the terminator had been glimpsed by Mariner 10 and is called Vivaldi, after the Italian composer.

Messenger has shot more photos during the fly-by, but transmission to Earth has been slow so far. The main reason is that also on Monday, the Ulysses spacecraft passed the north pole of the Sun, taking lots of exciting data, and the transmission bandwidth had to be shared between Ulysses and Messenger. You find many interesting details about this delay, and the Messenger mission in general, on the site and blog of the Planetary Society, including a discussion why despite the obvious resemblance, there are are also differences between Mercury and the Moon that can be seen in the photos.

Messenger has been launched in August 2004 and is under way on a quite complicated trajectory that will, eventually, bring it in a closed orbit around Mercury in March 2011. It's quite surprsing to me that it's so complicated to get rid of the extra kinetic energy one gains when falling into the potential well of the Sun.

So, Mercury will stay quite elusive for three more years.

Despite rumours to the contrary, it's very well possible that Copernicus had seen Mercury in his lifetime. (Source: Wikipedia)
Apropos elusiveness: Despite rumours to the contrary, Mercury can be spotted by the naked eye in the morning or evening sky, albeit only a few times a year - I've seen it once as a bright "star" in the evening twilight. There is the "very pretty tale" that Copernicus complained that he had never seen Mercury himself. However, this most probably is only a myth, originating from a misreading of quotations from Copernicus' "De Revolutionibus" and from the "Life of Copernicus" by philosopher and astronomer Pierre Gassendi (Gassendi was the first to observe a transit of Mercury across the Sun in 1631). It seems that this myth goes to back to the much-read accounts "Astronomie populaire", by the French Astronomer François Arago, and "Kosmos", by his friend, the German naturalist Alexander von Humboldt. These accounts were extremely popular in the mid-19th century, and the catchy story developed a life on its own, despite complaints by contemporary astronomers that there was actually no real evidence for it. (PS: If someone could help me with translations of the Latin quotes from Copernicus and Gassendi as cited in the W. T. Lynn paper (The Observatory 15 (1892) 321-322), I will appreciate. It seems that in the 1890s, Latin quotes did not demand translations in astronomy papers...)

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  1. Hmm, with the bare eye it looks to me as if the craters are less deep than on the moon, or is this only apparently so because the moon is smaller? best,


  2. Actually, Mercury is not that much bigger than the Moon (4900 km in diameter versus 3500 km), and on the lower photo, craters look quite deep - so, that's difficult to estimate, I would say. It also depends much on the illumination and contrast of the photo.

    On the other hand, at the Planetary Society Blog they make indeed the point that the topography of Mercury is much more unifrom than that of the Moon.

    And, Mercury has not the extended darker plains, the "Maria", which are responsible for the "Man in the Moon" look of the Moon's disk.

    Best, Stefan

  3. Yes, sure, it is almost impossible to tell anything from the photos only, especially without knowing exactly how the photo was taken, processed etc. I've played around with pictures enough myself to know how much turning up and down contrast and brightness can bring out our hide features. What I vaguely meant are not so much the craters on the surface but the periphery, the 'roundness' of the whole picture. The Mercury shot looks to me almost perfectly smooth, whereas pictures of the moon that popped up in my mind e.g. that look more rough. But you are of course right, it might be an artifact of the image, let's see what the data says. Best,


  4. Given comprehensive photography of Mercury and decades of detailed analysis. we will gain a deeper uderstanding of Earth's climate.

    No, wait! Abundant He-3 mines for safe hot fusion! A platform for solar power stations to save the Earth? Bed and breakfast for space aliens? A new gravel resource?

  5. Hi Bee,

    Thanks Bee, I’ve been a life long space freak. That is from sputnik on. It’s been often reminded by NASA that in terms of plotting trajectories, as it concerns burn times and what not, that Newton’s Mechanic’s is what is used in the related calculations. It would be interesting to know that since Mercury does have an orbit that can only be predicted by General Relativity (it served as an initial proof) does NASA in this case use GR or do they insert some sort of fudge factor within a Newtonian Model? This compounded by all the gravity boosts and gravity braking that is going to be used to finally have it make final insertion orbit in 2011 I would be curious if they have been forced to us GR in this case.

    I am also curious about the photos. One that you show, have all the craters appear elliptical rather then round. This suggests the photo was taken from a steep angle for no impact angle could seem to account for it and yet the craters don’t appear very deep. It could be that Mercury’s surface is much denser as opposed to that of the moon’s.



  6. Hi Phil:

    Glad you liked the post, but you should thank Stefan for it. Best,


  7. Nice pics. It's fascinating to people, how hot Mercury can be overall due to proximity to the Sun, but have ice at the poles since the vacuum doesn't conduct heat. I have seen Mercury a few times, it's a pretty little thing. I watched it transit the Sun back in maybe the 70s.

    My girlfriend and I went to a Halloween party as Venus and Mercury, complete with toga and put-up hair, winged golden helmet and sandals, etc. I have to say, she can get away with playing Venus! Go to

  8. Nice article Stefan, thanks. Nice images, aren't they?

    One of the main factors in the difference in the morphology of craters on the Moon and Mercury is that of surface gravity, g. The Moon has a smaller g, therefore deeper craters can occur, and conversely, the craters on Mercury appear flatter.

    Also, regarding the question of whether one should take into account GR in designing spacecraft trajectories: for Mercury/Sun the relativistic effects are quite infinitesimal, and so you wouldn't need to take it into account. In the far future, when we try to put probes in orbit about white dwarves/neutron stars/black holes, we will certainly have to take into account GR effects!

  9. Thanks Stefan!

    Had not seen the images.

    The Sun appears 2.5 times wider at Mercury's surface, which would soften the edges of shadows a bit.

    Best, Kris

  10. Hi Changcho, Kris, Bee:

    good point about the differences in surface gravity and shadows - that sounds convincing!

    Either way, I now see your point about the ruggedness of the surface - Mercury looks much smoother, indeed, and that may not be just because of the light and the quality of the image. Emily Lakdawalla at the Planetary Society Weblog is discussing this point just in her latest post, with two very nice photos comparing horizon views of Mercury and the Moon!

    Best, Stefan

  11. Hi Phil,

    thanks for pointing out the elliptic shape of the craters in the detail photo - I didn't realise that before!

    Yes, this shape comes from the perspective: the area, close to the terminator, is near the rim of the planet's disk (but on the "backside" of the upper shot), so one looks into the craters at an flat angle, and sees ellipses instead of circles.

    And, true, you are right, I would say: shadows then are remarkably short, which is evidence for quite flat structures!

    Best, Stefan

  12. Hi Stefan,

    Thanks so much for the interesting piece on Messenger’s first fly past of Mercury. I’m sorry I didn’t pay attention to the author line. With the 2nd fly by in October this year and another in September next year before finally coming around in 2011 to hold orbit, there is a lot more to look forward too.

    I still find it amazing that with Mercury being the planet (closest to the sun) that they can still use Newton’s 1687 theories (and mathematical method) to calculate all the trajectories, six gravity assists, travelling nearly 6 billion miles over seven years and hit the mark. Would you think that even Newton would have thought such a thing was possible? Makes you want to ask those MOND fellows to show a little respect for 321 year old brilliance. I recall all the (well deserved) tributes and accolades heaped on Einstein just a few years back on the 100th anniversary of his 1905 beginnings. When are we going to afford at least the same to Newton? So how about in four years we pay tribute on the 325th anniversary by marking the greatest turning point in the history of science. So no disrespect for Einstein, Galileo, Bohr, Heisenberg, Maxwell, Faraday, Schrödinger, Kepler, Copernicus, Archimedes and all the others; for when you put it all together, what can you say. So let’s plan the Newton Fest.



  13. Another good blog posting Stefan. I never thought Mercury would look like this.


    IN regards to Newton you might never feel the same? :)

    Some will look past the transgressions. :)

  14. Hi Phil, Changcho,

    that's a very good question, concerning relativistic effects and if and how they are considered for steering the Messenger probe. -

    I am not so sure about that, but I understand that yes, they are are taken into account!

    True, effects are tiny, and when mentioning the perihelion motion of Mercury, one has to keep in mind that the GR contribution to the shift is only about 10 percent of the perturbative contributions of all the other planets, so it is small indeed.

    On the other hand, the precision of the trajectory is incredibly high. Again, citing from Emily Lakdawalla's blog:

    ... the last time MESSENGER fired its rockets to fine-tune its trajectory and aim for the 200-kilometer-altitude flyby point was nearly a month before the flyby, on December 19, 2007, when the spacecraft was more than 100 million kilometers away from Mercury. They missed their aimpoint by only 1.43 kilometers in altitude after traveling that 100-million-kilometer distance!

    Now, I remember that for the calculation of the JPL ephemerides of the planets (in order to know where actually to find Mercury...), general relativity is definitely taken into account. Then, I did a google search for "spacecraft trajectory general relativity JPL", and found this very interesting document on the JPL website: Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation by Theodore D. Moyer, which describes how the JPL calculates the trajectories of its space probes.

    From the Introduction: Section 4 presents the equations used in program PV for the acceleration of the spacecraft due to gravity only (Newtonian and relativistic terms) in the Solar-System barycentric and local geocentric frames of reference.

    And from Section 4: The relativistic equations of motion for the Solar-System barycentric frame of reference, which apply for a spacecraft anywhere in the Solar System, are given in Section 4.4. [...] Section 4.4.1 specifies the point-mass Newtonian acceleration plus the relativistic perturbative acceleration due to a body. These equations are used to calculate the acceleration of the spacecraft and the acceleration of the center of integration due to the celestial bodies of the Solar System.

    The equation which they integrate to obtain the position of a spacecraft is given on page 19 of this document, it's an awesome post-Newtonian parametrisation, with lots of extra terms added to the Newtonian potential! The extra term are not always necessary, but they can be taken into account.

    Now, I guess if this is the state of the art for the calculation of trajectories, it has for sure been used for Messenger, which is travelling in the "most relativistic" region of the Solar System. - Meaning, yes, general relativity is taken into account for Messenger, via the PPN parameters of GR!

    Perhaps someone who knows more about that can correct me if I am wrong? Anyway, all this is really fascinating!

    Best, Stefan

  15. Hi Plato,

    “IN regards to Newton you might never feel the same? :)”

    “Some will look past the transgressions. :)”

    Yes I’m aware of all of Newton’s reported tyranny, super ego and transgressions. There were many. Not only Leibniz and Hooke still further Flamsteed; yet most horribly the humble of manner and station Stephen Gray, the true father of electrical communication. I for one can look past all these to admire the brilliance. I will admit he was certainly lucky there were no paparazzi in those days :-)



    P.S. If you want to read about the John Flamsteed (first Astonomer Royal) , Stephen Gray saga there is a interesting book co-authored by a father and son team, David & Stephen Clark, published by W.H. Freeman and Company (2000) called “Newton’s Tyranny - the suppressed scientific discoveries of Stephen Gray and John Flamsteed

  16. Hi Phil,

    sorry, our comments just crossed... never mind about the confusion...

    About trajectories, to my knowledge, Newton was convinced that HE was adjusting by hand from time to time the trajectories of the planets, so that the world would stay neatly ordered and stable.

    But to my understanding, nowadays things are a bit different:

    General relativity

    - enters the very definition of the barycentric coordinate system of the Solar System,

    - is taken into account to calculate the ephemerides (the coordinates as a function of time) of the planets, and

    - is taken into account to calculate trajectories of space probes (see Section 4: Spacecraft Ephemeris).

    All this is done essentially vie the Parametrized Post-Newtonian (PPN) Formalism, but it's Einstein gravity, nevertheless.

    If precise measurements are used to "check" GR, one actually tests if one really has to take into account in the PPN formalism those terms that follow from GR, and if the parameters, γ, δ etc. in the PPN series have to be used with those values that correspond to GR.

    Best, Stefan

    PS: Actually, about the PPN stuff, there is latecomer post from the plottl series which touches this topic - I hope we'll have finished it soon.

  17. Stefan, Thanks for the clarification. I was pretty sure GR effects would be very small and would not matter, but perhaps they do matter. As you say, someone actuallly working on the MESSENGER mision could elaborate?

    Also, please note that in your link to the JPL Ephemerides, HORIZONS is the first thing one notices: this is OK for low accuracy work. For high accuracy one would have to use the JPL DE406 ephemerides (as mentioned further in the link itself).

  18. Thanks Phil.

    While never considering what Mercury actually looked like, I did familiarize myself, with the advance of the perihelion of Mercury, and it's relation to Gr, along with the binary pulsar PSR 1913+16.

    What seem interesting to me in this relation, "satellite travel to Mercury," is how we would look at space differently if we considered the "Interplanetary Superhighway."

    How does one arrive at such a conclusion in relation to space, and one can't help look at what we are doing with regards to those satellite travels, and it's relation to this venture.

    The trajectory of an object is determined by finding a path that minimizes the action over time.

    These considerations on pictures would had have to be important when knowing the path the satellite would take?

  19. Hi Stefan,

    Thanks again for the clarifications and expansion on the GR vs. Newton query. See what happens when one asks a question of a physicist? You get an answer that requires more study. That’s my way of acknowledging I now have more to consider (and read) then I bargained for. What is does seem to indicate is that as I had suspected is that NASA may have used a Newtonian model with a fudge factor thrown in. That fudge of course being GR. Perhaps they should invest in computers/software that don’t have a problem with removing the fifth postulate, considering the effects of gravity and acceleration as equivalent and realizing time to be a dimension:-) All joking aside though I still am amazed how far the Newtonian perspective can serve in terms of accuracy and believe that Newton should be recognized for such an initial breakthrough.



  20. Hi Plato,

    “What seem interesting to me in this relation, "satellite travel to Mercury," is how we would look at space differently if we considered the "Interplanetary Superhighway."”

    In bring up the Lagrangian points when you consider three or more bodies is interesting. What I find interesting when the Lagrangian perspective is incorporated is that elements of GR and QM are already built into what is still considered a classical model. That is with a rudimentary space-time already considered (GR) with the mandate of least action (QM). I was always under the impression that it took far too long to take Fermat seriously. In fact in a manner of speaking he still isn’t for least action is considered as a consequence (anomaly) of average rather then a true postulate of nature. Space and time on the other hand is something that is widely considered to exist as being quantilized. I’ve always believed that until these two aspects of nature are truly decided for what they are unification will still prove elusive.

    Also thanks for pointing out that tie in with Binary Pulsar PSR 1913+16 as this serves to exemplify the relative strength (influence) when considering the difference between what is involved with plotting Mercury’s course and that of the binary pulsar in regards to GR. I would like to share a quote in this regard

    “The orbit of the pulsar appears to rotate with time; in the diagram, notice that the orbit is not a closed ellipse, but a continuous elliptical arc whose point of closest approach (periastron) rotates with each orbit. The rotation of the pulsar's periastron is analogous to the advance of the perihelion of Mercury in its orbit. The observed advance for PSR 1913+16 is about 4.2 degrees per year; the pulsar's periastron advances in a single day by the same amount as Mercury's perihelion advances in a century.”

    So thanks Plato for between what you offered and Stefan I have enough to chew on for some time.



  21. Phil:I was always under the impression that it took far too long to take Fermat seriously.

    Interesting observation. There had to be culminating vision of gravity adopted, eh?:)

    The least-action principle is an assertion about the nature of motion that provides an alternative approach to mechanics completely independent of Newton's laws. Not only does the least-action principle offer a means of formulating classical mechanics that is more flexible and powerful than Newtonian mechanics, [but also] variations on the least-action principle have proved useful in general relativity theory, quantum field theory, and particle physics. As a result, this principle lies at the core of much of contemporary theoretical physics.

    For instance, "the geological structure of Mercury?" What would "time variable measures" tell us about the "gravity field of Mercury?"

    This is taken in consideration, as a "gravity field measure" in the Messengers duties?

  22. Copernicus:
    To us who inhabit a chillier region, nature has denied that convenience, where stillness of the air is less frequent, and also because of the great obliquity of the globe, more rarely allows us to see Mercury.
    For this reason this planet tormented us with many detours and much work, as we examined its wanderings. Therefore we chose three positions from those which were painstakingly observed at Nuremberg.

  23. Hi smekhovo,

    thank you very much :-)

    My Latin was pretty good when I left high school, but I realised quickly that it was that segment of knowledge from school with the by way shortest half-life. Usually, I do not really miss it, but in this case, it would have been convenient... It's good to know that we have readers who still have that expertise ;-)

    So, thanks again, and best regards,


  24. Lateinisch ist immer bestes deutsch :-)

  25. Hi Stefan,

    “About trajectories, to my knowledge, Newton was convinced that HE was adjusting by hand from time to time the trajectories of the planets, so that the world would stay neatly ordered and stable.”

    Stefan, thanks again for the info. I will continue to track down all the leads you pointed to. As a consequence of reviewing what you said, I finally gave attention to what you inferred above. In as you are described as a physicist that has an interest in Science history I was somewhat surprised that you had this take on Newton. I suspect what you referred to as HE is what others call the great architect. From my reading of the Principia (English translation) all I gathered in this regard is that Newton suggested that HE had made the large heavenly bodies so greatly and sparsely spaced that this is what would account for them not all collapsing upon each other (Big Crunch). I never read anywhere that he considered HE made adjustments beyond this. I realize this is somewhat off topic and yet since you hold this interest in Science history (which I also share) I wanted to ask as to how you arrived at this conclusion.



  26. Great fotos. So as I see these fotos shows us big craters on Mercury. We'll waiting for next pictures!

  27. Hi Phil,

    I never read anywhere that he considered HE made adjustments beyond this. [...] I wanted to ask as to how you arrived at this conclusion.

    good point, and I have to admit that I knew this story (Newton's belief that God has to intervene from time to time to keep up the orderly running of the Solar System) so far only from secondary sources (I've never studied the Principia...), without references to the actual writings of Newton. You find an example in the text by Glashow mentioned by Plato in this thread, The Errors & Animadversions of Honest Isaac Newton, see "Part 3. Reason versus Revelation — Newton as Creationist": Newton knew that the solar system would endure for ‘many ages’ in its present form, but he also believed that the small irregularities in planetary motions and the gravitational effects of the planets on one another, “will be apt to increase, til this System wants a Reformation,” and again, “Motion is more apt to be lost than got, and it is always upon the Decay... Seeing therefore that the amount of Motion which we find in the World is always decreasing, there is a necessity of conserving and recruiting it by active principles.” Eventually the clock would run down and the world would tend to dissolution, unless the Creator would intervene.

    So, I've spent the weekend trying to figure out the sources, unfortunately with not too much success so far.

    It seems that this can be traced back to Newton's later writings, the Optics, and the second edition of the Principia (1713), and to the Leibniz-Clarke correspondence.

    To the second edition of the Principia, he added as an appendix the General Scholium, which contains statements as this: This most beautiful System of the Sun, Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. Maybe you refer to these statements which argue that the Solar System with the nearly circular orbits of the planets cannot be explained by contingency but demands an intelligent designer? But this doesn't say yet anything about the need for a continuous intervention by the designer.

    Now, while I am not sure about sources for this in Newton's papers, at least it is the interpretation by Leibniz of Newton's writings. In the first letter of the Leibniz-Clarke Correspondence, "Mr. Leibnitz's First Paper, being an Extract of a Letter Written in November, 1715.", Leibniz writes:

    Sir Isaac Newton, and his Followers, have also a very odd Opinion concerning the Work of God. According to their Doctrine, God Almighty [1] wants to wind up his Watch from Time to Time: Otherwise it would cease to move. He had not, it seems, sufficient Foresight to make it a perpetual Motion. Nay, the Machine of God's making, is so imperfect, according to these Gentlemen; that he is obliged to clean it now and then by an extraordinary Concourse, and even to mend it, as a Clockmaker mends his Work.

    and the footnote (1) refers Leibniz' remark to the Optics. The second edition (1717) is available online, in an English edition, and the respective paragraph seems to be on page 378: For while Comets move in very excentrick Orbs in all manner of Positions, blind Fate could never make all the Planets move one and the same way in Orbs concentrick, some inconsiderable Irregularities excepted which may have risen from the mutual Actions of Comets and Planets upon one another, and which will be apt to increase, till this System wants a Reformation.

    ... and this Reformation has to have a cause.

    Anyway... this seems roughly to be the background, and a starter for further reading and research, if you are interested.

    Best, Stefan

  28. Hi changcho,

    I was pretty sure GR effects would be very small and would not matter, but perhaps they do matter. As you say, someone actuallly working on the MESSENGER mision could elaborate?

    Well, I have no idea either how big these effects might be. But I have contacted the people at the Johns Hopkins University Applied Physics Laboratory who did the actual calculations and planning of the trajectory - maybe we get a first-hand answer.

    Best, Stefan

  29. Just one more source may be of interest?

    For Newton the universe lived in an infinite and featureless space.There was no boundary, and no possibility of conceiving anything outside of it. This was no problem for God, as he was everywhere. For Newton, space was the "sensorium" of God-the medium of his presence in and attachment to the world. The infinity of space was then a necessary reflection of the infinite capacity of God.The Life of the Cosmos By Lee Smolin Oxford University Press; New York, N.Y.: 1997, Page 91

  30. Before we get the idea of a intelligent observer I think it necessary to understand the limits to which Sir Isaac Newton's views saw Space. The previous quote will suffice.

    So without sanctioning a symbolic adjustment to views of Newton it is important to see "the context." AS well, that growth through Reformation.

    Lee Smolin:

    I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

    The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

    This may lead to the differences in positioning we see in the way our scientists see the world? It should not attribute "intelligent design" in any symbolic context, for it is an very "associative complex" people assign to what they see might be relevant to God today, whilst, these are thoughts contained in the history.

    The "truer depth" is through the understanding, which always still leaves room for those who want to believe in God, regardless, of this symbolic attachment some would like to post mark.:) Not you Stefan.:)

  31. Hi Stefan,

    Thanks again as for all of what you write is indeed interesting. Not that I ever doubted that you had grounds for the opinion you expressed as that is why I was prompted to ask the question. I will admit to never having read Optics only being aware that it was a particle take on the nature of light. This you have clearly demonstrated to be a mistake on my part. In reading the passage you included as well as the surrounding context, I can’t say I agree with Leibniz that it is referring to a clockwork that has to be wound up; rather that the order would deteriorate and adjustments would be need to be made if things were to be maintained to be the same in perpetude. This relates more closely to our modern concept of entropy rather then any notion of a non perpetual mechanism. As for Leibniz’s critique and interpretation in seems he either misunderstood or misrepresents what Newton said. He above all others had suffered the consequence of Newton’s slander and therefore would have motivation to put Newton in a bad light.

    What I do find interesting is that Newton felt that HE would be predisposed to make corrections to lend everything permanence as this would run contrary to the religious notions of the time (and even some today) that all certainly was made with a beginning and intended end. I would say that Newton here demonstrates that he was skirting very close to what would be considered hierarchy at the time. This is indeed consistent with other things I have read. Anyway I will certainly read all of Optics for what further may be gathered. By the way, I would like it to be made clear to all that my sole interest in this is from a purely historic perspective and I have no agenda beyond this.



  32. Stefan:
    Now, I guess if this is the state of the art for the calculation of trajectories, it has for sure been used for Messenger, which is travelling in the "most relativistic" region of the Solar System. - Meaning, yes, general relativity is taken into account for Messenger, via the PPN parameters of GR!

    Perhaps someone who knows more about that can correct me if I am wrong? Anyway, all this is really fascinating!

    Hi Stefan, I asked someone on the Messenger team and the answer is No, general relativity was not taken into account for the orbital trajectory calculations. I also learned that these photos are a small portion of what has been allowed to be released. The raw photos are apparently so good that they could go to the public immediately, with little data processing. Also I understand that while most of the Messenger color images released look sort of gray, in fact, the spectrally processed images are loaded with color that correlate well with the topography of the planet. The scientists working on it are drowning in a gold mine of great data.

    The policy for public release for this mission is more constrained than for previous missions; a combination of NASA directives and Science magazine directives. Results can be given to the public via press conferences (there is a Messenger press conference, one week from today), scientific conferences (the LPSC in March is loaded with Messenger papers), and the special Science issue, but at least so far, there is not the ready-release of images into the public like what we have, for example, the Cassini images and the Mars Rover images. Very unfortunate, I think.

  33. Dear Amara,

    thanks for the inside update about Messenger!

    Hm, this policy about photos, I don't quite understand that either. Is it to secure data to the scientist directly working on the project? That can be an argument. But why does Science insist on keeping back photos until that special number? I mean, it's not sold at the newsstand, so they probably won't triple the print run for that issue and make big money out of it?

    As for General Relativity in the calculation of the trajectory, via Emily Lakdawalla of the Planetary Society Weblog I heard that the Messenger planning team uses trajectory software that does take relativistic effects into account, but that "they are pretty much negligible"... I still would like to learn more about this. Anyway, this trajectory business seems to be quite complicated and quite distributed over different teams.

    Best, Stefan

  34. Stefan,
    NASA missions usually (or always) publish a kind of thirty-day report in Science; the idea of that special publication issue is to present the data and a quick scientific interpretation as soon as possible after the encounter/event. There will be a Science issue from this Mercury flyby, and so they've probably convinced the project managers that releasing data and results before that special issue violate their publication agreement. That's my guess about what is happening, but I don't agree with that policy.

    NASA missions have changed over the years their policies for how long to give the scientists exclusive rights to their data before releasing it to the public. Each mission is different, and it seems to me that the exclusive time before data public release is getting shorter, but I could be wrong. But yes, there is usually some period of time that the scientists have first rights to the raw data.

  35. Hi Stefan, I finally had some time to research this interesting topic further.

    I looked in my files and forgot about a long, very detailed and quantitative JPL memo 33-451 I had in my files, dating from the early 70's, which describes in detail an old program called DPTRAJ, and which was used to compute trajectories of the old Mariner missions. Unfortunately I don't have any inside information about the software the MESSENGER misison team uses, but Amara stated they considered GR efects negligible.

    Anyway, the author of this JPL memo states that "...the term relativistic acceleration means the perturbative inertial acceleration caused by general relativity, which is added to the Newtonian inertial acceleration." Further, "The relativistic acceleration terms caused by the sun affect the motion of bodies throughout the solar system. However, the terms caused by a planet or the moon are significant only in a "small" region (small in relation to the scale of the solar system) surrounding the body, which is called the relativity sphere; its center is located at the c.m. of the body" (p. 53). In other words, any spacecraft within the relativity sphere of a massive planet/moon should have the relativistic perturbations taken into account in the integration of the equations of motion (the relativistic perturbations due to the sun should always be taken into account). For Mercury, the radius of its relativity sphere is given as 2e6 km, which is certainly much larger than the closest passage of MESSENGER to Mercury a couple of weeks ago.

    Further, the author states that "the actual method for determining the motion of a system of n heavy bodies directly from the field equations was obtained for the first time by Einstein, Infeld and Hoffman in 1938".

    A few more observations. I can tell you that for computing trajectories of geostationary spacecraft, relativistic corrections are tiny and can in fact be ignored. Indeed, Montenbruck & Gill state that "As a rough rule, the size of general relativistic effects [for an Earth satellite] is given by the Schwarchild (see Bee's later post for the correct pronunciation!) radius of the Earth ~ 1 cm. Any application in satellite geodesy that approaches this level of accuracy must carefully consider the effects of general relativity ( Satellite Orbits, p. 111).

    However, for low earth satellites such as the GPS, one must take GR into account (see Physics Today, May 2002).

    Sorry for the long post; cheers!

  36. Ah - FYI. regarding the Eintein, Infeld and Hofmmann work of 1938, the reference I have is (from the JPL memo aforementioned)

    Bazanski, S. "Recent Developments in General Relativity", pp. 137-150. Pergamon Press, New York, 1962.

    I'd be surprised if there's not a more recent reference, but I don't know of it.

  37. Hi Amara,

    “and so they've probably convinced the project managers that releasing data and results before that special issue violate their publication agreement.”

    It seems clear, that when the science of business comes up against the business of science, which will prevail ;-)



  38. Hi Changcho,

    “(the relativistic perturbations due to the sun should always be taken into account). For Mercury, the radius of its relativity sphere is given as 2e6 km, which is certainly much larger than the closest passage of MESSENGER to Mercury a couple of weeks ago.”

    “Huston, Phil calling, we seem to have a problem” :-)

    I’m sorry yet the more that’s explained the greater my confusion. My initial question related to GR effects and all the trajectory calculations. In terms of explanation SR and other things have been brought into play (as of course is necessary). I have to admit however I can’t find a definite answer in all this. So can anyone confidently say, with everything taken and considered is QM used in the calculation of Messenger’s path and in what manner? Also is it the total methodology in replacement of Newton’s; a fudge factor that accounts for the difference or not considered at all.



  39. Hello Phil - whether to use GR (presumably you meant GR, not QM) or not in the trajectory planning is a matter of how much accuracy you need.

    My guess is that it may not be needed in computing the trajectory of MESSENGER when passing by Mercury (as Amara implied).

  40. Hi changcho,

    thank you very much for your comment!

    What you write fits very well to the idea I've got from the "Monograph 2: Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation" of the JPL... It also mentions, for example, the sphere of influence (section 4, page 4-4), and gives the relativistic equations of motion (page 4-19) - I think the PPN formalism of Will and Nordtvedt (1972) mentioned there superseeds Einstein/Infeld/Hoffmann. Unfortunately, I have no idea if and how what is described there has actually been realised in the Messenger project.

    What I had in mind is that GR may come into play for Messenger via the influence of the deep gravitational well of the Sun, not by Mercury. And I what I would really like to know the following:

    There was a correction of the Messenger trajectory on December 19, called the TCM-19 fine-tuning, and since that time, the probe had travelled more than 100 million kilometres up to the fly-by at a surface-distance of 200 km, and was at that moment 1.43 km off the expected point (see the Planetary Society Blog). Now, I wonder: If one calculates the Messenger trajectory using the December 19 data as initial conditions, once including and once without all PPN terms for the gravitational acceleration - how big is the integrated difference at the flyby? Is it 1 cm, 1 m, 10 m, 1 km? It's probably less than 100 km - since an uncertainty of that order may have resulted in an impact instead of a flyby, and would clearly not be negligible ;-).

    Unfortunately, I couldn't get an answer to that question so far. But I also have not yet understood who is in charge of the actual trajectory calculations? It seems that this is something different than the overall planning of the journey.

    So, Amara, changcho, or whoever else reads this - if you know more details, I'll be glad if you can tell men :-)

    Best, Stefan

  41. Dear Stefan,

    There should be a navigation team for Messenger. I don't know the inside organization of the Project, but I asked more questions of a colleague who is on the Messenger team, who also asked questions of the Messenger project navigation folks. The answer that I gave previously here in your comments section, came from a Messenger project official, who, after talking with one of the navigation experts: Bobby Williams, associated with the Messenger team, says he was wrong. The correct answer, quoted from the Messenger Project official (whose name I don't know; all of this is coming second-hand from my colleague who is on the team), is the following:


    "The general relativistic effect of the Sun on MESSENGER'ss trajectory IS included. You will recall that this adds a very small r^-3 component to the effective scalar potential and is responsible for the precession of the perihelion of Mercury. The velocity-dependent, weak-field limit corrections (that provide for the Lense-Thirring effect) are NOT included for MESSENGER's trajectory.

    Special relativity effects are taken into account as well for dealing with observables.

    So the corrections are there, but are not based upon a full-up integration of the GR equations of motion.

    Sorry for my error and the confusion it caused."


    I hope that helps!


  42. FYI. --Amara

    Jan. 28, 2008
    Dwayne Brown
    Headquarters, Washington


    WASHINGTON - NASA will hold a press conference at 1 p.m. EST on Wednesday, Jan. 30, to announce scientific findings and release never-before-seen images of Mercury. The images were taken during a NASA spacecraft's January flyby of the planet. The briefing will take place in the NASA Headquarters' James E. Webb Auditorium, 300 E Street, S.W., Washington, and will be carried live on NASA Television.

    NASA's MErcury Surface, Space ENvironment, GEochemistry, and Ranging (Messenger) spacecraft is the first mission sent to orbit the planet closest to our sun. After a journey of more than 2 billion miles, the spacecraft made its first flyby of Mercury on Jan. 14. The spacecraft's cameras and other sophisticated, high-technology instruments collected more than 1,200 images and made other observations. Data included the first up-close measurements of Mercury since the Mariner 10 spacecraft's third and final flyby on March 16, 1975.

    Participants in the press conference will be:
    - James Green, director, Planetary Science Division, NASA Headquarters, Washington
    - Sean Solomon, Mesenger principal investigator; director, Department of Terrestrial Magnetism, Carnegie Institution of Washington
    - Maria Zuber, Messenger science team member; head, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of
    Technology, Cambridge
    - Robert Strom, Messenger science team member; professor emeritus, Lunar and Planetary Laboratory, University of Arizona, Tucson
    - Louise Prockter, instrument scientist for the Mercury Dual Imaging System, Johns Hopkins University Applied Physics Laboratory, Laurel, Md.

    Reporters may ask questions from participating NASA locations. The briefing also will be streamed live on NASA's Web site at:

  43. Stefan - thanks for the link to the monograph, that indeed is more recent. Very interesting, I will study it!

    With respect to how far off they are from their computed trajectory, in general what is usually done at these points is to do an orbit differential correction (i.e., use the 'observed' position/velocity of the spacecraft in your database and proceed from there), sort of like a reset. The more complete your integration/propagation model, in principle the smaller the discrepancy between your predicted and observed orbits.

    Interestingly, the group in charge of the MESSENGER trajectory is KinetX, a company that NASA outsourced the flight dynamics to.

    Amara, thanks for the MESSENGER flyby science results. Looks like the main finding is for evidence of volcanism at Mercury.

  44. Hi Stephen, Amara & Changcho,

    Thanks everybody, this has all been quite a journey in more ways then one. What then it all seems to boil down to is that they start with Newtonian Mechanics and then make adjustments for what are the GR and SR effects (not counting frame dragging). I’m pretty happy with all this since it relates to what were only my initial intuitive thoughts on the matter. My way of looking at it was seeing that except for Mercury all the other planets orbits were pretty much well described by Newton’s method. The one that stuck out from this was of course Mercury. In the centuries before Einstein it was thought that there must be some unseen and yet to be discovered body (planet) that was causing Mercury to have this orbital shift. With that considered I couldn’t image how they would have a space craft be delivered to Mercury’s position (especially with all gravity boosts and such) without in some way taking GR into account. Other then to perhaps correct from time to time (ham handed method) to adjust for what they didn’t account for.

    Now what about the solar wind, do you think they took this into account:-)



  45. Phil - "Now what about the solar wind, do you think they took this into account:-)"

    Probably not, but they surely must take into account solar radiation pressure.

  46. Dear Amara,

    thank you very much for the update about relativity in the trajectory calculation, and the publication of results :-)

    Dear Changcho,

    yes, I find it also remarkable that parts of the trajectory calculations and the navigation have been outsourced to external contractors. It's funny that there are such private companies!

    Dear Phil,

    about solar sailing, check out the last paragraphs of Emily Lakdawalla's blog post New MESSENGER image release: Mercury at high resolution...

    Best, Stefan

  47. Dear all,

    thank you for your interesting comments!

    I have tried to sum up the issue of General Relativity in the Messenger business in a new post - I would suggest to move the discussion about this point to there, if there is a need...

    Best, Stefan

    Best, Stefan



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