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Astrophysics, abstract

From: Stan Peale [view email]

Date: Mon, 14 Nov 2005 22:21:56 GMT (314kb)

The proximity of Mercury's spin to Cassini state 1

Authors: S. J. Peale

Comments: 23 pages,12 figures, In press in Icarus

In determining Mercury's core structure from its rotational properties, the value of the normalized moment of inertia, $C/MR^2$, from the location of Cassini 1 is crucial. If Mercury's spin axis occupies Cassini state 1, its position defines the location of the state. The spin might be displaced from the Cassini state if the spin is unable to follow the changes in the state position induced by the variations in the orbital parameters and the geometry of the solar system. The spin axis is expected to follow the Cassini state for orbit variations with time scales long compared to the 1000 year precession period of the spin about the Cassini state because the solid angle swept out by the spin axis as it precesses is an adiabatic invariant. Short period variations in the orbital elements of small amplitude should cause displacements that are commensurate with the amplitudes of the short period terms. By following simultaneously the spin position and the Cassini state position during long time scale orbital variations over past 3 million years (Quinn {\it et al.}, 1991) and short time scale variations from JPL Ephemeris DE 408 (Standish, 2005) we show that the spin axis will remain within one arcsec of the Cassini state after it is brought there by dissipative torques. We thus expect Mercury's spin to occupy Cassini state 1 well within the uncertainties for both radar and spacecraft measurements, with correspondingly tight constraints on $C/MR^2$.
Paper (*cross-listing*): gr-qc/0511137

Date: Fri, 25 Nov 2005 13:47:02 GMT (4kb)
Date (revised v2): Tue, 29 Nov 2005 11:55:15 GMT (4kb)
Date (revised v3): Thu, 1 Dec 2005 12:41:58 GMT (4kb)

Title: Can Solar System observations tell us something about the cosmological

Authors: Lorenzo Iorio

Comments: Latex2e, 4 pages, 2 table, no figures, 11 references. Table 2 added,
typos in the units of Lambda corrected
In this note we show that the latest determinations of the residual Mercury's
perihelion advance, obtained by accounting for almost all known Newtonian and
post-Newtonian orbital effects, yields only very broad constraints on the
cosmological constant. Indeed, from \delta\dot\omega=-0.0036 + - 0.0050
arcseconds per century one gets -2 10^-34 km^-2 < Lambda < 4 10^-35 km^-2.

The currently accepted value for Lambda, obtained from many independent
cosmological and large-scale measurements, amounts to almost 10^-46 km^-2.

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Paper (*cross-listing*): gr-qc/0511138

Date: Fri, 25 Nov 2005 13:50:40 GMT (8kb)

Title: Solar System planetary motions and modified gravity

Authors: Lorenzo Iorio

Comments: Latex2e, 8 pages, 4 tables, no figures, 25 references
According to the braneworld model of gravity by Dvali, Gabadadze and Porrati,
our Universe is a four-dimensional space-time brane embedded in a larger,
infinite five-dimensional bulk space. Contrary to the other forces constrained
to remain on the brane, gravity is able to explore the entire bulk getting
substantially modified at large distances. This model has not only cosmological
consequences allowing to explain the observed acceleration of the expansion of
our Universe without resorting to the concept of dark energy, but makes also
testable predictions at small scales. Interestingly, such local effects can
yield information on the global properties of the Universe and on the kind of
expansion currently ongoing. Indeed, among such predictions there are extra
precessions of the perihelia and the mean longitudes of the planetary orbits
which are affected by a twofold degeneration sign: one sign refers to a
Friedmann-Lemaitre-Robertson-Walker phase while the opposite sign is for a
self-sccelerated phase.

In this paper we report on recent observations of planetary motions in the Solar System which are compatible with the existence of a fifth dimension as predicted in the Dvali-Gabadadze-Porrati model with a self-accelerated cosmological phase, although the errors are still large. The Friedmann-Lemaitre-Robertson-Walker phase is, instead, ruled out.

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Mercury a Possible Hit-and-Run Planet

New computer modeling shows that the planet Mercury might have formed in a
hit-and-run collision that stripped off its outer layers.

* Catch Mercury While You Can

Once again it is time to seek out what has often been cited as the most
difficult of the five brightest naked-eye planets to see: Mercury.
QUOTE (ljk4-1 @ Feb 17 2006, 03:49 PM) *
...cited as the most difficult of the five brightest naked-eye planets to see

The first time I ever saw Mercury was from behind, during its 1999 transit of the sun wink.gif
QUOTE (odave @ Feb 18 2006, 04:26 AM) *
The first time I ever saw Mercury was from behind, during its 1999 transit of the sun wink.gif

I was lucky to catch that one, too -- it was immediately before sunset at my location. But that was about the hundredth time I'd seen it.

Given its elusiveness, one of the surprising things about it is that it is one of a very few objects that can be, at certain times, the brightest object in the sky. I've seen that.

For anyone capable of programming an ephemeris-generating program, I'd like to propose the challenge of generating all the instances in the last/next X years in which Mercury is the brightest object in the sky. Off topic, but...
Tomorrow at 7:00 pm, the Mercury will be in half visible as shown in the below picture:
Click to view attachment
The Mercury view will vanish after March 3.

Rob Pinnegar
QUOTE (JRehling @ Feb 18 2006, 08:55 AM) *
For anyone capable of programming an ephemeris-generating program, I'd like to propose the challenge of generating all the instances in the last/next X years in which Mercury is the brightest object in the sky. Off topic, but...

Actually, it might also be interesting to find out how many objects are capable of being the brightest object in the sky. After the Sun, the Moon, Mercury, Venus, Mars, Jupiter and Sirius, how many stars can do it? Can Saturn do it?
Note that Mercury is actually brightest when it is at superior conjunction, on the far side of the sun. It's not a whole lot further from Earth than when at maximum elongation, is 100% instead of 50% illuminated, and, maybe most importantly, is near zero phase angle where backscatter and the hiding of soil-grain shadows makes the surface dramatically brighter than at phase angles of even 30 or 15 degrees, much less 90 deg.

The Venus cloud-haze is forward scattering, so, together with the much greater size change of the Venusian disk between crescent and gibbous phase, results in a rather fat crescent being the geometry where Venus appears brightest.
NASA Science News for February 21, 2006

Mercury makes a rare appearance in the evening sky this week.


Find out about the Science@NASA Podcast feed at .
A paper currently in press with Icarus:

Evolution of Mercury's obliquity
Icarus, In Press, Corrected Proof, Available online 17 February 2006
Marie Yseboodt and Jean-Luc Margot

- Early Mercury Impact Showered Earth

Leicester, England (SPX) Apr 05, 2006 - New computer simulations of Mercury's
formation show some of the resulting ejected material ended up on Earth and
Venus. The simulations, which track the material's path over several million
years, also shed light on why Mercury is denser than expected.
A question that's nagged me for a long time...

Mariner 10 was in a solar orbit that intersected Mercury's orbit in resonance with the planet, so that it revisted Mercury multiple times (the spacecraft was actually alive for the first three; presumably more encounters, if farther ones, continued to take place after the craft died).

The rub was that Mercury's rotation is also in resonance, so that the same face of Mercury was lit at all three encounters. This is because the orbital period of Mariner 10 was 2 Mercury "years", and the 3/2 resonance of Mercury's revolution and rotation meant that it rotated precisely twice while Mariner 10 and the planet were apart.

The delta-v budget for getting to Mercury was a limiting factor, so the mission could not have gotten into any old Mercury-crossing orbit we wished, but to me, the ten million dollar question is: Why not put it into a solar orbit with a LONGER period that intersected Mercury's orbit at the same location every THREE Mercury "years"? If that had been the mission profile, the likely outcome would have been that the craft would have only survived two such flybys (as it was, it was limping into the third), but they would have shown opposite sides of the planet, giving us an almost full global map, instead of the half-planet coverage we've had to live with for the last 33 years.

In terms of pure delta-v, the longer period should have been easier to achieve. Unless the gravity assist with Venus had some stringent requirements that forbade the longer period, it seems like it would have been a win-win scenario to take the longer period and the full coverage.

This is now a moot point in many ways, but it's stuck in my craw for a long time. Any ideas?
Greg Hullender
Have a look at chapter 2 from "The Voyage of Mariner 10"

"Early in 1970, Guiseppe Colombo of the Institute of Applied Mechanics in Padua, Italy, who had been invited to JPL to participate in a conference on the Earth-Venus-Mercury mission, noted that in the 1973 mission the period of the spacecraft's orbit, after it flew by Mercury, would be very close to twice the period of Mercury itself. He suggested that a second encounter with Mercury could be achieved. An analytical study conducted by JPL confirmed Colombo's suggestion and showed that by careful choice of the Mercury flyby point, a gravity turn could be made that would return the spacecraft to Mercury six months later."

Sounds as though even the delta-v to get into the 2x orbit was hard to come by.

QUOTE (Greg Hullender @ Sep 28 2007, 03:49 PM) *
Have a look at chapter 2 from "The Voyage of Mariner 10"

"Early in 1970, Guiseppe Colombo of the Institute of Applied Mechanics in Padua, Italy, who had been invited to JPL to participate in a conference on the Earth-Venus-Mercury mission, noted that in the 1973 mission the period of the spacecraft's orbit, after it flew by Mercury, would be very close to twice the period of Mercury itself. He suggested that a second encounter with Mercury could be achieved. An analytical study conducted by JPL confirmed Colombo's suggestion and showed that by careful choice of the Mercury flyby point, a gravity turn could be made that would return the spacecraft to Mercury six months later."

Sounds as though even the delta-v to get into the 2x orbit was hard to come by.


It definitely was. My question stems from the fact that a 3x orbit should have been easier (less delta-v, anyway) AND scientifically more desirable.

Basically, Earth (and therefore the spacecraft before it was launched) is in a 4x Mercury-period orbit. It takes more delta-v to get the probe down to 2x than just down to 3x.
My understanding has always been that it was pure luck that the planned mission trajectory was such that it was possible to modify it into a multiple encounter mission.

Remember that this encounter trajectory was not purely a function of the flyby altitude, but also of when and how you flew past Venus.

I really doubt they could have just as easily switched gears and get it into a '3X' orbit. Such an orbit would have had a substantially greater Solar apopasis (I'm probably using the wrong term here), and hence a lot of delta-vee would have had to somehow been introduced into the mission to get there. Since they didn't have much fuel on board Mariner 10, we might have been looking at multiple Venus flybys, or even Venus-Earth-Venus-Mercury scenarios.

Rmember that this was the very first multiple planet flyby. It was hard enough for them to figure out how to get the Venus-Mercury-Mercury-Mercury thing to work. The billiard-ball style of mission planning (such as Venus-Venus-Earth-Jupiter-Saturn) didn't spring into existance over night.
A couple of points:

* The 2x period was desirable because with the needed higher altitude sunward second pass, almost the entire sunlit hemisphere could be observed. This allowed the inbound and outbound flyby 1 mosaics to be stitched together.

* IIRC, the post encounter orbit wasn't realized to be near 2 X 88 days until pretty late in the mission planning, and Mariner 10 was just about the cheapest planetary mission ever flown. No big changes would have been possible. Bruce Murray had overseen a slew of changes in the mission up to that point (the 1500 mm telephoto lens, advanced computer control, high data rate telemetry, lunar flyby on leaving earth vicinity, etc.) and the mission managers most likely would not have gone along with another change.

* A 3 X 88 day orbit will have perihelion beyond earth's orbit. Modifications to Mariner 10 for this would be a problem (IIRC, the space craft antenna would not have been able to slew properly earthward there) Additionally, there might be a problem with a gravitational deflection at Venus changing the eccentricity of the resultant orbit that much, (I am not smart enough to do the math on that one) there might not be a flyby distance above the solid Venusian surface to realize the math for that trajectory change.
{Anticipating a bad joke}

Yeah, we have discussed litho-braking here before.

Now I am bringing up litho-deflection.

It is interesting, now that we are on the verge of Messenger orbiting Mercury, to contemplate the Mariner 10 mission in a hypothetical 3X88 orbit.

Let's keep the geometry of the first flyby the same. One big difference would be the encounter speed. To come back after 264 days, instead of 176, Mariner 10 would need to go faster to climb further away from the sun. Mercury is well lit, so spacecraft motion won't blur the pictures, but with a faster flyby, we have less time to take all the pictures. This would probably cut the # of close range pictures, and probably reduce the extent of the mosaics.

The 2nd flyby, if at a similar 50,000 km sunward direction, would have imaged the opposite hemisphere. Foreshortening along the terminator in the pictures would have made it harder to stitch the mosaics together, however, the Caloris basin would have been seen in it's entirety (in 2 strips) , and the outer ring would have helped align them. We might have had some coverage of 75 to 80 % of Mercury, but with lower resolution along the edges of the covered areas of the 2 flybys.

If a second flyby could have had a geometry similar to the actual first or 3rd Mariner 10 flyby, we would have seen the west adjacent area of Caloris on approach, and on departure, we would have seen the eastern adjacent area of the first flybys approach hemisphere. We would have 4 large 'stripes' of coverage of Mercury. Stitching the 4 bands together would be tricky, all the adjoining areas on the limb would be foreshortened, and all the terminator seams would have illumination from 180 degrees around.

This would have been an interesting flyby. We would have perhaps double the areal coverage, but with less of an overall global context. I would be cautiously optimistic that perhaps Mariner 10 might have still accomplished 3 flybys. Due to the loss of attitude gas, Mariner 10 used the solar panels to help control the spacecraft attitude between the flybys. This technique would still work in the 264 day orbit, so maybe, just maybe, they could have squeezed a third pass out of the old girl. Another problem however, was the thermal effects on the craft. In the 3X orbit, Mariner 10 would have been a lot further out at perihelion. The antenna feed had a temperature sensitivity problem, and this might have exacerbated that severely. This problem has the potential to drastically cut the data rate of the antenna system. Also, the on board tape recorder would still have been lost, and with the high flyby speed, this would seriously impact the amount of data returned.

All in all, the mission as flown was most excellent. Given the twitchiness of the craft, I bet the controllers and flight personnel were relieved they did not have the 3X orbit, but I bet they could have still done a magnificent mission if they had.
Maybe someone with a bit more ken of orbital mechanics can address this; but is the obstacle to the 3X orbit in getting the perihelion of the spacecraft orbit beyond earth's orbit? It would seem a deflection at Venus into a 264 day orbit would be 'easier' than a deflection into a 176 day orbit, but achieving the eccentricity needed for the former implies a much faster approach speed to Venus than you would get than from simply 'falling' from earth's distance from the sun towards Venus.

(even with my limited understanding of the math, I love this trajectory stuff)

Now that we already have pretty good coverage of Mercury from the Messenger flybys, if someone would like to 'markup' some global Mercury pictures appropriately, we could get a pretty good idea of what Mariner 10 might have pictured in the hypothetical 3X orbit. Just transpose the second flyby coverage 180 degrees for the distant flyby option, or shift the first flyby coverage 180 degrees for the close option 2 Mercury 'days' later.

(I might even be able to do this with scissors and paste, LOL!)

Seems you are having a good chat with yourself, tasp.
I don't understand why a spacecraft with an orbital period three times that of Mercury has to have a perihelion outside Earth's orbit. 264 d < 365 d. This requires a smaller semi-major axis (and consequently, a lower perihelion).
I was extrapolating from the 176 day orbit having an aphelion between Venus and earth, and accepting a perihelion at Mercury. Enlarging that orbit would seem [[based on pure assumption] to get you uphill of earth's orbit. Sadly, I can't do the math to get a precise dimensions.

And sorry about mixing up perihelion and aphelion. I am home sick today with a nasty head cold. Snowed in too. Beautiful day here for Titan, not so good for midwest USA.
Greg Hullender
From Kepler's laws, I figure an orbit with a period of 264 days to have a semi-major axis of 0.8 AU. If that orbit's perihelion was at Mercury's aphelion (0.467 AU) then it's aphelion should be at 1.14 AU.

Anyone want to double-check that?

I get -1.137, so I probably have a sign error somewhere:)
QUOTE (Greg Hullender @ Feb 2 2011, 04:31 PM) *
Anyone want to double-check that?

checked. That's correct.
264 days = 0.72 years = T
a = T^(2/3) = 0.80 AU (from Kepler's law)
q = 0.467 AU

from q = a*(1-e)
e = 1-q/a = 0.42 (orbital eccentricity)
hence Q = a*(1+e) = 1.14 AU
As always, the folks with the math gene are very much appreciated!

Interesting orbit, compare to Phaeton that we were discussing on the Hyabusa thread.

Bruce Murray had a nice scaled drawing of the Mariner 10 176 day orbit in his book Journey Into Space, and also a veritable treasure trove of insider information on the amazing Mariner 10 mission.

Bruce met Beppe Columbo! That's how they all found out about the resonant orbit they had accidentally set up. Murray had tremendous respect for Beppe. So too his colleagues setting up their own Mercury mission to be named after him.
QUOTE (tasp @ Feb 2 2011, 09:26 PM) *
Bruce met Beppe Columbo!

ColOmbo, not ColUmbo
Thanx for the correction!

Ebay has a copy of Murray's book Journey Into Space for $4.99 if any one is interested.

The Mercury reminisces are worth that, and he also writes about exploring Mars, the Venera series, and Voyager. The story behind the 1500 mm Mariner 10 camera system and the radio upgrades that made the transmission of those great pictures is especially interesting.
QUOTE (Littlebit @ Feb 2 2011, 11:07 AM) *
I get -1.137, so I probably have a sign error somewhere:)

I keep getting 1.8675309 over and over again. I should probably turn off the radio while I'm working on orbital calculations.
Googling "Mariner 10 orbit" and checking the images, (it's the first one tonight) will show the 176 day orbit diagram. It has aphelion further out from the sun than Venus. Intuitively, just glancing at that diagram, suggests an aphelion for the 264 day orbit that is going to be a nice bump further out than that. (And I realize that doesn't help with the calculations)

Like I said, sorry I can't do the math, but I really appreciate those that can.

Does the perihelion velocity for the 176 and the 264 day orbits 'pop out' of the calculations easily? (It would give an ~ idea of the Mercury encounter speed of the craft)
Greg Hullender
Quite easily. Mercury at Aphelion should be about 39 kps. Mariner X was 55 kps. Your probe would be 58 kps.

As before, someone should double-check this before you reply on it to actually launch something. :-) I used this formula from Wikipedia


That is getting right up there.

Appreciate the calculations. Gives a vivid idea of the challenges in navigating that region of the solar system. All those sharp, unblurred Mariner 10 pictures are quite an achievement, considering the flyby speed.

(I am not likely to be sending any of my own spacecraft on this trajectory, the Legos would melt)
Phil Stooke
Not much action on here, but every workday there's a new image from MESSENGER. Here I have joined two nice color images of the Tolstoj area.


Click to view attachment
Wow ! It looks like a deep field with many galaxies, nebulas and stars. Magnificent !
Reminds me of Callisto
First burn in orbit around Mercury (ever!)
QUOTE (Explorer1 @ Jul 28 2011, 05:03 AM) *
First burn in orbit around Mercury (ever!)

First burn Messenger successfully completed June 15, 2011

Phil Stooke
Another composite of two images from the big color basemap now being compiled.


Click to view attachment
Phil Stooke
A comparison of presumably vent-like structures on Mercury and the Moon at the same scale. The Mercury pic was part of the press conference on JUne 16th, where it was captioned 'Etched Terrain"


Click to view attachment
New results on mercury shrinkage discussed in at a meeting of the American Geophysical Union in San Francisco, yesterday :

Studies of Mercury show that it has shrunk by about 11 kilometres across since the Solar System's fiery birth 4.5 billion years ago. As the planet cooled and contracted, it became scarred with long curved ridges similar to the wrinkles on a rotting apple.

A new census of these ridges, called lobate scarps, has found more of them, with steeper faces, than ever before. The discovery suggests that Mercury shrank by far more than the previous estimate of 2-3 kilometres, says Paul Byrne, a planetary scientist at the Carnegie Institution for Science in Washington DC. He presented the results today at a meeting of the American Geophysical Union in San Francisco, California.

The finding helps explain how Mercury's huge metallic core cooled off over time. It may also finally reconcile theoretical scientists, who had predicted a lot of shrinkage, with observers who had not found evidence of that — until now. “We are resolving a four-decades-old conflict here,” Byrne told the meeting.

Planetary scientists have been arguing over Mercury's lobate scarps ever since the Mariner 10 spacecraft flew past the planet three times in 1974-75. Researchers can use measurements of the length and height of the scarps to calculate how much planetary shrinkage they represent.

That shrinkage is a product of Mercury's odd composition — “like a core floating through space with a thin outer blanket,” says Byrne. Most of the planet is made of that large core, and so it would have cooled rapidly as heat rushed toward its surface. Modelling studies have long suggested that the planet should have shrunk by 10-20 kilometres over its lifetime, compared to the 2-3 kilometres estimated from Mariner 10 data1.

The latest estimates come from NASA’s MESSENGER probe, which photographs and measures Mercury's topography. Last year, Italian scientists used MESSENGER data covering one-fifth of the planet to show that its shrinkage was probably greater than the Mariner 10 estimates.

The latest work, covering the entire planet, revealed many lobate scarps with sharp vertical relief, Byrne said. It also uncovered details on another kind of surface feature that may be related to shrinkage. These ‘wrinkle ridges’ are less pronounced than the lobate scarps but may also have formed during contraction. Combined, the data on the lobate scarps and the wrinkle ridges suggest that Mercury's diameter has shrunk by 11.4 kilometres, Byrne said. Even leaving out the wrinkle ridges gives 10.2 kilometres of contraction.

Those numbers are plausible to at least one planetary scientist who studied Mercury’s shrinkage using Mariner 10 data in the 1970s. Jay Melosh, a planetary geologist at Purdue University in West Lafayette, Indiana, suspects that even more lobate scarps may be lurking out there. “Many of these things may still be hiding,” he says. “As far as I'm concerned, this may be an underestimate of the amount of shrinkage.”

Nature news Nature doi:10.1038/nature.2013.14331
Phil Stooke

John Lennon's on Mercury now...



Nobody told him there'd be days like these. An excellent tribute.
I suppose that's appropriate. "Imagine there's no atmosphere . . "
QUOTE (Phil Stooke @ Dec 16 2013, 11:04 PM) *

John Lennon's on Mercury now...


Roll on John! Perhaps they can bend the rules for Bob Dylan.
And when will they add Freddy Mercury ?? ;-)

Related news. the dark surface of Mercury might be caused by carbon delivered by comets, so does this make Mercury a painted planet?
For this study, the team launched projectiles in the presence of sugar, a complex organic compound that mimics the organics in comet material. The heat of an impact burns the sugar up, releasing carbon.

Sugar on the dayside of Mercury would probably transform to a black carbon-rich crust, even without micro-meteorites.

Nevertheless the idea of comets as a source for carbon sounds reasonable.
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