Planetary Science - Science topic

All you need is here: PDS Geosciences Node https://pds-geosciences.wustl.edu/

Gáspár Albert INRE:"idea', if you found it useful, 'recommend' the answer so that others down the line can discover it.

What follows has a huge caveat, the specifics of your work is way over my head, but my work does have an aspect of dealing efficiently with all sorts of coordinate systems and data representations, so the following are more for possibly sparking trains of thought which someone far more capable than me might find useful - somewhat inspired by the false dichotomy between vector and raster formats in a GIS.

The 'spherical' issue is as old as geography itself, and up until now has been addressed piecemeal mostly by projecting geographic coordinate systems, and the performance limitations of computational infrastructure available. Relatively recently, the notion of DDGs (Discrete Global Grids) is undergoing an explosion of refinement as a 'sphere' ( ... and 'sphere-ish) as a recursive n-dimensional data representation (cursory, rough overview at https://spatialparalysis.xyz/blog/dggs-eli5/ but a quick Google Scholar finds more detailed descriptions: https://scholar.google.com/scholar?lookup=0&q=A+Review+of+the+Research+on+Discrete+Global+Grid+Systems+in+Digital+Earth ). Although on first appearance it would seem complex to calculate through these fields, there are now methods which mitigate this. These are already making their way into weather modeling ( https://www.abccolumbia.com/2019/01/11/ibm-to-deliver-worlds-highest-resolution-weather-model/ ).

From my naive reading of your project, it seemed to be analogous to a sort of 'weather' model, except with 'rock' instead of 'gas'.

The other vauge 'hunch' is how modern GPUs use quaternion representations and maths to short circuit the need for Cartesian calculations and transformations (quaternion interpolation) - and not just the 'spatial' sorts of computation, but for physics engines ( collision detection, etc. like when there are two spinning irregular objects with different rotational axes).

I am interested to learn if it is possible "Ram Chandra Pageni" since I am doing research in Space Science.

You are most welcome dear Claudio Orlanducci .

Wish you the best always.

Dear Yoshinari Minami,

Thanks for answering the question:

Thank you very much for providing interesting publications describing important issues of the discussed issues.

Thank you, Regards,

Dariusz Prokopowicz

Extraterrestrial life is hypothetical life which may occur outside Earth and which did not originate on Earth. Such life might range from simple prokaryotes (or comparable life forms) to intelligent beings and even sapient beings, possibly bringing forth civilizations which might be far more advanced than humanity. The Drake equation speculates about the existence of sapient life elsewhere in the universe. The science of extraterrestrial life in all its forms is known as astrobiology. https://en.m.wikipedia.org/wiki/Extraterrestrial_life

What about the scientific return of an asteroid mission? Up to now, stony (Eros and Itokawa) and carbonaceous (Bennu and Ryugu) near-Earth asteroids have been studied extensively, while in the main belt Vesta and Ceres have been visited by mission Dawn. Also, in the near future, mission Psyche will visit a metallic asteroid for the first time, and mission Lucy will explore some Jupiter Trojans.

What next? Is there any other type of asteroid to prioritize in order to help answering some important question?

Hi! I don't know if it would help but this article is about hapke modeling calculations with IDL.

You can go through MIT courses on YouTube.

Hello Al, if I understood correctly the problem you described is known as Lambert's Problem. I am not aware of a specific software, but I know of two great solver scripts that can be found on github:

In Python:

In Matlab:

If you look for Lambert's Problem or Lambert solver I'm sure you will find code for other languages as well.

All the best!

Gloria, while I agree with James generally that it is hard for people to empathise with 'inanimate objects', I don't think the issue is quite so black and white.

I think most people have lost interest in what's happening on the Space Station, despite there being humans involved. I'm sure the research done there is important, but there's nothing to see - in a dramatic sense.

By contrast, the photos from the Voyager probes, the images from the Mars Rovers, and the Rosetta/Philae comet rendezvous, I feel, all generated a lot of public interest, because they were all going where no one had been before, showing us better, closer images than available from Earth, and doing things that we previously never thought we could do.

This is an old debate. 'Mere' scientific research will never attract the public interest unless it is something new and exciting. Human missions will, because we can relate to them, personally. It might not be me up there, but it's someone like me, and isn't it incredible that we can do that.

That's what opens the doors to Government funding for all sorts of other space research. People want to see something for their money.

And if we don't put people into space, and open the possibility of living on other worlds, then there are a lot of people out there ready to dismiss all space research as a waste of money - everyone from those who don't want to believe any of it was real in the first place, to the Green lobbies who want to know why we're wasting money on such stuff when the world is in so much trouble.

Certainly there is a relationship

In ancient times Jupiter was called the rain god, and here today we barely get to the reliable scientific conclusion on this matter

If i may add my 5 cents to this:

--> Depends how you want to see Elon Musk: as the visionary who wants humanity to thrive and improve? Or just as the one who seeks fame and fortune for being the first in doing things?

In my humble opinion, humanity has yet to reach a level of mindset to overcome cultural and religious differences. We might have satellites and smart phones, but in our thinking we still behave like cave-men.

For example, the Americans, when setting foot on the Moon, put an American flag there. Not one showing Earth. How would it be on Mars, when Chinese, Indians, Europeans and Americans set foot there? Whom will it belong to? For sure not the entire humanity, so we would just bring all of our archaic thinking into a new world. All our problems and issues, and soon the new planet will suffer all the same problems as we have on Earth.

As long as we do not manage to live as one humanity on one planet (i.e. having a global government), there is no point in making humanity multi-planetary.

--> As mentioned above: if you want to colonise something, who does it belong to? Is there indigenous life (whether intelligent or not)? Or is it a barren rock?

Now given the barren rock case: Who does it belong to? Imagine it has a huge amount of rare minerals on it. Is it "whoever finds it can keep it"? In the outer space treaty from the 1960s, they addressed this topic, saying that space belongs to all humanity, yet not all nations have signed this and yet when it comes to mining/farming/inhabiting these space environments, how is that regulated? And if violated, who prosecutes the violators?

There is a huge legal issue in regards to occupying space environments.

Now given the planet is not a barren rock, but an obviously inhabited planet: Now we can either develop yourselves as species and not touch the ecosystems of these planets, leaving them pristine for the indigenous life. Or we can act in the human way and do the same mistakes as we did in the past over and over again and just go there, exploit and trash the planet until its depletion.

The most difficult and realistic case is actually the case of Mars:

Why is Mars so interesting? Because in its past it was very similar to Earth, it had a denser atmosphere, a magnetic field, volcanism, starting plate tectonics, liquid water and all chemical ingredients for forming life. Mars might have gone through a similar evolution as Earth, forming microbial life, or maybe even be the origin of terrestrial life, as interplanetary transportation of rocks after impact events is proven to occur. Now, Mars is the perfect (and maybe only) place to actually study how life on Earth could develop and if life could develop on other planets as well, if life is unique or if it appears quite common throughout the universe.

But, if we send now a bunch of colonists there, who will bring lots and lots of organic material from Earth, we might spoil Mars to a degree where we cannot study this anymore, loosing a very unique opportunity.

Given the case there is still life around, wouldn't it be best to first study it, before building houses, schools and hospitals next to it?

And then there is another ethical consideration that needs to be taken into account:

Sending colonists to space with current technologists would use up significant amounts of terrestrial resources. Sending just 30000 colonists to Mars would already use up all the remaining mineral oil reserves on Earth, not to mention the metals, materials, supplies, etc shipped with the settlers. In order to send these few privileged people to Mars, the rest of humanity will have to sacrifice their lifestyle, their future and their environment. Is that ethical?

--> If we could terraform Mars, why not first terraform Earth? Reverse the effects of climate change, stop and reverse desertification. Earth is better studied than Mars, but as long as here high-ranked people make money with pollution and deny scientific facts, nothing will happen for the better. The money that Musk wants to spend on the colonisation could as well be spent to cover parts of the Earth's desert areas with solar power plants, providing humanity with CO2-free energy. That would benefit more people.

Also, terraforming Mars will not be sustainable. Mars is loosing its atmosphere, because of the lack of a global magnetic field. it might become a home for a while, but thinking into the far future, Mars will be back to where it is now.

Plus, how do we know we can potentially manage to create stable living conditions on Mars, when we are all about destabilising every environment we enter?

--> Maybe because it is easier messing up something new, rather than fixing something old?

--> Musk's rockets use RP1 (refined kerosine) like all other rockets, and as long as this remains the cheapest fuel, nothing will change. Rockets are basically 95% fuel that is burnt. Using synthetical fuels is a huge cost factor. And especially since the CO2-concentrations (despite being high enough to significantly influence the climate) in the atmosphere are too low for economical use, I do not see any of this happening any time soon.

--> No. We need to politically, economically and ecologically get our shit together first. We need to all reduce our negative imprint on the environment on Earth, foster international collaboration not wars, fear or hate, we need to change our thinking not towards maximising the monetary output, but in maximising our own happiness and humanity towards others.

Also, we should (must) explore Mars first. The right step is to first send a small groups of astronauts to carefully study Mars (and come back) over an extended period of time (~20 years) to really answer all our open scientific questions, before we can even think of inevitably spoiling the pristinity of the planet.

==> this would be the right way, and would avoid many of the mistakes that human explorers on Earth have done in the past (i.e. settling at their first arrival to a new place)

The ringlets that share the same radial locations as small moons in the gaps follow horseshoe like orbits. An example is Pan orbiting inside the Encke Gap which has a number of associated co-orbital ringlets.

So typically librating about the L4 & L5 Lagrange points in the Saturn - moon three body problem. If you just look at the Saturn - moon systems and particles in the presence of these two bodies you can replicate the ringlet shapes which can exist for long periods of time.

I personally have not come across gaplets or endlets before though. However, in very dynamic rings like the F ring partial rings do exist. The rather destructive environment means there are spiral like rings and parts of the ring detached from the main core. These evolve on fairly fast time scales where as I presume the features you mention exist in areas of some kind of stable resonances? 

I want to thank everybody for their interest in my writing contest and their helpful comments.  When the school year begins in the fall, if you are in a position to do so, please inform teachers and students in your country of my contest.

Kenneth-

I understand that you do not believe that there is life on Trappist-1e.  But students are welcome to enter the contest with arguments against the possibility of life.  The point is to get them thinking on the subject, not to be a demagogue and insist that there is or is not life there.  Nobody knows for sure and there are many respected scientists that believe it is a possibility.

Please check out http://iopscience.iop.org/article/10.1086/505112/fulltext/ . Nuclear reactions in the corona are observed during large flares. The reactions tend to involve heavier nuclei and are not the same as the p-p and CNO reaction chains that fuel the Sun and other stars.

I like Professor Decker,s  way of deriving the ODE  for  v  as a function of  the path   r (hiding the other fashion of a function of  time  t ).  Let me  add, that fortunalety this leads immediately to the energy conservation law.  Consequently one can get the impact speed formula for arbitrary initial speed. The problems then still is not beyond the high school math, unless the starting speed is greater or equal the first cosmic one (appropriate to the initial height). . . 

. . .  OR the starting direction should ensure return to the earth - and this is already over elementary one dimensional calculus.

Professor Decker, thanks for pointing at this nice and simple way of  solving the problem of this question.

Best regards, Joachim Domsta

Dear Dr Kumar

There is no doubt today that a major dimension of the present multidimensional crisis, which extends to the economic, political, cultural and general social level, is the ecological crisis.  The upsetting of ecological systems, the widespread pollution, the threat to renewable resources, as well as the running out of non-renewable resources and, in general, the rapid downgrading of the environment and the quality of life have made the ecological implications of economic growth manifestly apparent in the past  years.

By contrast to the focus on wild places, relatively little attention has been paid to the built environment, although this is the one in which most people spend most of their time.Ecosystem destruction is already happening.

Humans destroy ecosystems. Our lifestyle creates pollution and we overuse our natural resources. Today,  We build roads, hunt animals, cut down trees destroying forests and just litter the planet . We waste resources that are not infinite and will soon run out, if we continue our practice.

The Moon is moving away from the Earth due to the action of the tides, it also slows the rotation of the Earth so that angular momentum is conserved.

Thanks Joachim for your comment and interesting link.

Regards.

Dear David Finkleman

You is right it is a complicated integral not a complex one. p is a constant its value could be between 0 and 1, but not 0 and not 1/2.

Roshny,

The above three answers are not helpful to you, because they throw the ball over the wall.

If you can define the Venus Solar Orbital (VSO) coordinates and the Mean Field Aligned Coordinates with respect to the Venus (equatorial) centered inertial, VCI say, then the rotation matrix for the transform in the (Planetary or Heliocentric) Sun Centered Inertial (SCI) coordinate system is easy to construct. 

I am an Astrodynamicist working with Earth centered satellites and debris in Earth Centered Inertial (ECI) coordinate system and its transformations to other spacecraft and planet coordinate systems all the times. However, I know only a little about Sun Centered Inertial (SEI) coordinate system, but their transformation should be similar. If you can define the VSO and any coordinate system you want, I can give you the few lines of code you need in a short time. Glad to help.

Gim

Actually, Cassini team worked at doing exactly the opposite! As James stated, the problem is the contamination. Although not as probable as for Europa, extraterrestrial life is still a possibility for Enceladus (if there is cryo-volcanism there may be liquid water). In such case, major space agencies have a clear policy: avoid any risk of contamination. That is why all probes sent toward Jupiter and Saturn are deliberately crash on the planet.

Mohamed,

There is no simple equation.

You have radiative input (sunlight), convective transfer (wind), and conduction (loss or gain from the subsurface).

If you know the thermal conductivity of the regolith, its heat capacity, then you can make a 1D model based on radiative forcing.

Sadly there aren't many (any!) vertical measures of either of those thermal properties from actual probes and estimates have been made based on the thermal lag that regions have when viewed with orbiting radiometers.

But why re-invent the wheel?

I am not aware of any actual measurements. To my knowledge, the area has not been been explored yet at all on the ground. Furthermore, the volcanic dome is probably of heterogeneous composition. However, you may be able to find information on the geology obtained by remote sensing, and could use data on similar terrestrial rocks (basaltic lava, volcanic ashes).

I think more efforts should be taken for mitigation...... adaptation sometime may be natural.... If we gave more importance to adaptation this means we are neglecting the causes of climate change. And everyone's capacity of adapting is different than those who can not able to adapt with change what is the solution? can we leave them to die or suffer?

The original composition of micrometeorites is lost due to atmospheric entry heating in most cases, e.g. in cosmic spherules and scoriaceous micrometorites. However i) some micrometeorites classified as "unmelted" preserve the original composition of the micrometeoroid and ii) although melting and evaporation is important in cosmic spherules and scoriaceous micrometeorites, the original composition of their micrometeoroid can be inferred based on geochemical and mineralogical combined studies (e.g. the study of the relic mineral phases they contain, oxygen isotope bulk composition, etc. see Folco and Cordier (2015, EMU Notes in Mineralogy) for a recent review. 

@Martin,

The IAU official definition is:

A planet has to meet all three of the following criteria

A planet has to meet all these to count.

It is not quite clear what 'cleared it's neighbourhood' means - several of the planets in the solar system including the earth have asteroids sharing the same orbit so according to the definition should not be planets. Also there are several thousand artificial satellites orbiting the Earth which have not been 'cleared from the neighbourhood' by the Earth's graviry so the Earth is not a planet either !

Venus & Mercury might be Ok as they don't seem to have asteroids in the same orbit so the number of planets in the Solar System is 2 !!

It would help to understand why you want to know this. E.g. The Solar System's barycentre is within 1 million kilometers of the surface of the Sun. If you are concerned with interstellar (galactic) distances, that is trivial, for interplanetary distances it might be relevant depending on the need. Do you mean Apogee or Aphelion of the planets? Etc..

Dear sirs.

This is interesting. 

I'm interested in finding the link between pragmatism and emotions, and the moon cycles offer us exactly that.

I have been analysing dear Narayanan's pragmatic answer to the link between women's menstrual cycle and the cycle of the moon. Indeed quite acurate in his analysis.

I have spent much of my academic life to the study of the human Endometrium .

Surprisingly, even if the uterus has always been and still is the subject of scientific research and the most widely subjected to medical management (the cesarian section was the earliest human surgical intervention ever performed and is still the most widely performed to our days...), surprisingly, there are still inumerous scientific data about the female genital system that remain unresolved.

The relation between the moon cycle and human female menstrual cycle is a good example of those unresolved (mysterious) problems...

Would you find a scientifical explanation to the fact that there is an increase of natural births on full moon nights?

Would you find a reasonable scientific explanation to the fact that when you bring women close together, as in prison cells or religious monasteries, they will tend to adapt their menstrual cycles to the same week of the month ? 

(One nearly-scientific hypothesis I read, tells me that primitive cave-humanoids would preferably leave their women to go hunting on full-moon nights, every month, to benefit from the natural moonlight to improve their hunting sight.

In this sense, and as a consequence, humanoid females may have adapted their primitive mammal estrous cycling to menstruate during their mates' absence... thus, ovulation would occur on New moon phase, when the male humanoids would stay home to rest. This enhanced our primitive instinct to maintain our species.

As much as this analysis may fail to be accurate in some points, it might explain why in fact, as Narayanan well pointed out, that female humans are the only mammals that have monthly regular menstrual cycling, adapting their hormonal levels to the 28 day cycling of the moon.

Most other mammals, such as the rat, will adapt their hormonal erstrous cycle to the proximity of males, through the effect of Pheromones.

I don't know that particular article. The two mentioned in the first comment and the two in the third were discovered in common missions so it would make sense for them to be presented in the same article.

Here is a nice uptodate overview of habitable exoplanets from Kepler Missions. I'm assuming the article would have been about two of these planets.

Our solar system began forming within a concentration of interstellar dust and hydrogen gas called a molecular cloud. The cloud contracted under its own gravity and our proto-Sun formed in the hot dense center. The remainder of the cloud formed a swirling disk called of the solar nebula.

The cloud had a net angular momentum and was spinning, but it was initially gas, dust, and plasma. Planets spin quickly because the gas cloud they condensed out of had a very small amount of angular momentum. Similarly, an ice skater who started out spinning relatively slowly with their arms extended, will spin much faster when they pull their arms in towards their body. Thus as gravity pulls in and contracts the gas cloud, whatever rate of rotation it had would be greatly increased as the Sun and the planets form. Planets spin and in fact planets exist because of the conservation of angular momentum. 

But where did the initial angular momentum of the gas cloud that became the protoplanetary disk come from? Well, it did not need to have a large scale coherent rotation as a whole, all it needed was to have different parts of the gas cloud moving in different (even random) directions. That would be enough to create some small amount of non-zero angular momentum which would eventually cause rapid rotation as gravity condenses the gas cloud to a protoplanetary disk (similar to when an ice skaters arm pulls arms in). The random initial velocities of different parts of the cloud were probably caused by nearby supernovae explosions, that led to the cloud to collapse in the first place.

Moreover, during planetary accretion, not all of that matter will hit (collide) the forming planet on a vector aligned exactly with the center of mass of the planet. Some will hit a glancing blow and put a rotation on the planet due to torque, leading to rotation of the planet.

Not yet !

 Nicolai,

This is not a terribly new idea.

It has never been clear that late-stage bombardment by discrete cosmic bodies is required to provide a significant fraction of the total water inventory of earth. There are plenty of arguments for alternative paths.

You will also have to address the D/H anomaly - although the role of fractionation by terrestrial life is complex - as it's not just a matter of delivering water, the nature of the water is also crucial in understanding the origin of the Earth's oceans.

>(lacking the skill set in mathematics and detailed education).

That is a rather large obstacle, but is remedied with time and study. One cannot take short-cuts in this matter.

Thank you very much Ambalika! It is a very good and informative paper

Curiosity's deepest drilling was 5 cm (as initially planned).

when in this discussion is read about impact craters on Mars, I think that we should first tray to find chronology of impact craters on Mars. which was first, which was last.

impact craters on north in my opinion are very old, younger are Hallas and Agryre,

when I compare positions of magnetic and gravitational concentrations I found that these large impacts from north couldn't    create present shape of magnetic field

The Titus-Bode law likely represents some kind of tidal/gravitational resonance involving various zones of accretion.   I would suspect this to be relatively Universal and "missing planets" are likely the result of processes similar to that which produced the asteroid belt in our Solar system.

We wrote that methanogens is one of the options. Please read our article, which is fully available here on the RG :

Article:

N. S. Duxbury, S S Abyzov, V E Romanovsky, K Yoshikawa

A combination of radar and thermal approaches to search for methane clathrate in the Martian subsurface, 2004, Planetary and Space Science , 52,p. 109--115.

The central repository for solar-system-object orbital elements is the IAU Minor Planet Center at the Smithsonian Astrophysical Observatory. Their main web page is at:

If you want complete sets of orbital elements, that’s the place to get them. If you want apparent positions of objects for a particular epoch or range of epochs, JPL’s Horizons is definitely a very good place to go.

It should be borne in mind that the vast majority of solar-system objects have highly perturbed orbits, so that the Keplerian orbital elements change significantly with time. JPL Horizons takes this into account for you. If you want a complete set of all elements, the Minor Planet Center is the place to get them, but I am not personally familiar with how they handle the epoch issue. On their main web page near the bottom there is a section named “Large Data Sets” with links to files; probably the MPCAT link is what you want.

I recently retired, but at the time I did, the number of objects was approaching half a million. Back in the early 80s it was just 4000. Today a complete set of elements will involve a file size on the order of 100 MB. To use these elements, you will need a computer program that implements the standard solution of Kepler’s equation and does the appropriate coordinate transformations. The orbits are represented as “osculating ellipses”, basically time-dependent Keplerian orbits in a plane that precesses.

Where I worked for many years, the Caltech IPAC, we have done a number of all-sky infrared surveys, and we need to predict the appearance of all solar-system bodies in our images in order to distinguish them from inertial infrared sources, A description of how this was done is at:

Hope that helps!

This is an interesting question, one suggestion I have relates to a method for deriving air density based on the terminal impact velocity of raindrops (density 1), although several process-related assumptions are necessary.  I learned of this method from Dave Pyle (Oxford) in discussion for use with soft pyroclastic ash and possibly impact ejecta, and there are now a few papers applied to the Archaean, see Som et al (Nature 484, 359-362) Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints. If splash textures related to terminal velocities of fall-back impact spherules could also be established, it might then be possible to extract more precise estimates based on heavier particles (density >>1), but I am not sure such rock surfaces exist for the Precambrian.  In the ~end Cretaceous Chicxulub global ejecta, potential atmospheric interactions are complex, but may hint at a separate method for future extraction of chemical evidence for oxygen in Precambrian impact ejecta/spherule beds. An on line PhD thesis by Tamara Goldin (university of Arizona, 2008) sets the scene for atmospheric interactions from Chicxulub ejecta, and Precambrian impact spherule beds have been reviewed by Johnson and Melosh (2012, Nature 485, 75-77) and Glass and Simonson (2013) Distal impact ejecta layers (Springer). 

May I propose the authors in the 19th century who – on the basis of the existence of stony, iron, and stony-iron meteorites – suggested the idea of asteroidal or planetary differentiation.

Diagram of my how I calculate the specular reflection angle, which is a prerequisite to calculating the glint angle:

Thanks, Artem! I've glanced over the paper quickly and it is impressive - I think I'll get all my answers from it.

Making such a calculation from scratch is a bit complicated, it is better to use existing model such as the SPICE kernel from NASA: http://naif.jpl.nasa.gov/naif/toolkit.html or the web-interface of JPL's Horizons: http://ssd.jpl.nasa.gov/?horizons.

For Europa Clipper check e.g.  

or

But maybe you wanted to know how to solve the equation.  There are three approaches:

1) use Newton's method to approximate the root.

2) Use a series expansion. I believe there are several different series. See, for example 

where the use Bessel function.

3)  There are some definite integral expressions that solve the Kepler equation. See for example

 Ioakimids, N. I. and Papadakis, K. E. "A New Simple Method for the Analytical Solution of Kepler's Equation." Celest. Mech. 35, 305-316, 1985.

Ioakimids, N. I. and Papadakis, K. E. "A New Class of Quite Elementary Closed-Form Integrals Formulae for Roots of Nonlinear Systems." Appl. Math. Comput. 29, 185-196, 1989.

Other references:

 Wintner, The Analytical foundations of Celestial Mechanics (page 212).

Danby's book "Introdution to Celestial Mechanics ", discusses a series expansion due to Lagrange.

Maybe this link and the references in there can also be useful: http://mathworld.wolfram.com/KeplersEquation.html

Dear Hector,

The current LHB discussion or let’s say the understanding of the lunar Impact chronology and the current astronomical models to explain the heavy bombardment now go into a direction similar to your ideas.

The repeated claims that there are no Impact reset lunar rocks older than 3.9 Ga is based on a limited knowledge of the literature published since 1973 (for new data and old references see the paper by Fernandes et al. (2013). You can also find a short review on the lunar Impact chronology and the new views on the orbital evolution of the Solar System in our paper Fritz et al. (2014). Both papers can be downloaded from my Research Gate page.

Lunar chronology: It gets more and more obvious that the initial claims by Baldwin (1974) are in excellent agreement with primary observation from global element maps of the Moon and the knowledge of the lunar meteorites (which come from various random places on the Moon and thus are more representative than the Apollo mission samples). Baldwin (1974) argues that all Apollo missions mainly samples the Imbrium ejecta. This correlates with the global Th element maps of the Moon (KREEP region) and the observation that the Mg-rich suite of Apollo mission samples (a clan of lunar rock types) are both characteristic for the region around Imbrium and are different from all other regions of the Moon.

Astronomical models: The quite popular Nice model (initial version from 2005) explained the brief LHB spike. However it was found that the proposed model would be able to provide a LHB spike but as a drawback would lead to a destabilization of the terrestrial planets. The updated Nice model now assumes a slightly different type of orbital reconfiguration (Jumping Jupiter scenario) which allows for terrestrial planets with stable orbits but could not provide enough Near Earth Objects to explain a LHB spike. And therefore the E-belt model was proposed (Bottke et al. 2012). The people still call this long lasting bombardment LHB besides that it resembles the lunar impact chronology favored by those opposing the LHB.  Or in other words the current astronomical models explain the extended tail of the Heavy bombardment.

In summary, I am cannot judge your math, but your basic claims that the abundance of 3.9 Ga ages is a bias seems to be along the line with what is now going to be main stream understanding of lunar chronology.

Any trajectory design of a spacecraft involves the knowledge of orbit and attitude both (i.e. position, velocity and orientation w.r.t an inertial frame of reference). Off course the desired trajectories are optimized for delta-V requirement for the transfer. There are many ways of attitude representations viz. Euler angles, Quaternions etc. and can be found in associated literature..... 

I would suggest

1) "Fundamentals of Astrodynamics and Applications" by D A Vallado

2) "Spacecraft Attitude Determination and Control" by James Wertz and

3) "Orbital Mechanics" by V A Chobotov

Go through these and you will find your answer.

Hello,

At http://ssd.jpl.nasa.gov/ there are, among other information, tools to generate ephemerides of planets and minor bodies of the Solar System.

The order of the planets arises from knowledge of their sidereal periods computed by the ancient Babylonians.  They clearly recognized that closer objects closer moved faster while objects further away moved slower.  The initial order of increasing sidereal periods: Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn; the Sun was later placed in the middle of the listing. This order was later adopted by the Greeks, which was acquired, in translation, by Renaissance astronomers.

The value of the angular momentum of a planet has some relationship with the revolution angular momentum, but only because both are part of the total angular momentum. In a non-dissipative system (meaning: no tide, no atmospheric friction...), the total angular momentum of a system does not change, but its value changes from system to system. For example, concerning the Earth and Moon, tidal effects have an action on both Earth and Moon rotation, slowing it down until an equilibrium, double-spin orbit resonance for Earth, but also increasing the distance between the Earth and the Moon. So, to sum up, rotation and revolution are not linked when you are observing a system, but their evolutions are, and dissipative effects tend to lock systems in spin-orbit resonance.

What you need to think about is *why* water may act as a lubricant for plate tectonics. Not just any liquid would do it, and it's not that plates are sliding around on a sheet of water, it's the interaction of water with mantle rocks and the decrease in viscosity in the asthenosphere. So what is the analogue for methane/ethane on Titan? Adding these compounds to water ice doesn't make the water ice partially melt under Titan conditions, instead it forms a clathrate. This could lead to volume changes or density changes (see recent abstracts by Mathieu Choukroun about Titan) and perhaps vertical tectonics via basin loading, but I don't see a physical mechanism by which this would promote an Earth-like plate tectonic system.

The two adiabatic invariants, namely, the magnetic flux and the angular momentum will not allow the formation of a non-rotating star. The gravitational collapse of a molecular cloud leads to the formation of a protostar that is surrounded by an accretion disc. The transfer of the angular momentum between the protostar and the inner regions of the accretion disc establishes the final rotational period of the star. The interaction of the accretion disc with the magnetosphere of the protostar significantly influence the acquired rotation. It would be a real miracle if all these interactions result in the production of a non-rotating star.

The planets are formed by the accretion of planetesimals. The hits received by the accreting planet from the numerous planetesimals will determine the rotation of the planet. The interaction of the accretion disc with the protoplanet would also influence its rotational period.

The accretion disc formations required not only gravitational fields, but also involved magnetic fields to generate the angular momentum transport.

The atmosphere of a planet comes up from inside the planet.

I suspect that all planets produce an atmosphere. The question is,

can the planet keep the atmosphere with the solar wind effectively stripping the atmosphere away.

The Earth has developed an atmosphere, and has developed a means of keeping

its atmosphere by developing a protective magnetic shield.

The process is one of " Fractional Distillation " where lighter materials migrates

upward in the planet, and denser materials, like iron, migrate

downward, and concentrate in layers of similar density.

The concentration of iron is beneficial in that the size of the planet,

the amount of iron, the confining pressure at depth, and the applied torque of the

Sun's magnetic field all work together to apply torque of the Earth's accumulating,

and growing magnetic iron core, which creates internal fluid motions

that generate the protective magnetic field.

This has created two + questions in my mind. Why did it take nearly 4,000

million years for life to evolve to larger life forms on this planet ? AND

Why has life managed to stay large and prosper for roughly 630 million years, and

why has Earth's life sustaining processes managed to continue

within a fairly narrow atmospheric temperature and pressure range for

630 million years ?

It does not seem probable that the Earth could manage to stay in such

a narrow , improbably life sustaining " Goldilocks " zone for such a

totally improbably long period of time.

The only possible mechanism that I can envision is one that is cyclical,

or semi cyclical and allows the atmosphere to vary in depth, density. and surface

pressure and temperature in a way that allows it to vary on average

between a low of 6 C and a high of 26 C, with a long term dominate

temperature average of 22 C.

Small pulsed growths and expansions of the Earth would accomplish this

including a glacial period following a pulsed expansion, that gradually returns to

normal over several thousand years, as continents sink, and sea floors rise.

and the atmosphere is replenished from inside the planet and as it becomes thicker

and gradually rises along. with rising sea levels and sinking continents.

It would be a dynamic form of isostacy in concert with a dynamic form of

atmospheric equilibrium replenishment from inside the planet, which

also is working in concert with a growing and expanding planet.

Perhaps a gas giant stage occurs when the planet reaches a point where it can no longer grow and expand, so it the heats up too much internally, and releases

gas at too fast a rate, and the atmosphere grows essentially without bounds.

The Earth's atmosphere is largely a biological construct; Venus's isn't.

First, notice that, although Venus has Nitrogen and Argon as apparently minor constituents, the partial pressure of Nitrogen in the Venus atmosphere is 3.2 bars, actually more than the Earth's 0.78 bars, and the Argon partial pressures are very close, 0.009 and 0.006 bars. (The total mass of Venus and the Earth are close enough that you can regard the partial pressure as a proxy for the total mass in comparing the two atmospheres.)

The real difference is in the location of the Carbon. The Earth has 3.5 x 10^-4 bars of CO2 in the atmosphere, while Venus has 89 bars of CO2. However, it turns out that both planets have about the same amount of crustal carbon, but the Earth has most of its carbon in the ground, and some in the oceans and the biosphere. If you convert mass to partial pressure, we have the equivalent of 0.02 bars of CO2 in the oceans, 0.001 bars in the biosphere, and at least 29 bars in crustal rocks. If you could somehow heat the Earth's surface to 470 C, all of that carbon would be driven into the atmosphere as CO2, and the Earth would have an atmosphere a lot like Venus.

The real major difference (in terms of total mass) between the surface regions of Earth and Venus is in the presence or absence of water. The Earth has a lot of water, enough to cover the surface to several km depth if the surface was a perfectly smooth sphere, while Venus has very, very little (enough to cover a smooth surface to a depth of maybe 2 cm). Unless there is some unknown means of sequestering hydrogen in the hot crust of Venus, almost all of its hydrogen has presumably been lost to space. As it happens, models show that the Earth has a "cold trap," that keeps water out of our stratosphere (where solar UV would disassociate it and create free Hydrogen which could be lost to space), while Venus does not, so the current thinking is that this fairly slight difference in atmospheric dynamics is sufficient to dessicate Venus, leaving it in the dry state it is today. There has been a lot of recent debate as to how cold traps affect the "habitable zone" of exoplanets, and the real question is, how do you keep a hot planet from drying out. (I have a feeling there is a biological connection here as well, but that is just my intuition.)

Mars is a different case, which I'll cover in a separate post (unless someone beats me to it).

The oblateness of the Sun and of the major bodies of the Solar System, all the natural satellites of the planets, the Trans-Neptunian Objects (both individual objects and a ring), the asphericity of the Moon itself to the best of current modeling. It would be fine to leave a certain degree of flexibility to your software by allowing for explicit modeling extra-effects accounted for by one or more parameters (e.g. PPN parameters, cosmological constant, MOND, or whatsoever one wants to add) to be estimated in global fits dedicated to this or that effect(s).

An updated earthquake catalog is published in this paper, noting the correlation with ancient rifts: Saskia M. Schulte and Walter D. Mooney

An updated global earthquake catalogue for stable continental regions: reassessing the correlation with ancient rifts, Geophys. J. Int. (2005) 161 (3): 707-721 doi:10.1111/j.1365-246X.2005.02554.x

and recently on correlation with lithosphere properties:

Crustal seismicity and the earthquake catalog maximum moment magnitude (Mcmax) in stable continental regions (SCRs): Correlation with the seismic velocity of the lithosphere, Walter D. Mooney, Jeroen Ritsema, Yong Keun Hwang

Earth and Planetary Science Letters. 12/2012; 357-358:78-83. DOI:10.1016/j.epsl.2012.08.032

Seth Stein and Walter Mooney's back-catalogs are good places to start reading.

Are the conditions on Mars such that they seem to preclude life or is it more that we have not found evidence of life on Mars?

(I wrote an answer this morning, but it seems to got lost in cyberspace; in hindsight I think that I did not answer the question correctly, so I try again).

My answer:

In the absence of a model for the origin of life on earth we cannot prepare tests for whether life is possible on a specific extraterrestrial site (I prefer not to use the word planet, as extraterrestrial dust, comets, meteorites, moons, Kuiper Belt Objects, planetary nebulae and even the atmospheres of cold stars should be considered as potential habitats as well).

We can only check whether life as we know it on Earth could live at a certain site; this already yields an immense variety, as life seems to be present almost everywhere on Earth: from deep down in sediments to high up in the atmosphere. Terrestrial ecology therefore yields many possible shapes of life. But is this set comprehensive?

Schulze-Makuch's book described several shapes that extraterrestial life could take. But again, this set is possibly not comprehensive.

We do not how life on Earth emerged, i.e., the first stages that life on Earth assumed are unknown. Those first stages may be difficult to recognize, as we do not know how they looked like. The eyes can only see what is already in the mind.

Obviously finding out how life on Earth emerged would help. I myself have come up with a model for the origin of life in which the first organisms were essentially heat engines. Such organisms could live on thermal cycling (as in a convection current) or on a thermal gradient; they would NOT need sunlight. My papers state that such conditions are present in many extraterrestrial places (for instance: organisms living in the dark on convection underneath surface ice).

To get back to the stated question. If one could demonstrate that life on Earth could live on thermal cycling or in a thermal gradient, one would have done a convincing test that extraterretrial life is possible almost everywhere. Candidates abound for such life: they range from microorganisms growing in tap water to the jelly fish clogging up the cooling water inlets of Swedish nuclear reactors that are in the news today.

To provide the contrasting view (Martin has given some info), most impact cratering specialists doubt the Younger Dryas impact. Most impacts are identified on the basis of two primary geochemical/mineralogical features: shocked quartz, and platinum group element (PGE) enrichment. Discovery of a crater is also quite important, and one that was 12900 years old would certainly be obvious in the geologic record.

The Younger Dryas event has none of these. In the original paper, Firestone and others (see Firestone, R. B., et al. (2007). PNAS 104(41), 16016-16021) provided a number of lines of ambiguous evidence, including iridium enrichment of magnetite (a meteoritic indicator would be iridium enrichment of the bulk soil), charcoal, soot, and fullerenes with extraterrestrial He, among others. These studies may have been replicated, but replicating ambiguous data still only gives ambiguous results. The main research group still hasn't produced the key lines of evidence for an extraterrestrial impact: notable PGEs and shocked quartz. Instead, there is an appeal to cosmic airbursts (no crater), and cometary impactors (hypothetically low in PGEs, but not really).

That said, there's still some new data coming in for the idea that have been obtained independently. I wouldn't completely discard the impact hypothesis, but also note that not all extinctions require an extraterrestrial impact.

Firstly, space-originating complex molecules are nothing new. Amino acids have long been known to exist in extraterrestrial sources, such as meteorites (e.g. [1, 2]) and interstellar clours [3]. Thus, it is not surprising that they form rather "easily" (whatever that means) like in the impact simulations like in the news piece you linked to. However, the formation method as such is quite interesting, and it does give a clue on the possible abundance of amino acids on early planetary surfaces.

The answer to your question depends entirely on what is meant by "extreterrestrial". During planetary accretion everything comes from space. Whether the amino acids are already present in the body falling from space and come straight from space, or if they form at the instant of impact, may not be that important. I suspect there are several delivery methods - and quite possibly there are several ways of forming them in-situ on the planetary surface from simpler molecules.

The main *slight* problem is actually making anything living from mere amino acids. The latter are, after all, quite simple in comparison to anything that can be considered even remotely "alive". The machinery needed for self-replication is quite extensive. Even virus particles, virions, are much more complex than just amino acids.

[1] http://www.nature.com/nature/journal/v228/n5275/abs/228923a0.html

[2] http://www.nature.com/nature/journal/v389/n6648/full/389265a0.html

[3] http://physicsworld.com/cws/article/news/2003/aug/11/amino-acid-detected-in-space

The Dominion Astrophysical Observatory (Victoria, B.C., Canada) has 72-inch and 48-inch telescopes that are equipped with first rate spectrographs.

Hello James, if Mars is still living depends on our definition of living. In my opinion a planet is living IF there is volcanic activity, IF there is enough internal heat to sustain a geodynamo and subsequent magnetic field that can shield the planet from deadly radiations. Both conditions have gone long time ago, 4.1 Ga for the geodynamo at least and 3.5-3.0 Ga for the volcanism at least. But these dates could be pushed back further. So only the InSight mission can say if there are still traces of internal "life" in a almost dead Mars, I'm personally skeptical about it but we'll see.

Regarding the plate tectonics on Mars, even a blind can see that there are neither traces of subduction zones nor rift zones on the map of Mars. All the features that can be seen on Mars are superimposed on the Martian dichotomy, which is the oldest features of Mars, so nothing disappeared or has been reworked in the meanwhile. If the Valles Marineris is a rift, where is the relative subduction zone??? So I really find incredible how somebody can still talk of Plate Tectonics on Mars today. I explain in a paper that is currently under review the real origin of Valles Marineris, so hopefully in a few time you will see the real nature of it. Stay tuned on my ReserachGate page following me. Cheers, Giovanni.

Grain size of mantle rocks is to be expectet do be higly variable due scale invariance produced by both fragmentation and annealing processes. I collected a rich documentation in this paper:

Power law olivine crystal size distributions in lithospheric mantle xenoliths

P Armienti, S Tarquini - Lithos, 2002 - Elsevier

Alexander Bagrov writes that a collision of two Lunar-sized bodies will not result in the release of fragments since they will be gravitationally bound. Although this is certainly true - it is not a problem for our understanding of the origin of differentiated meteorites from asteroids. Cooling rates of iron meteorites range from 1-1000 K/My. These cooling rates constrain the cooling rate of the asteroid core shortly after it crystallized. Since largfe asteroids cool slower than small asteroids they may be used to infer sizes of asteroids. Diameters were genererally less than 50 km - much smaller than the Moon - and sufficiently small that it is not a problem to catastrophically destroy them.

We know that fragments of asteroids escape our Solar System and it thus follows that fragments must also escape other Solar System provided they include minor bodies. It should therefore be possible to find an extrasolar rock in our Solar System. Unfortunately, it is unlikely that it will heat our atmosphere slowly enough to survive. Also, the frequency of such a fall makes it unlikely that we will ever observe it or even find an old extrasolar meteorite fall here on Earth. I have seen an estimate concluding that we should expect a extrasolar meteorite fall here on Earth every 10 billion years.

In other words, extrasolar meteorites are not impossible but the exceedingly low fall rates makes it less than likely that we will ever come across one.

If we were ever to find one there is no doubt that we be able to tell that it is extraolar - it would be different in terms of bulk chemistry, isotope chemistry and its ages would be way off anything we have seen before.

The collisions between particles in Saturn's rings occur at VERY low velocities (typically less than 1 cm/s). On the other hand they are constantly bombarded by interplanetary micrometeoroids at impact speeds of several 10's of km/s. The result of the external impacts is to pulverize the outer layer of the ring particles producing a fine powder regolith that is primarily composed of water ice. The meteoroids bring darker material into the ring system, however. Over time this should reduce the reflectivity of the rings and make them darker than they are if the rings have been around for the age of the solar system. It may be that the impact flux is not as well known as we think and is actually lower or that events in the rings can effectively reset their apparent age by exposing the pristine water ice in the particles' interiors.

Yes but i think that is it possible to compute the value of αf_d(α) for each resonance. Any way the problem is how Murray & Dermott plot the resonances becuase with the two method i use they overlap only in the second case (i.e.: when i put a as a costant) but this is a correct method ?

This is a great question that I've had fun thinking about over the past few days.

Building structures out of formed Martian blocks will be a starting point (think earthen blocks, or bricks, but on Mars...). If water is present beneath the surface, then clays are probably present as weathering products. Those will be useful as building materials.

Human ability to manipulate Martian regolith will likely follow the course from simple compouds like clay and packed-mars bricks to minerals and finally to elements. Based on the energy and catalysts needed to extract elements from rock, lighter elements will be easier and more available to extract than heavier ones, at least initially. It's like compressing the human industrial experience up to the end of the 19th century into one workflow.

Mas has plenty of iron, but there's other regolith elements common to both Earth and Mars like aluminum and silicon. Water, oxygen, and various carbon compounds will be fairly easy to extract using electrolysis. As catalysis become available, aluminum can be created via electrolysis.

Available energy may initially be electricity from nuclear, wind, or solar. All of the mining and milling will have to be done using manual labor and electrically powered tools. Milling and refining will all have to be reformulated based on different densities, melting points, and atmospheric pressures present on Mars. Eventually, there may be geothermal resources available. If there's a rig, I would bet someone will start prospecting for hydrocarbons.

Hope this helps.