# In planetary and astronomical science, what exactly is, or is not, a tidal force?

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I'm wondering exactly in which situations forces between bodies are, and are not consider to be tidal forces in the context of planetary and astronomical science.

If two rigid, non-deformable spherical masses with shperically symmetric mass distributions orbit each other, can we say there are no tidal forces or tidal effects there?

If one of them has a permanent, static deformation (e.g. quadrupole moments and higher) are there tidal forces then? If both do?

Or are dynamic, induced deformations required before we invoke the "T-word"?

Can tidal forces be radial, such that they do not tend to raise or lower an orbit over time, or must they have tangential components, like the one that is slowly raising the Moon's orbit?

Is it possible to draw a clear line here, at least within the scope of this SE site and This month's focus tag which is tidal-forces?

According to that tag's Tag Info:

There is no usage guidance for this tag… yet!

Slightly related: Constraints on the mass distribution within each body such that their mutual orbits are Keplerian?

I'm wondering exactly in which situations forces between bodies are, and are not consider to be tidal forces in the context of planetary and astronomical science.

Don't overthink it. All a tidal force is, is the net force you get when two gravitational forces aren't quite the same. The force of gravity is the first derivative of potential (the "slope"), whilst the tidal force is the second derivative of potential (the change in "slope"). The classic example is spaghettification. You're falling into a black hole, and the force of gravity is greater at your feet than at your head. So you get stretched by a tidal force.

$$phi(mathbf{r}) = -frac{GM}{|mathbf{r}|}$$

$$mathbf{F}(mathbf{r}) = abla phi = -frac{GMm}{r^2}mathbf{hat{r}}$$

$$mathbf{F_{Tidal}}(mathbf{r'}-mathbf{r}) = -GMm left( frac{1}{r^2}mathbf{hat{r}} - frac{1}{r'^2}mathbf{hat{r'}} ight)$$

where $$mathbf{r})$$ is the position of the secondary body relative to the "main" or more massive body, and $$mathbf{r'}-mathbf{r}$$ is the position of the particular point relative to the secondary body's center of mass where the tidal force is experienced, and $$m$$ is the mass of the test particle at that point experiencing the tidal force.

If two rigid, non-deformable spherical masses with spherically symmetric mass distributions orbit each other, can we say there are no tidal forces or tidal effects there?

No. Like Mark said, the tidal force is independent of your non-deformable spherical masses.

If one of them has a permanent, static deformation (e.g. quadrupole moments and higher) are there tidal forces then? If both do?

There are tidal forces because one side of each object is closer to the other object than the other side is.

Or are dynamic, induced deformations required before we invoke the "T-word"?

No deformations are required!

Can tidal forces be radial, such that they do not tend to raise or lower an orbit over time, or must they have tangential components, like the one that is slowly raising the Moon's orbit?

They're usually radial. The simplest case is where one object is falling straight towards another much larger object. Things get more complicated when you've got two large orbiting objects like the Earth and the Moon.

Is it possible to draw a clear line here, at least within the scope of this SE site and This month's focus tag which is tidal-forces?

Probably not, because to really understand the tidal force you have to understand the force of gravity. A lot of people don't, even though Einstein made it clear. I said something about that yesterday in this answer, but I don't think it was appreciated.

The "tidal force" is simply a manifestation of good old inverse-square-law gravity. It doesn't need a rigid body to be present to manifest.

Consider a giant circular ring of dozens of space stations established in interstellar space. They're far away from any star and just sit there happily doing whatever it was they were set up to do. Suddenly, a star sweeps in from stage left (perhaps a fast-moving star created by a supernova-disrupted close binary system). What happens to the ring of stations?

They are attracted towards the rogue star, of course and start moving noticeably towards it when it gets close enough. They accelerate towards it pulled by the force of the star's gravity, which follows the inverse square law. But they don't all accelerate at the same rate. The station on the edge of the circle closest to the star accelerates fastest, stations half-way around the circle accelerate, but not as much, and the station on the far side of the circle accelerates least.

Soon the circle becomes an oval with its long axis pointing towards the star. This is the tidal effect. Let's say that the rogue star was dark -- a neutron star, perhaps, which had been stripped of its accretion disk by the explosion. What would the people on the stations observe? They wouldn't notice the acceleration per se because they're in free fall. Unless they were doing doppler spectroscopy of distant stars, they wouldn't detect their velocity (at least not at first), but they would see their neat ring of stations turning into an oval. From their point of view, some force was tugging on them and dragging them out of alignment. That's the tidal force.

From the point of view of the omniscient observer (us!) there are no tides, there's just simple gravity. But from the point of vie of the freely falling observers in the gravity field, most of the effects of gravity disappears and what's left looks like a force.

Wikipedia has an article on the tidal force which gives a mathematical treatment. (Personally, I don't think the article is terribly clear, though it appears to be correct.)

## Astronomy and Space Science: Astronomy Emerges from Astrology

Astrology is the study of planetary positions to predict the future and provide an explanation for personality traits. Today astrology is considered a pseudoscience (false science). Astronomy, on the other hand, is the study of phenomena and objects beyond Earth's atmosphere, and it is an accepted scientific discipline.

It was not always this way. Before the seventeenth century, astrology and astronomy were most often considered a single pursuit. Astrology was classified as a form of applied astronomy, and its predictions were thought to be important in medicine and meteorology.

This article will briefly trace the general history of astrology within its astronomical context from the ancient Babylonians to the Western European Renaissance. Occurring over centuries, a gradual separation of astrological and astronomical beliefs culminated in the sixteenth century in the work of German astronomer and astrologer Johannes Kepler (1571–1630). Subsequent scientific discoveries as well as socio-cultural factors led to the emergence of astronomy as an independent scientific discipline by 1700.

## No, the eclipse and a planetary alignment will not cause massive earthquakes. Sheesh.

Oh, crackpots. They're so ubiquitous! It makes me wonder sometimes if there are there no pots left to crack.

If you're in the debunking of nonsense game, as I have been for so many years, you can't help but notice that a lot of crackpottery is just rehashed from older stuff, as stale and unhealthy as month-old Thanksgiving leftovers (I give you, for example, the Maya Notpocalypse of 2012, which was as wrong as it was unoriginal). Sometimes, these wild claims are just lifted wholesale from earlier ones, too, with nothing more than cosmetic changes.

Such is the case with the latest doomsday fear-mongering fertilizer I'm seeing around the 'net: A huge earthquake will be triggered very soon, either by — take your pick — the lunar eclipse tomorrow, or a planetary alignment in February.

What these two claims have in common is they're both about as accurate as, say, anything Donald Trump says about climate change. Well, that, and they also talk about astronomical alignments. And here they diverge just a wee bit. Oh, they're both wrong, but since I represent science here (read: reality) I have to be a little more careful. Here's the deal.

Earthquakes are typically caused by tectonic movement the rubbing of continental plates together, say, or magma rumbling around a volcano (or, more recently, wastewater injection into fracking wells, yay!). Earthquakes happen all over the world all the time, it's just that most are too weak to cause much notice.

It's natural to wonder if outside influences can trigger earthquakes. Turning to space is also natural the Moon and Sun have a profound influence on our planet in the form of gravity. Tides are an effect of gravity the Moon stretches and compresses the Earth roughly twice a day as we spin underneath it, and this effect waxes and wanes as the Moon moves around the Earth in its elliptical orbit. The Sun, though farther away, is far more massive than the Moon, and also elicits tides on Earth, about half as strong as the Moon's.

Their tidal influence adds together when they are aligned when the Moon is either new (between us and the Sun) or full (when it's opposite the Sun). We do see phenomena related to this tidal flooding gets a bit worse when the Sun and Moon align. If the Moon is closer to Earth than usual, too, this can add to the effect (called a proxigean spring tide, a phrase that is just intrinsically cool).

Can this affect earthquakes too? Scientists have spent decades looking for some connection between the cycle of tides and seismic events. There is some small correlation between the Moon and weak, shallow earthquakes, but it's tenuous. But what about major quakes?

It turns out that's not easy to answer definitively. A recent paper states that there may be a correlation between the cycle of the Moon's orbit and strong earthquakes. However, their sample size is very small, and the effect they see is very tiny. For contrast, a more recent paper also looked at a lot of data and concludes there is no correlation… and makes the case in the paper's abstract rather concisely, I'll add:

The point is that any connection is so weak it's incredibly hard to measure. One problem is simply time: Magnitude 8 quakes only happen on average once per year (mag 7 about a dozen times per year), and then you have to look at how often they align in time with the Moon. It's rare. That should tell you that any connection is weak.

And it should certainly tell you that predicting an earthquake due to the Moon is nonsense. That hasn't stopped some folks from doing exactly that, though, but of course they are always wrong. If there were indeed something to this geologists would be all over it like tephra on a cinder cone * .

What about planetary alignments? It turns out their effect is far weaker than the Moon's! At best, if you aligned all the planets and put them as close to Earth in their orbits that you can, combined they have an effect only 2% of the Moon! And that's just straight gravity. Tides are far weaker, and are dominated so much by Venus that no planetary alignment comes close to touching it. So there is literally no way the planets can cause earthquakes.

So why the doomsday prediction? Well, in this case it all comes from Ditrianum Media, a doomsday mongering YouTube channel run by a man named Frank Hoogerbeets, an astrologer (oh, sigh) based in the Netherlands. I've debunked him before, when he made exactly this same claim.

He is doing what we in science call anomaly hunting looking for things that are odd and then trying to see if anything else aligns with them. This is very bad sleuthing you will always find some correlation between some events with other things — in this case, quakes and planetary positions, but you might as well look at the fluctuations in the stock market or baseball scores. Without any actual physical reason for the connection you're spinning Just So Stories.

Hoogerbeets does claim to have a cause, but it's, um, wacky. You can try to puzzle it out for yourself if you like, but when he got to “electromagnetic amplification” I stopped. It's word salad. He uses lots of sciencey-sounding words, but not in any way that makes sense.

THIS IS NOT HOW ALIGNMENTS WORK! Not that they work at all. But still. Credit: From a video by Diatranium Media

When I watched his new video on all this and laughed out loud: He claims there will be earthquakes in February due to an alignment of Mercury, Mars, and Uranus… but in his video he shows the line being perpendicular to Earth! That literally has no effect whatsoever. It's nonsense.

Not that this will slow down Hoogerbeets. His site is filled with such easily disprovable stuff, but I have no doubt he'll continue to make these videos as long as people will watch them.

And I'll be clear: I have no idea if people like him are con artists looking to make a buck by scaring people (a time-tested and successful method of extracting money and/or votes from people), or simply crackpots who truly believe what they say.

Either way they are wrong. And that shouldn't exactly be earth-shaking news.

So watch tomorrow's eclipse and feel safe, and don't worry about planetary alignments. We have enough things to worry about on this planet of ours — earthquakes are a good example — without making up things to fret over.

* You're welcome for that joke, geologists.

My thanks to my friends and geologists Mika McKinnon and Holly Brunkal for their help.

## An explanation of the rotational state of Mercury

Planetary scientists announced a new explanation of the current rotational state of the planet Mercury. The report was presented by Dr. Benoit Noyelles of the University of Namur, Belgium, to the meeting of the Division for Planetary Sciences of the American Astronomical Society, held in Denver, CO. This work has been carried out in collaboration with Drs. Julien Frouard of the University of São Paulo, Rio Claro, Brazil, and Valeri Makarov and Michael Efroimsky of the US Naval Observatory, Washington, DC. The study explains why the rotation period of Mercury is exactly two thirds of its orbital one, and how the planet avoided being trapped into higher spin-orbit resonances or into synchronous rotation. The released study sheds light on the likely state of Mercury during the early stages of its dynamical history.

Mercury is the innermost planet of the solar system, orbiting at one third of the Sun-Earth distance. Its dynamics is unique in that it has a significantly elongated orbit around the Sun, and its rotation period with respect to distant stars is exactly two thirds (58 days) of the period of its orbital revolution (88 days). This state is a particular case of dynamical resonance, whose origin has been discussed since the 1960s. Mercury is believed to have had a much faster rate of rotation at its creation, which declined to its current value relatively quickly on the scale of its lifetime, probably within a few tens of million years. The challenge is to explain why Mercury stopped to slow down at the 3:2 resonance, instead of synchronizing its rotation in the commonly observed 1:1 resonance, examples whereof are rendered by the Moon and other natural satellites.

A critical difficulty of this problem resides in adequate modeling of the tidal torques inducing rotational deceleration. In the case of Mercury, this is a torque due to the solar tides. The gravitational pull exerted by the Sun raises bodily tides on Mercury—a complex picture of time-dependent tidal stress and of the resulting tidal strain in the planet. A tidal bulge of a complex shape and spectrum emerges on Mercury's surface and runs across the circumference of the planet, causing relatively small in amplitude but nevertheless massive upheavals of the solid material. Internal friction dissipates the kinetic energy of Mercury's rotation. Slightly leading the direction of the external gravitational force, the tidal bulge elongates the figure of Mercury, which gives rise to an additional torque responsible for the deceleration. The tidal torque gets superimposed with a larger torque caused by the permanent figure of the planet. To model the deceleration adequately, it is necessary to take both factors into account.

The mills of God grind slowly but relentlessly. Tidal dissipation in the planet and the ensuing deceleration of its spin inevitably carry the planet through a sequence of the spin-orbit resonances. The question then becomes in which of these resonances the planet should eventually get trapped. The intensity of tidal dissipation strongly depends on the properties of the material constituting Mercury, affecting the way the tidal response depends on the frequency of excitation. Classical models proposed a few decades ago by planetary scientists failed to account for subtle variations of this response in the vicinity of resonances, which resulted in persistent difficulties in explaining the current 3:2 spin-orbit resonance of Mercury.

Recently, Michael Efroimsky and Valeri Makarov of the US Naval Observatory developed a new model of bodily tides, a model based on the laws of solid-state physics and on up-to-date geodetic, seismological, and laboratory measurements. Utilizing this model of tidal response, the international team revisited the problem of tidal evolution of Mercury's spin and found that the 3:2 resonance is indeed the most probable end-state. The frequency-dependent tidal torque acts as an efficient trap for the planet trying to traverse a resonance. The efficiency of the trap strongly depends on the value of orbital eccentricity, as well as on the temperature and viscosity of Mercury's mantle. Among the implications of the released study are, to name a few, a fast tidal spin-down, a relatively cold (i.e., not fully molten) state of the planet at the early stages of its life, and a possibility that the internal segregation and formation of the massive liquid core happened after Mercury's capture into the resonance.

This study has also shown that entrapment into the 3:2 spin-orbit resonance is likely to occur in exoplanetary systems, which are often tighter and more eccentric than in the solar system. Mercury-like states should be common among the hundreds of discovered and confirmed exoplanets, including potentially habitable super-Earths orbiting M dwarf stars. The results of this investigation provide additional insight into the possibilities of known exoplanets to support extraterrestrial life.

Mercury is currently the target of the American NASA space mission MESSENGER and will be visited by the European/Japanese ESA/JAXA mission Bepi-Colombo during the next decade. The data collected by these two spacecraft should help to further refine the tidal models of Mercury and similar planets of terrestrial composition.

## Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science

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Is it possible to imagine/construct a planet-like object where a "geo"-stationary Orbit is very, very close to the surface, eg 1 metre above? What would it be like?

Geostationary orbits are circular orbits where the orbital period is the same as the rotational period of the planet. So, given any planet, you can imagine speeding up its rotation until it matches the orbital period 1m above the surface.

However, it's gonna be a bad time for the planet if you do this. Let's switch to the (non-inertial!) rest frame of the spinning planet. Then the 1m orbit is where the inward gravitational force equals the outward centrifugal force. One meter below, at the surface of the planet, then, there is (effectively) almost no gravity, because the centrifugal force is almost completely cancelling it out. Since planets are held together gravitationally, this rapidly spinning planet will be quite unstable and have a huge equatorial bulge.

It's unlikely that you will be able to make such a planet out of normal planet stuff. The exception to this argument is, perhaps, a rapidly rotating neutron star (pulsar) or a rotating black hole.

Quickly estimating for a 1.5-solar-mass neutron star with 10km radius, ignoring general relativity (a bad approximation) puts the orbital period just outside the star at

500 microseconds, or half a millisecond. But we have observed pulsars with periods just over one millisecond, so it's not that far off!

How can we determine the "shape" of space time, and what consequences does that have for our understanding of the universe?

The Einstein field equations let you solve for the metric tensor, which describes how infinitesimal distances are calculated, which, in turn, tells you how spacetime curves.

Is it possible to make the planet mars same as earth?

It is beyond our capability right now but that is not to say it is impossible. There are two main issues with this. The first being the lack of a thick atmosphere. The second being no strong global magnetic field.

The first issue isn't too much of an issue as there is plenty of CO2 at the poles you would have to melt in order to get a thicker atmosphere. You could also introduce extremophiles that produce CO2 as a waste product although there would be many ethical problems with this until we discern if there isn't or is life on mars to start.

The second issue would most likely need to be taken care of first before dealing with the atmosphere. When there is no magnetic field to divert the solar radiation, it will literally strip the planet of its atmosphere and bombard anything on the surface with harmful radiation.

If you take a physucs formula, let's say this one,

Lets say we wanted to find t. Maybe not this formula in particular but is there a formula, that proves that objects move can move back in time (taking the square root of t gives you +t or-t, so does that imply thibgs do move backwards?)

In formulas like this, multiple solutions just means there are multiple ways for the equation to be satisfied. In this example, the equation is quadratic in t, and has two (unless it has zero or one. ) real solutions. Physically that means there are two times when the object has the position you're solving for, because (for example) you threw it upwards, it passed the position of interest, turned around, and came back down again at a later time. 'Negative' t just means 𧯯ore t=0' and our choice of t=0 was arbitrary in the first place. (It definitely doesn't mean moving backwards in time.) Of course, if our equation wasn't valid before t=0 (say, you hadn't thrown the object yet, so the acceleration was different), then the negative t solutions aren't physical--we just throw them away, because they don't represent reality.

There are areas of physics where solutions that 'look like' travel backwards in time appear. These get handled in different ways, usually by realizing that a different interpretation makes more sense.

Example: special relativity. If you have two events A and B, and event A causes event B to happen, we can ask what it looks like according to different observers who are moving with respect to us. If you ask about an observer moving faster than light (this is tricky to even define, but suppose you did) then that observer sees B happen before A. So instead of violating causality, we say that such frames of reference aren't valid. And it's consistent to do so, because we can independently show that things moving slower than light will never end up faster than light, and vice-versa, so we can just disregard those solutions as unphysical.

Example: relativistic quantum mechanics. If you write down the equation for a relativistic electron, you find it has solutions that look like the electrons traveling backwards in time. (Actually it looks like they have negative mass-energy, which is equivalent in QM to traveling backwards in time.) This is a problem for causality (if you take the backwards-in-time interpretation) or stability of empty space (if you take the negative mass-energy interpretation). However, if you treat everything properly in a quantum field theory context (this took a while to sort out, historically) you see that those solutions ARE physical but are NOT either negative energy or backwards in time---they're antimatter (positrons).

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before i ask my question i want to review two points:

1. place a body like a moon or a planet near a black hole, as the body approaches the extreme gravity affects the body deferentially.

2. review the tidal forces on Jupiter's moon Io leading to volcanic/tectonic consequences.

now take an identical copy of the earth and let it head through space with a velocity close the speed of light. even at these fantastic speeds nothing would be different on this new earth as compared to the original. however, the copy earth is still rotating so the side that is rotating into the direction of travel is getting even closer the speed of light. while the opposite side rotating away is going slower. even though this difference in velocities is only about 1 km/s can speeds sufficiently close to the speed of light yield a differential tidal force across the planet resulting affects on the geologic behavior of the planet [i.e. earthquacks, tectonics, etc. ]?

As far as the copy earth is concerned it isn't moving at all, so there would be no stress. In fact since there is no moon, there would be less stress.

You COULD include the moon. Nothing would change. Physics is (are?) the same in every inertial reference frame. It might look strange to an outsider, but that's just too bad. Our Earth would look that way to an observer moving by at relativistic speeds.

## In planetary and astronomical science, what exactly is, or is not, a tidal force? - Astronomy

Angular momentum conservation places severe restrictions on the possible steady-state differential rotation of any body. The only terms that survive the time-averaging of the zonal momentum equation (which expresses this conservation rule) are due to tidal torques, Lorentz (magnetic) forces, and friction. These terms are all much smaller than the canceling terms due to Coriolis forces and Reynolds stresses. So numerical models which do not solve the equations of motion exactly will inevitably give erroneous results. On the other hand, the time-average equations are straightforward to solve analytically. The results are that the balance between tidal torques and friction determines the differential rotation and the tidal dissipation and friction together determine the diabatic heating which maintains the required baroclinicity (horizontal temperature gradients). In conducting regions, the dynamo equation and the time-average zonal momentum equation form a nonlinear, but dissipative, system which is mathematically equivalent to the famous Lorenz system. The behavior of the resulting αω dynamo can be quite various, but depends on only a few parameters (the strength of the α-effect [α], the strength of the differential rotation [ω], and the magnetic Prandtl number [ν/λ] being the most important). It is totally independent of the Coriolis force, which does not appear in the time-average zonal balance. Equilibrium is reached when there is a balance between the Lorentz force and friction with B 2 R 2

## 1.2 The Nature of Science

The ultimate judge in science is always what nature itself reveals based on observations, experiments, models, and testing. Science is not merely a body of knowledge, but a method by which we attempt to understand nature and how it behaves. This method begins with many observations over a period of time. From the trends found through observations, scientists can model the particular phenomena we want to understand. Such models are always approximations of nature, subject to further testing.

As a concrete astronomical example, ancient astronomers constructed a model (partly from observations and partly from philosophical beliefs) that Earth was the center of the universe and everything moved around it in circular orbits. At first, our available observations of the Sun, Moon, and planets did fit this model however, after further observations, the model had to be updated by adding circle after circle to represent the movements of the planets around Earth at the center. As the centuries passed and improved instruments were developed for keeping track of objects in the sky, the old model (even with a huge number of circles) could no longer explain all the observed facts. As we will see in the chapter on Observing the Sky: The Birth of Astronomy, a new model, with the Sun at the center, fit the experimental evidence better. After a period of philosophical struggle, it became accepted as our view of the universe.

When they are first proposed, new models or ideas are sometimes called hypotheses. You may think there can be no new hypotheses in a science such as astronomy—that everything important has already been learned. Nothing could be further from the truth. Throughout this textbook you will find discussions of recent, and occasionally still controversial, hypotheses in astronomy. For example, the significance that the huge chunks of rock and ice that hit Earth have for life on Earth itself is still debated. And while the evidence is strong that vast quantities of invisible “dark energy” make up the bulk of the universe, scientists have no convincing explanation for what the dark energy actually is. Resolving these issues will require difficult observations done at the forefront of our technology, and all such hypotheses need further testing before we incorporate them fully into our standard astronomical models.

This last point is crucial: a hypothesis must be a proposed explanation that can be tested. The most straightforward approach to such testing in science is to perform an experiment. If the experiment is conducted properly, its results either will agree with the predictions of the hypothesis or they will contradict it. If the experimental result is truly inconsistent with the hypothesis, a scientist must discard the hypothesis and try to develop an alternative. If the experimental result agrees with predictions, this does not necessarily prove that the hypothesis is absolutely correct perhaps later experiments will contradict crucial parts of the hypothesis. But, the more experiments that agree with the hypothesis, the more likely we are to accept the hypothesis as a useful description of nature.

One way to think about this is to consider a scientist who was born and lives on an island where only black sheep live. Day after day the scientist encounters black sheep only, so he or she hypothesizes that all sheep are black. Although every observed sheep adds confidence to the theory, the scientist only has to visit the mainland and observe one white sheep to prove the hypothesis wrong.

When you read about experiments, you probably have a mental picture of a scientist in a laboratory conducting tests or taking careful measurements. This is certainly the case for a biologist or a chemist, but what can astronomers do when our laboratory is the universe? It’s impossible to put a group of stars into a test tube or to order another comet from a scientific supply company.

As a result, astronomy is sometimes called an observational science we often make our tests by observing many samples of the kind of object we want to study and noting carefully how different samples vary. New instruments and technology can let us look at astronomical objects from new perspectives and in greater detail. Our hypotheses are then judged in the light of this new information, and they pass or fail in the same way we would evaluate the result of a laboratory experiment.

Much of astronomy is also a historical science—meaning that what we observe has already happened in the universe and we can do nothing to change it. In the same way, a geologist cannot alter what has happened to our planet, and a paleontologist cannot bring an ancient animal back to life. While this can make astronomy challenging, it also gives us fascinating opportunities to discover the secrets of our cosmic past.

You might compare an astronomer to a detective trying to solve a crime that occurred before the detective arrived at the scene. There is lots of evidence, but both the detective and the scientist must sift through and organize the evidence to test various hypotheses about what actually happened. And there is another way in which the scientist is like a detective: they both must prove their case. The detective must convince the district attorney, the judge, and perhaps ultimately the jury that his hypothesis is correct. Similarly, the scientist must convince colleagues, editors of journals, and ultimately a broad cross-section of other scientists that her hypothesis is provisionally correct. In both cases, one can only ask for evidence “beyond a reasonable doubt.” And sometimes new evidence will force both the detective and the scientist to revise their last hypothesis.

This self-correcting aspect of science sets it off from most human activities. Scientists spend a great deal of time questioning and challenging one another, which is why applications for project funding—as well as reports for publication in academic journals—go through an extensive process of peer review, which is a careful examination by other scientists in the same field. In science (after formal education and training), everyone is encouraged to improve upon experiments and to challenge any and all hypotheses. New scientists know that one of the best ways to advance their careers is to find a weakness in our current understanding of something and to correct it with a new or modified hypothesis.

This is one of the reasons science has made such dramatic progress. An undergraduate science major today knows more about science and math than did Sir Isaac Newton, one of the most renowned scientists who ever lived. Even in this introductory astronomy course, you will learn about objects and processes that no one a few generations ago even dreamed existed.

Planetary Compressions from Atmospheres

From the definition of Bulk Modulus (B) (above), we have that:

10 11 N m -2 (for rock), we can estimate the atmospherically induced Planetary Compressions of Venus, Earth, & Mars:

I'm afraid your planetary compression is nonsense.

If 15 psi of atmosphere causes the earth to "sag" by 2.1 meters, another 15 psi will surely cause it to sag by another 2.1 meters. So a car, which might push down on the 4 tire contact points with a pressure of 32 psi, should sink about 14 or 15 feet into the ground.

That should make it evident that your model is oversimplified to the point of being completely wrong.

That is not correct. The Bulk Modulus only applies, when the whole surface of the object, is subjected to uniform pressure .

1. If you put such cars across the whole surface of the Earth
2. Thenit would "sag" another 2 m

A better example, is the Isostatic Compression of the planet, from the massive Glaciers, of the Last Ice Age.

1 km of ice compressed the crust around 100 m*. The column mass of said ice created base pressures of about 10 7 Pa, or roughly 100 Atm. My model would predict, then, a

CONCLUSION: My analysis is Order-of-Magnitude accurate . By way of comparison, Carroll & Ostlie often describe the underlying physics of Astronomical situations w/ simple models that are Order-of-Magnitude accurate, to w/in factors of 3-4. My model matches that standard.

ADDENDUM: Areas in Montana have experienced " about 328 meters of isostatic uplift "*. And, around Hudson's Bay,

300 m of uplift have been recorded**. Assuming a 2 km column height, for the Laurentide Ice Sheet over Montana, my model predicts 400 m of "sag". And, Isostatic Uplift is ongoing, even today. Again, this analysis is Order-of-Magnitude accurate, as advertised. I have not "pressed" the Significant Digits.

The word is often used in reference to the Sun, Earth, and either the Moon or a planet, where the latter is in conjunction or opposition. Solar and lunar eclipses occur at times of syzygy, as do transits and occultations. The term is often applied when the Sun and Moon are in conjunction (new moon) or opposition (full moon). [5]

The word syzygy is often used to describe interesting configurations of astronomical objects in general. For example, one such case occurred on March 21, 1894, around 23:00 GMT, when Mercury transited the Sun as would have been seen from Venus, and Mercury and Venus both simultaneously transited the Sun as seen from Saturn. It is also used to describe situations when all the planets are on the same side of the Sun although they are not necessarily in a straight line, such as on March 10, 1982. [6]

On June 3, 2014, the Curiosity rover on Mars observed the planet Mercury transiting the Sun, marking the first time a planetary transit has been observed from a celestial body besides Earth. [4]

Syzygy sometimes results in an occultation, transit, or eclipse.

• An occultation occurs when an apparently larger body passes in front of an apparently smaller one.
• A transit occurs when a smaller body passes in front of a larger one.
• In the combined case where the smaller body regularly transits the larger, an occultation is also termed a secondary eclipse.

Transits and occultations of the Sun by Earth's Moon are called solar eclipses regardless of whether the Sun is completely or partially covered. By extension, transits of the Sun by a satellite of a planet may also be called eclipses, as with the transits of Phobos and Deimos shown on NASA's JPL photojournal, as may the passage of a satellite into the planet's shadow, as with this eclipse of Phobos. The term eclipse is also used more generally for bodies passing in front of one another. For example, a NASA Astronomy Picture of the Day refers to the Moon eclipsing and occulting Saturn interchangeably.

As electromagnetic rays are somewhat bent by gravitation, when they pass by a heavy mass they are bent. Thus, the heavy mass acts as a form of gravitational lens. If the light source, the gravitating mass and the observer stand in a line, one sees what is termed an Einstein ring.

Syzygy causes the bimonthly phenomena of spring and neap tides. At the new and full moon, the Sun and Moon are in syzygy. Their tidal forces act to reinforce each other, and the ocean both rises higher and falls lower than the average. Conversely, at the first and third quarter, the Sun and Moon are at right angles, their tidal forces counteract each other, and the tidal range is smaller than average. [7] Tidal variation can also be measured in the earth's crust, and this may affect the frequency of earthquakes.