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Nebular Theory Might Explain How Our Solar System Formed

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Image of blue light and orange clouds surrounded by black space and white stars

Our solar system contains the sun, inner rocky planets, the gas giants , or the outer planets, and other celestial bodies, but how they all formed is something that scientists have debated over time.

The nebular theory , also known as nebular hypothesis , presents one explanation of how the solar system formed. Pierre-Simon, Marquis de Laplace proposed the theory in 1796, stating that solar systems originate from vast clouds of gas and dust, known as solar nebula, within interstellar space.

Learn more about this solar system formation theory and some of the criticism it faced.

What Is the Nebular Theory?

Criticisms of the nebular theory, solar nebular disk model.

Laplace said the material from which the solar system and Earth derived was once a slowly rotating cloud, or nebula, of extremely hot gas. The gas cooled and the nebula began to shrink. As the nebula became smaller, it rotated more rapidly, becoming somewhat flattened at the poles.

A combination of centrifugal force, produced by the nebula's rotation, and gravitational force, from the mass of the nebula, left behind rings of gas as the nebula shrank. These rings condensed into planets and their satellites, while the remaining part of the nebula formed the sun.

The planet formation hypothesis, widely accepted for about a hundred years, has several serious flaws. The most serious concern is the speed of rotation of the sun.

When calculated mathematically on the basis of the known orbital momentum, of the planets, the nebular hypothesis predicts that the sun must rotate about 50 times more rapidly than it actually does. There is also some doubt that the rings pictured by Laplace would ever condense into planets.

In the early 20th century, scientists rejected the nebular hypothesis for the planetesimal hypothesis, which proposes that planets formed from material drawn out of the sun. This theory, too, proved unsatisfactory.

Later theories have revived the concept of a nebular origin for the planets. An educational NASA website states: "You might have heard before that a cloud of gas and dust in space is also called a 'nebula,' so the scientific theory for how stars and planets form from molecular clouds is also sometimes called the Nebular Theory. Nebular Theory tells us that a process known as 'gravitational contraction' occurred, causing parts of the cloud to clump together, which would allow for the Sun and planets to form from it."

Victor Safronov , a Russian astronomer, helped lay the groundwork for the modern understanding of the Solar Nebular Disk Model. His work, particularly in the 1960s and 1970s, was instrumental in shaping our comprehension of how planets form from a protoplanetary disk.

At a time when others did not want to focus on the planetary formation process, Safronov used math to try to explain how the giant planets, inner planets and more came to be. A decade after his research, he published a book presenting his work.

George Wetherill's research also contributed to this area, specifically on the dynamics of planetesimal growth and planetary accretion.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

Observed features any origin model of the solar system/planets must explain

Atoms in your body, collapsing clouds of gas and dust in nebular hypothesis.

The Spinning Nebula Flattens

Condensation of Protosun and Protoplanets

The composition of the sun, the two classes of planets, etc. explained by the nebula hypothesis:, evidence for the nebular hypothesis.

Historical Geology

A free online textbook for Historical Geology courses

Nebular theory and the formation of the solar system

In the beginning….

How and when does the story of Earth begin? A logical place to start is with the formation of the planet, but as you’ll soon see, the formation of the planet is part of a larger story, and that story implies some backstory before the story, too. The purpose of this case study is to present our best scientific understanding of the formation of our solar system from a presolar nebula, and to put that nebula in context too.

Nebular theory

The prevailing scientific explanation for the origin of the Earth does a good job of not only explaining the Earth’s formation, but the Sun and all the other planets too. Really, it’s not “the Earth’s origin story” alone so much as it is the origin story of the whole solar system . Not only that, but our Sun is but one star among a hundred million in our galaxy, and our galaxy is one of perhaps a hundred million in the universe. So the lessons we learn by studying our own solar system can likely be applied more generally to the formation of other solar systems elsewhere, including those long ago, in galaxies far, far away. The vice versa is also true: Our understanding of our own solar system’s origin story is being refined as we learn more about exoplanets, some of which defy what we see in our own system; “ hot Jupiters ” and “ super-Earths ,” for instance, are features we see in other star systems but not our own.

When we use powerful telescopes to stare out into the galaxy, we observe plenty of other stars, but we observe other things too, including fuzzy looking features called nebulae. A nebula is a big cloud of gas and dust in space. It’s not as bright as a star because it’s not undergoing thermonuclear fusion, with the tremendous release of energy that accompanies that process. An example of a nebula that you are likely to be able to see is in the constellation Orion. Orion’s “belt,” three stars in a row, is a readily identifiable feature in the northern hemisphere’s night sky in winter. A smaller trio of light spots “dangle” from the belt; this is Orion’s sword scabbard. A cheap pair of binoculars will let you examine these objects for yourself; you will discover that the middle point of light in this smaller trio is not a star. It is a nebula called Messier 42.

The Messier 42 nebula, shown in the context of the "scabbard" of the constellation Orion. Graphic art by Callan Bentley, reworking material from several OER sources.

Nebulae like Messier 42 are common features of the galaxy, but not as common as stars. Nebulae appear to be short-lived features, as matter is often attracted to other matter. All that stuff distributed in that tremendous volume of space is not as stable as it would be if it were all to be drawn together into a few big clumps. Particles pull together with their neighboring particles under the influence of various forces, including “static cling” or electrostatic attraction. This is the same force that makes tiny dust motes clump up into dust bunnies under your couch!

Three dust bunnies and a pencil tip to provide a sense of scale. The dust bunnies are each about 3 cm across and 1.5 cm tall. Photo by Callan Bentley, 2019.

Now, electrostatic force is quite strong for pulling together small particles over small distances, but if you want to make big things like planets and stars out from a nebula, you’re going to need gravity to take over at some point. Gravity is a rather weak force. After all: every time you take a step, you’ve overcoming the gravitational pull of the entire Earth. But gravity can work very efficiently over distance, if the masses involved are large enough. So static cling was the initial organizer, until the “space dust bunnies” got large enough, then gravity was able to take over, attracting mass to mass. The net result is that the gajillions of tiny pieces of the nebula were drawn together, swirling into a denser and denser amalgamation. The nebula began to spin, flattening out from top to bottom, and flattening out into a spinning disk, something between a Frisbee and a fried egg in shape:

An artist's conception of an oblique view of the protoplantary disk HL Tauri, using imagery originally gathered by the European Southern Observatory.

Once a star forms in the center, astronomers call the ring of debris around it a protoplanetary disk. Two important processes that helped organize the protoplanetary disk further were condensation and accretion.

Chondrules in the Grassland meteorite, with a scale showing a scale in mm. Sources: Zimbres on Wikimedia, CC-BY license.

Condensation is the process where gaseous matter sticks together to make liquid or solid matter. We have evidence of condensation in the form of small spherical objects with internal layering, kind of like “space hailstones.” These are chondrules, and they represent the earliest objects formed in our solar system. (Occasionally, we are lucky enough to find chondrules that have survived until the present day, entombed inside certain meteorites of the variety called chondrites.)

Chondrules glommed onto other chondrules, and stuck themselves together into primordial “rocks,” building up larger and larger objects. Eventually, these objects got to be big enough to pull their mass into an round shape, and we would be justified to dub them “planetesimals.” Planetesimals gobbled up nearby asteroids, and smashed into other planetesimals, merging and growing through time through the process of accretion. The kinetic force of these collisions heated the rocky and metallic material of the planetesimals, and their temperature also went up as radioactive decay heated them from within. Once warm, denser material could sink to their middles, and lighter-weight elements and compounds rose up to their surface. So not only were they maturing into spheroidal shapes, but they were also differentiating internally, separating into layers organized by density.

A cartoon model showing the evolution of our solar system from a pre-solar nebula, in four stages. In the first stage, a diffuse nebula is shown. In the second stage, most of the material has moved to the center, and it has started to rotate. Little flecks of solid material have accumulated. In stage 3, the flecks have grown into chunks, and there is much less diffuse fuzzy stuff in the background. The sun has formed as a discrete entity. In the fourth and final stage, the sun is a fat blob, surrounded by discrete planets. The space between them is mostly clear and clean.

Meteorites that show metallic compositions represent “core” material from these planetesimals; core material that we would never get to glimpse had not their surrounding rocky material been blasted off. Iron meteorites such as the Canyon Diablo meteorite below (responsible for Arizona’s celebrated Meteor Crater) therefore are evidence of differentiation of planetesimals into layered bodies, followed by disaggregation: a polite way of saying they were later violently ripped apart by energetic collisions.

If you were to somehow weigh the nebula before condensation and accretion, and again 4.6 billion years later, we’d find the mass to be the same. Rather than being dispersed in a diffuse cloud of uncountable atoms, the condensation and accretion of the nebula resulted in exactly the same amount of stuff, but organized into a smaller and smaller number of bigger and bigger objects. The biggest of these was the Sun, comprising about 99.86% of all the mass in the solar system. Four-fifths of the remaining 0.14% makes up the planet Jupiter.  Saturn, Neptune, and Uranus are huge gas giants as well. The inner rocky planets (including Earth) make up a tiny, tiny fraction of the total mass of the whole solar system – but of course, just because they are relatively small, that doesn’t mean they are unimportant!

The process of accretion continues into the present day, though at a slower pace than the earliest days of the solar system. One place you can observe this is in the asteroid belt, where there are certain asteroids that are basically nothing more than a big 3D pile of space rocks, held together under their own gravity. Consider the asteroid called Itokawa 25143, for instance:

The asteroid 25143 Itokawa, imaged by the Japanese Space Agency (JAXA) during the Hayabusa mission. Labels and scale added by Callan Bentley.

Only about half a kilometer long, and only a few hundred meters wide, Itokawa doesn’t even have enough gravity to pull itself into a sphere. If you were to land on the surface of Itokawa and kick a soccer-ball-sized boulder, it would readily fly off into space, as the force of your kick would be much higher than the force of gravity causing it to stay put.

Another example of accretion continuing to this day is meteorite impacts. Every time a chunk of rock in space intersects the Earth, its mass is added to that of the planet. In that instant, the solar system gets a little bit cleaner (fewer leftover bits rattling around) and the planet gets a little more massive. A spectacular example of this occurred in 1994 with Comet Shoemaker-Levy 9, a  comet which had only been discovered the previous year. Jupiter’s immense gravity broke the comet into chunks, and then swallowed them up one after another. Astronomers on Earth watched with fascination as the comet chunks, some more than a kilometer across, slammed into Jupiter’s atmosphere at 60 km/second (~134,000 mph), creating a 23,700°C fireball and enormous impact scars that were as large as the entire Earth. These scars lasted for months.

A photograph (through a telescope) showing a prominent red/brown concentric-ring shaped "scar" on Jupiter's atmosphere where Comet Shoemaker-Levy 9 impacted it.

This incredibly dramatic event perhaps raises the hair on our necks, seeing the violence and power of cosmic collisions. It’s a reminder that Earthlings are not safe from accretionary impacts even today – as the dinosaurs found out. For the purposes of our current discussion, though, bear in mind that the collision was really a merger between the masses of Comet Shoemaker-Levy 9 and the planet Jupiter, and after the dust settled, the solar system had one fewer object left off by itself, and Jupiter gained a bit more mass. This is the overall trend of the accretion of our solar system from the presolar nebula: under gravity’s influence, the available mass becomes more and more concentrated through time.

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A star is born

Because the Sun is so massive, it is able to achieve tremendous pressures in its interior. These pressures are so high, they can actually force two atoms into the same space , overcoming their immense repulsion for one another, and causing their two nuclei to merge. As two atoms combine to make one more massive atom, energy is released. This process is thermonuclear fusion. Once it begins, stars begin to give off light.

In the Hertzprung-Russell diagram the temperatures of stars are plotted against their luminosities. The position of a star in the diagram provides information about its present stage and its mass. Stars that burn hydrogen into helium lie on the diagonal branch, the so-called main sequence. Our Sun is an example of a main sequence star, about halfway through its "life" expectancy. Red dwarfs lie in the cool and faint lower right corner. When a star exhausts all the hydrogen, it leaves the main sequence and becomes a red giant or a supergiant, depending on its mass (upper right corner). Stars with the mass of the Sun which have burnt all their fuel finally develop into a white dwarf (lower left corner).

The ability of stars to make big atoms from small ones is key to understanding the history of our solar system and our planet. Planet Earth is made of a wide variety of chemical elements, both lightweight and heavy. All of these elements must have been present in the nebula, in order for them to be included in Earth’s “starting mixture.” Elements formed in the Sun today stay in the Sun, fusing low-weight atoms into heavier atoms. So all the elements on Earth today came from a pre-Sun star. We can go outside on a spring day and enjoy the Sun’s warmth, but the carbon that makes up the skin that basks in that warmth was forged in the heart of another star, a star that’s gone now, a star that blew up.

This exploding star was the source of the nebula where we began this case study: it’s the backstory that occurred before the opening scene. Our solar system is like a “haunted house,” where billions of years ago, there was a vibrant, healthy main-sequence star right here, in this part of the galaxy. Perhaps it had planets orbiting it. Perhaps some of those planets harbored life. We’ll never know: the explosion wiped the slate clean, and “reset” the solar system for the iteration in which we live. The ghostly remnants of this time before our own still linger, in the very stuff we’re made from. This long-dead star fused hydrogen to build the carbon in our bodies, the iron in our blood, the oxygen we breathe, and the silicon in the rocks of our planet.

This is an incredible realization to embrace: everything you know, everything you trust, everything you are , is stardust.

Age of the solar system

So just when did all this happen? An estimate for the age of the solar system can be made using isotopes of the element lead (Pb). There are several isotopes of lead, but for the purposes of figuring out the age of the solar system, consider these four: 208 Pb, 207 Pb, 206 Pb, and 204 Pb.

208 Pb, 207 Pb, 206 Pb are all radiogenic: that is to say, they stable “daughter” isotopes that are produced from the radioactive “parent” isotopes. Each is produced from a different parent, at a different rate:

Parent isotope Stable daughter Half-life
Th Pb 14.0 b.y.
U Pb 4.5 b.y.
U Pb 0.70 b.y.

204 Pb is, as far as we know, non-radiogenic. It’s relevant to this discussion because it can serve as a ‘standard’ that can allow us to compare the other lead isotopes to one another. Just as if we wanted to compare the currencies of Namibia, Indonesia, and Chile, we might reference all three to the U.S. dollar. The dollar would serve as a standard of comparison, allowing us to better see the value of the Namibian currency relative to the Indonesian currency and the Chilean currency. That’s what 204 Pb is doing for us here.

Lead (Pb) isotope ratio evolution: 206Pb, 207Pb, and 208Pb ratioed by 204Pb, over the past 5 billion years, including both terrestrial (Earth rock) measurements and projections of primordial evolution, though no Earth rocks of that age persist. Redrawn by Callan Bentley (2019) from an original in SOME TEXTBOOK *** FIND THIS OUT.

This is a plot showing the modeled evolution of our three radiogenic lead isotopes relative to 204 Pb. It is constrained by terrestrial lead samples at the young end, and projected back in time in accordance with our measurements of how quickly these three isotopes of lead are produced by their radioactive parents. Of course, if we go back far enough in time, we run out of samples to evaluate. The Earth’s rock cycle has destroyed all its earliest rocks. They’ve been metamorphosed, or weathered, or melted – perhaps many times over! What would be really nice is to find some rocks from the early end of these curves – some samples that could verify these projections back in time are accurate.

Such samples do exist! But they are not from the Earth so much as “from the Earth’s starting materials.” If the nebular theory is correct, then a few leftover scraps of the planet’s starting materials are found in the solar system’s asteroids. Every now and again, bits of these space rocks fall to earth, and if they survive their passage through the atmosphere, we may be lucky enough to collect them, and analyze them. We call these space rocks “meteors” as they streak through the atmosphere, heating through friction and oxidizing as they fall. Those that make it all the way to Earth’s surface are known as “meteorites.” They can be often be distinguished by their scalloped fusion crust, as with this sample:

Lead (Pb) isotope ratio evolution: 206Pb, 207Pb, and 208Pb ratioed by 204Pb, over the past 5 billion years, including terrestrial (Earth rock) measurements and projections of primordial evolution, and values derived from measurement of meteorites. All three radiogenic isotopes of lead give the same answer for the starting date of the solar system's lead isotope system: 4.6 billion years ago. Redrawn and modified by Callan Bentley (2019) from an original in SOME TEXTBOOK *** FIND THIS OUT.

Meteorites come in several varieties, including rocky and metallic versions. It is very satisfying that when measurements of these meteorites’ lead isotopes are added to the plot above, they all fall exactly where our understanding of lead isotope production would have them: at the start of each of these model evolution curves. Each lead isotope system tells the same answer for the age of the Earth, acting like three independent witnesses corroborating one another’s testimony. And the answer they all give is 4.6 billion years ago (4.6 Ga). That’s what 208 Pb says. That’s what 207 Pb says. And that’s what 206 Pb says. They all agree, and they agree with the predicted curves based on terrestrial (Earth rock) measurements. This agreement gives us great confidence in this number. The Earth, and meteorites (former asteroids), and the solar system of which they are all a part, began about 4.6 billion years ago…

…But what came before that?

The implications of meteorites

In 1969, a meteorite fell through Earth’s atmosphere and broke up over Mexico. A great many pieces of this meteorite were recovered and made available for scientific analysis. It turned out to be a carbonaceous chondrite, the largest of its kind ever documented. It was named the Allende ( “eye-YEN-day” ) meteorite, for the tiny Chihuahuan village closest to the center of the area over which its fragments were scattered.

One of the materials making up Allende’s chondrules was the calcium feldspar called anorthite. Anorthite is an extraordinarily common mineral in Earth’s crust, but the Allende anorthite was different. For some reason, it has a large amount of magnesium in it. When geochemists determined what kind of magnesium this was, they were surprised to find that it was mostly 26 Mg, an uncommon isotope. The abundances of 25 Mg and 24 Mg were found to be about the same level as Earth rocks, but 26 Mg was elevated by about 1.3%.  And after all, magnesium doesn’t even “belong” in a feldspar. The chemical formula of anorthite is CaAl 2 Si 2 O 8 – there’s no “Mg” spot in there. Why was this odd 26 Mg in this chondritic anorthite?

One way to make 26 Mg is the break-down of radioactive 26 Al. The problem with this idea is that there is no 26 Al around today . It’s an example of an extinct isotope: an atom of aluminum so unstable that it falls apart extremely rapidly. The half-life is only 717,000 years. But because these chondrules condensed in the earliest days of the solar system, there may well have been plenty of 26 Al around at that point for them to incorporate. And Al, of course, is a key part of anorthite’s Ca Al 2 Si 2 O 8 crystal structure.

So the idea is that weird extra 26 Mg in the chondrule’s anorthite could be explained by suggesting it wasn’t always 26 Mg: Instead, it started off as 26 Al ,and it belonged in that crystal’s structure. However, over a short amount of time, it all fell apart, and that left the 26 Mg behind to mark where it had once been. If this interpretation is true, it has shocking implications for the story of our solar system.

To understand why, we first need to ask, what came before the nebula? What was the ‘pre-nebula’ situation? Where did the nebula come from, anyhow?

It turns out that nebulae are generated when old stars of a certain size explode.

These explosions are called supernovae (the plural of supernova). The “nova” part of the name comes from the fact that they are very bright in the night sky – an indication of how energetic the explosion is. They look like “new” stars to the casual observer. Nova is Latin for “new.” Supernovae occur when a star has exhausted its supply of lightweight fuel, and it runs out of small atoms that can be fused together under normal conditions. The outward-directed force ceases, and gravitationally-driven inward-directed forces suddenly dominate, collapsing the star in upon itself. This jacks up the pressures to unbelievably high levels, and is responsible for the nuclear fusion of big atoms. Every atom heavier than iron is made instantaneously in the fires of the supernova.

That suite of freshly-minted atoms included a bunch of unstable isotopes, 26 Al among them.

And here’s the kicker: If the 26 Al was made in a supernova, started decaying immediately, and yet enough was still around that a significant portion of it could be woven into the Allende chondrules’ anorthite, that implies a very short amount of time between the obliteration of our Sun’s predecessor, and the first moments of our own solar system. Specifically, the 717,000 year half-life of 26 Al suggests that this “transition between solar systems” played out in less than 5 million years, conceivably in only 2 million years.

That is very, very quickly.

In summary, the planet Earth is part of a solar system centered on the Sun. This solar system, with its star, its classical planets, its dwarf planets, and its “leftover” comets and asteroids, formed from a nebula full of elements in the form of gas and dust. Over time, these many very small pieces stuck together to make bigger concentrations of mass, eventually culminating in a star and a bunch of planets that orbit it. Asteroids (and asteroids that fall to Earth, called meteorites), are leftovers from this process. The starting nebula itself formed from the destruction of a previous star that had exploded in a supernova. The transition from the pre-Sun star to our solar system took place shockingly rapidly.

Further reading

Marcia Bjornerud’s book Reading the Rocks . Basic Books, 2005: 226 pages.

Jennifer A. Johnson (2019), “ Populating the periodic table: Nucleosynthesis of the elements ,” Science. 01 Feb 2019 : 474-478.

Lee, T., D. A. Papanastassiou, and G. J. Wasserburg (1976), Demonstration of 26 Mg excess in Allende and evidence for 26 Al , Geophysical Research Letters , 3(1), 41-44.

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Chapter Contents

  • 1 In the beginning…
  • 2 Nebular theory
  • 3 A star is born
  • 4 Age of the solar system
  • 5 The implications of meteorites
  • 7 Further reading

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Key Concepts:

  • What are the key characteristics of our Solar System?
  • What do they tell us about the origin of our Solar System?
  • How do astronomers discover other solar systems?

Jovian Planets

Solar nebular theory, observational clues.

Quiz 13a: Dating Earth...

Quiz 13b: killer asteroids, planetary diversity.

Should all planetary systems be like our?

What variations should one expect?

  • Planets can eclipse the central star along the line of sight in some cases, and one can measure a brief dimming of the star and infer the presence of a planet.
  • A planet around a star passing in front of another star along the line of sight can cause signatures of light change to the prediction by Einstein.

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Nicolaus Copernicus. Nicolas Copernicus (1473-1543) Polish astronomer. In 1543 he published, forward proof of a Heliocentric (sun centered) universe. Coloured stipple engraving published London 1802. De revolutionibus orbium coelestium libri vi.

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  • Geosciences LibreTexts - Origin of the Solar System—The Nebular Hypothesis
  • Journal of Emerging Technologies and Innovative Research - The Origin of Solar System "The Nebular Model"

solar nebula , gaseous cloud from which, in the so-called nebular hypothesis of the origin of the solar system , the Sun and planets formed by condensation. Swedish philosopher Emanuel Swedenborg in 1734 proposed that the planets formed out of a nebular crust that had surrounded the Sun and then broken apart. In 1755 the German philosopher Immanuel Kant suggested that a nebula in slow rotation, gradually pulled together by its own gravitational force and flattened into a spinning disk, gave birth to the Sun and planets. A similar model, but with the planets being formed before the Sun, was proposed by the French astronomer and mathematician Pierre-Simon Laplace in 1796. During the late 19th century the Kant-Laplace views were criticized by the British physicist James Clerk Maxwell , who showed that, if all the matter contained in the known planets had once been distributed around the Sun in the form of a disk, the shearing forces of differential rotation would have prevented the condensation of individual planets. Another objection was that the Sun possesses less angular momentum (dependent on the total mass, its distribution, and the speed of rotation) than the theory seemed to require. For several decades most astronomers preferred the so-called collision theory, in which the planets were considered to have been formed as a result of a close approach to the Sun by some other star . Objections to the collision theory more convincing than those against the nebular hypothesis were raised, however, especially as the latter was modified in the 1940s. The masses of the original planets ( see protoplanet ) were assumed to be larger than in the earlier version of the theory, and the apparent discrepancy in angular momentum was attributed to magnetic forces connecting the Sun and planets. The nebular hypothesis has thus become the prevailing theory of the origin of the solar system.

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46 The Nebular Theory: Other Important Evidence

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Hypothesis Tests II

Announcements, concept questions.

  • PS 14: Hypothesis Tests II
  • RQ: Wrong By Design due Wed/Thu night at 11:59pm
  • Quiz 3 is in the first half of class on Thursday/Friday.
  • Problem Set 14 is due the Tuesday after break.

Which pair of plots would have the greatest chi-squared distance between them? (consider one of them the “observed” and the other the “expected”)

4 steps of nebular hypothesis

Chi-squareds Compared

4 steps of nebular hypothesis

\[ \frac{(1-1)^2}{1} + \frac{(10 - 1)^2}{1} + \frac{(1 - 10)^2}{10} \\ 0 + 81 + \frac{81}{10} = 89.1 \]

4 steps of nebular hypothesis

\[ \frac{(3-5)^2}{5} + \frac{(4-4)^2}{4} + \frac{(5-3)^2}{3} \\ \frac{4}{5} + 0 + \frac{4}{3} = 2.13 \]

An In-class Experiment

In order to demonstrate how to conduct a hypothesis test through simulation, we will be collecting data from this class using a poll.

You will have only 15 seconds to answer the following multiple choice question, so please get ready at pollev.com …

The two shapes above have simple first names:

Which of the two names belongs to the shape on the left ?

Steps of a Hypothesis Test

  • Assert a model for how the data was generated (the null hypothesis)
  • Select a test statistic that bears on that null hypothesis (a mean, a proportion, a difference in means, a difference in proportions, etc).
  • Approximate the sampling distribution of that statistic under the null hypothesis (aka the null distribution)
  • Assess the degree of consistency between that distribution and the test statistic that was actually observed (either visually or by calculating a p-value)

1. The Null Hypothesis

  • Let \(p_k\) be the probability that a person selects Kiki for the shape on the left.
  • Let \(\hat{p}_k\) be the sample proportion of people that selected Kiki for the shape on the left.

What is a statement of the null hypothesis that corresponds to the notion the link between names and shapes is arbitrary?

2. Select a test statistic

\[\hat{p}_k = \frac{\textrm{Number who chose "Kiki"}}{\textrm{Total number of people}}\]

Note: you could also simply \(n_k\) , the number of people who chose “Kiki”.

3. Approximate the null distribution

Our technique: simulate data from a world in which the null is true, then calculate the test statistic on the simulated data.

Which simulation method(s) align with the null hypothesis and our data collection process?

Simulating the null using infer

4. assess the consistency of the data and the null, the p-value.

What is the proper interpretation of this p-value?

The Bouba / Kiki Effect

Problem set 14: hypothesis testing ii.

COMMENTS

  1. Nebular hypothesis

    The nebular hypothesis is the most widely accepted model in the field of cosmogony to explain the formation and evolution of the Solar System (as well as other planetary systems).It suggests the Solar System is formed from gas and dust orbiting the Sun which clumped up together to form the planets. The theory was developed by Immanuel Kant and published in his Universal Natural History and ...

  2. How Was the Solar System Formed?

    Nebular Hypothesis: According to this theory, the Sun and all the planets of our Solar System began as a giant cloud of molecular gas and dust. Then, about 4.57 billion years ago, something ...

  3. 8.2: Origin of the Solar System—The Nebular Hypothesis

    The nebular hypothesis is the idea that a spinning cloud of dust made of mostly light elements, called a nebula, flattened into a protoplanetary disk, and became a solar system consisting of a star with orbiting planets [ 12 ]. The spinning nebula collected the vast majority of material in its center, which is why the sun Accounts for over 99% ...

  4. steps of the nebular theory Flashcards

    step two (2) -A disturbance. -caused the solar nebula to slowly contract and rotate. step three (2) -The solar nebula assumed a flat, disk shape. -with the protosun (pre-Sun) at the center. step four (2) -Inner planets began to form from metallic. -and rocky substances.

  5. 2.2: Origin of the Solar System

    Figure 2.2.1 2.2. 1: Small protoplanetary discs in the Orion Nebula. Our solar system formed as the same time as our Sun as described in the nebular hypothesis. The nebular hypothesis is the idea that a spinning cloud of dust made of mostly light elements, called a nebula, flattened into a protoplanetary disk, and became a solar system ...

  6. The Nebular Theory

    44 The Nebular Theory So…how did the solar system form and end up with all these different types of objects? Currently the best theory is the Nebular Theory .This states that the solar system developed out of an interstellar cloud of dust and gas, called a nebula .This theory best accounts for the objects we currently find in the Solar System and the distribution of these objects.The Nebular ...

  7. 7.6: The Nebular Theory

    This states that the solar system developed out of an interstellar cloud of dust and gas, called a nebula . This theory best accounts for the objects we currently find in the Solar System and the distribution of these objects.The Nebular Theory would have started with a cloud of gas and dust, most likely left over from a previous supernova.

  8. Nebular Theory Might Explain How Our Solar System Formed

    The nebular theory, also known as nebular hypothesis, presents one explanation of how the solar system formed. Pierre-Simon, Marquis de Laplace proposed the theory in 1796, stating that solar systems originate from vast clouds of gas and dust, known as solar nebula, within interstellar space. Learn more about this solar system formation theory ...

  9. The Origin of the Solar System

    While they are still condensing, the incipient Sun and planets are called the protosun and protoplanets, respectively. Evidence for the Nebular Hypothesis Because of the original angular momentum and subsequent evolution of the collapsing nebula, this hypothesis provides a natural explanation for some basic facts about the Solar System: the orbits of the planets lie nearly in a plane with the ...

  10. Nebular theory and the formation of the solar system

    Nebular theory. The prevailing scientific explanation for the origin of the Earth does a good job of not only explaining the Earth's formation, but the Sun and all the other planets too. Really, it's not "the Earth's origin story" alone so much as it is the origin story of the whole solar system. Not only that, but our Sun is but one ...

  11. Nebular Hypothesis STEPS Flashcards

    step 2. the nebula contracted into a rotating disk that was heated by the conversion of gravitational energy into thermal energy. step 3. cooling of the nebular cloud caused rocky and metallic material to condense into tiny solid particles. step 4. repeated collisions caused the dust-sized particles to gradually coalesce into astroid-sized bodies.

  12. Formation and evolution of the Solar System

    The nebular hypothesis says that the Solar System formed from the gravitational collapse of a fragment of a giant molecular cloud, most likely at the edge of a Wolf-Rayet bubble. The cloud was about 20 parsecs (65 light years) across, [9] while the fragments were roughly 1 parsec (three and a quarter light-years ) across. [11]

  13. Solar Nebular Theory

    Over 100 planetary systems are known and still counting. This technique is most effective for finding only massive planets, within a few AU of the stars. Planets can eclipse the central star along the line of sight in some cases, and one can measure a brief dimming of the star and infer the presence of a planet. HD 209458 is such an example.

  14. Nebular Theory

    The nebular hypothesis states that the Sun began to form approximately 4.6 billion years ago, and the rest of the solar system began to form around it ~4.5 billion years ago. Once a star begins to ...

  15. Solar nebula

    solar nebula, gaseous cloud from which, in the so-called nebular hypothesis of the origin of the solar system, the Sun and planets formed by condensation. Swedish philosopher Emanuel Swedenborg in 1734 proposed that the planets formed out of a nebular crust that had surrounded the Sun and then broken apart. In 1755 the German philosopher Immanuel Kant suggested that a nebula in slow rotation ...

  16. 1.29: Nebular Hypothesis of the Origin of the Solar System

    Proto-Earth Formed. Studies of meteorites and samples from the Moon suggest that the Sun and our Solar System (including proto-planets) condensed and formed in a nebula before or about 4.56 billion years ago. A recent Scientific American article places the current assumed age of the Earth is about 4.56 billion years old.

  17. seven steps of the nebular theory Flashcards

    one. The attraction between materials in a nebula increases. two. The center of the nebula becomes very dense and heats up. Over time the remaining gas and dust begins to rotate around this center. three. Particles grown in size and become planetesimals. Gravity attracts more gas and dust and the solar nebula flattens out into a vast rotating disk.

  18. History of Solar System formation and evolution hypotheses

    The most widely accepted model of planetary formation is known as the nebular hypothesis.This model posits that, 4.6 billion years ago, the Solar System was formed by the gravitational collapse of a giant molecular cloud spanning several light-years.Many stars, including the Sun, were formed within this collapsing cloud.The gas that formed the Solar System was slightly more massive than the ...

  19. 10.02: Origin of the Solar System—The Nebular Hypothesis

    The nebular hypothesis is the idea that a spinning cloud of dust made of mostly light elements, called a nebula, flattened into a protoplanetary disk, and became a solar system consisting of a star with orbiting planets [ 12 ]. The spinning nebula collected the vast majority of material in its center, which is why the sun Accounts for over 99% ...

  20. The Nebular Theory of Laplace Solar System

    The nebular theory of Laplace is a theory that suggests that the Solar System was created by the gravitational collapse of a gaseous nebula. Read further to know more about it. The first person to develop this theory was Pierre-Simon Laplace in 1796. This theory was developed before we had a good understanding of gravity or nuclear forces, so ...

  21. The Nebular Theory: Other Important Evidence

    46 The Nebular Theory: Other Important Evidence The types of objects found within the solar system provide significant clues and evidence to support the Nebular Theory. First, the types of Planets and their distributions: with the Rocky planets being close to the Sun, and Gas Giants planets being far from the Sun, Dwarf Planets or Plutoids, a class of Dwarf planets, are found far from the Sun ...

  22. Nebular Hypothesis Flashcards

    The nebula collapses under its own gravity and begins to shrink. What is a nebula? A cloud of gas and dust. Step 3 (Rotating disk) the nebula collapsed into a rotating disk that was heated by the conversion of gravitational energy into thermal energy. Step 4 (Protosun) Due to gravity, 99% of all mass collected in the center of the disk ...

  23. Stat 20

    Steps of a Hypothesis Test. Assert a model for how the data was generated (the null hypothesis) Select a test statistic that bears on that null hypothesis (a mean, a proportion, a difference in means, a difference in proportions, etc). Approximate the sampling distribution of that statistic under the null hypothesis (aka the null distribution)