Misplaced Pages

#865134

117-651: The novel is set in a future when the Moon, Mars, Venus and Jupiter's satellites have been colonized and the Solar System is governed by a parliamentary democracy under a constitutional monarchy from a capital city on the Moon. The indigenous alien race inhabiting Mars has recently been admitted to citizenship in the human-dominated solar system government. The story, which is told in the first person, centers on down-and-out actor Lawrence Smith (stage name Lorenzo Smythe, also known as "The Great Lorenzo"). A brilliant actor and mimic, he

234-462: A planetary nebula , returning some of the material that formed the Sun—but now enriched with heavier elements like carbon—to the interstellar medium . Astronomers sometimes divide the Solar System structure into separate regions. The inner Solar System includes Mercury, Venus, Earth, Mars, and the bodies in the asteroid belt . The outer Solar System includes Jupiter, Saturn, Uranus, Neptune, and

351-458: A 1970s UK edition of Double Star was the subject of an unlikely controversy when it was used as the basis of an entry for the 2000 Turner Prize for modern art. The artist in question, Glenn Brown , was accused of plagiarism. Solar System The Solar System is the gravitationally bound system of the Sun and the objects that orbit it. It formed about 4.6 billion years ago when

468-452: A dense region of a molecular cloud collapsed, forming the Sun and a protoplanetary disc . The Sun is a typical star that maintains a balanced equilibrium by the fusion of hydrogen into helium at its core , releasing this energy from its outer photosphere . Astronomers classify it as a G-type main-sequence star . The largest objects that orbit the Sun are the eight planets . In order from

585-408: A diameter of about 250 km (160 mi) and is one of the few minor planets possessing a ring system. Beyond the orbit of Neptune lies the area of the " trans-Neptunian region ", with the doughnut-shaped Kuiper belt, home of Pluto and several other dwarf planets, and an overlapping disc of scattered objects, which is tilted toward the plane of the Solar System and reaches much further out than

702-415: A few meters to hundreds of kilometers in size. Many asteroids are divided into asteroid groups and families based on their orbital characteristics. Some asteroids have natural satellites that orbit them , that is, asteroids that orbit larger asteroids. The asteroid belt occupies a torus-shaped region between 2.3 and 3.3 AU from the Sun, which lies between the orbits of Mars and Jupiter. It

819-426: A good chance of changing that at the next general election. Bonforte has been kidnapped by his political opponents, and his aides want Smith to impersonate Bonforte while they try to find him. Bonforte is rescued, but he is in poor health due to the treatment inflicted on him during his imprisonment. This forces Smith to extend his performance, even to becoming temporary Prime Minister and running in an election. (This

936-399: A molten planet or a rocky planet, but does not apply to a star or to a planet like the earth which has a dense metallic core. In 1737 Alexis Clairaut studied the case of density varying with depth. Clairaut's theorem states that the variation of the gravity (including centrifugal force) is proportional to the square of the sine of the latitude, with the proportionality depending linearly on

1053-511: A particularly simple equilibrium solution of the Navier–Stokes equations. By plugging the energy–momentum tensor for a perfect fluid T μ ν = ( ρ c 2 + P ) u μ u ν + P g μ ν {\displaystyle T^{\mu \nu }=\left(\rho c^{2}+P\right)u^{\mu }u^{\nu }+Pg^{\mu \nu }} into

1170-484: A rapid rotation and was in hydrostatic equilibrium, but that its shape became "frozen in" and did not change as it spun down due to tidal forces from its moon Weywot . If so, this would resemble the situation of Iapetus, which is too oblate for its current spin. Iapetus is generally still considered a planetary-mass moon nonetheless, though not always. Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium. For example,

1287-565: A relationship between these orbital distances, like the Titius–Bode law and Johannes Kepler's model based on the Platonic solids , but ongoing discoveries have invalidated these hypotheses. Some Solar System models attempt to convey the relative scales involved in the Solar System in human terms. Some are small in scale (and may be mechanical—called orreries )—whereas others extend across cities or regional areas. The largest such scale model,

SECTION 10

#1732920916866

1404-408: A rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the equator than from pole to pole. In his 1687 Philosophiæ Naturalis Principia Mathematica Newton correctly stated that a rotating fluid of uniform density under the influence of gravity would take the form of a spheroid and that the gravity (including the effect of centrifugal force ) would be weaker at the equator than at

1521-532: A shell surrounding the inert helium, and the energy output will be greater than at present. The outer layers of the Sun will expand to roughly 260 times its current diameter, and the Sun will become a red giant . Because of its increased surface area, the surface of the Sun will be cooler (2,600 K (4,220 °F) at its coolest) than it is on the main sequence. The expanding Sun is expected to vaporize Mercury as well as Venus, and render Earth and Mars uninhabitable (possibly destroying Earth as well). Eventually,

1638-413: A small fraction of the solar nebula, the terrestrial planets could not grow very large. The giant planets (Jupiter, Saturn, Uranus, and Neptune) formed further out, beyond the frost line, the point between the orbits of Mars and Jupiter where material is cool enough for volatile icy compounds to remain solid. The ices that formed these planets were more plentiful than the metals and silicates that formed

1755-558: A subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid-body forces). Even larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's Moon at 3,474 km (mostly rock), and the planet Mercury at 4,880 km (mostly metal). In 2024, Kiss et al. found that Quaoar has an ellipsoidal shape incompatible with hydrostatic equilibrium for its current spin. They hypothesised that Quaoar originally had

1872-402: A volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it. This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium. The fluid can be split into a large number of cuboid volume elements; by considering a single element,

1989-442: Is F bottom = P bottom A {\displaystyle F_{\text{bottom}}=P_{\text{bottom}}A} Finally, the weight of the volume element causes a force downwards. If the density is ρ , the volume is V and g the standard gravity , then: F weight = − ρ g V {\displaystyle F_{\text{weight}}=-\rho gV} The volume of this cuboid

2106-417: Is 30 AU from the Sun. With a few exceptions, the farther a planet or belt is from the Sun, the larger the distance between its orbit and the orbit of the next nearest object to the Sun. For example, Venus is approximately 0.33 AU farther out from the Sun than Mercury, whereas Saturn is 4.3 AU out from Jupiter, and Neptune lies 10.5 AU out from Uranus. Attempts have been made to determine

2223-596: Is The Great Lorenzo of Double Star . Lorenzo is complete all the way back to his childhood—the influence of his father upon what he thinks is one of the strongest motives in the story—and his growth under pressure is consistent with his character and no-one else's." Galaxy reviewer Floyd C. Gale praised the novel, finding it "an excellent example of Heinlein's ability to take one of the oldest plots in any literature ... and present it as an enjoyable reading experience." Admitting "a certain reservation, even disappointment," Anthony Boucher nevertheless concluded that Heinlein

2340-634: Is a change in pressure, and h is the height of the volume element—a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form. d P = − ρ g d h {\displaystyle dP=-\rho g\,dh} Density changes with pressure, and gravity changes with height, so the equation would be: d P = − ρ ( P ) g ( h ) d h {\displaystyle dP=-\rho (P)\,g(h)\,dh} Note finally that this last equation can be derived by solving

2457-1439: Is a characteristic mass of the baryonic gas particles) and rearranging, we arrive at d d r ( k T B ( r ) ρ B ( r ) m B ) = − ρ B ( r ) G r 2 ∫ 0 r 4 π r 2 ρ M ( r ) d r . {\displaystyle {\frac {d}{dr}}\left({\frac {kT_{B}(r)\rho _{B}(r)}{m_{B}}}\right)=-{\frac {\rho _{B}(r)G}{r^{2}}}\int _{0}^{r}4\pi r^{2}\,\rho _{M}(r)\,dr.} Multiplying by r 2 / ρ B ( r ) {\displaystyle r^{2}/\rho _{B}(r)} and differentiating with respect to r {\displaystyle r} yields d d r [ r 2 ρ B ( r ) d d r ( k T B ( r ) ρ B ( r ) m B ) ] = − 4 π G r 2 ρ M ( r ) . {\displaystyle {\frac {d}{dr}}\left[{\frac {r^{2}}{\rho _{B}(r)}}{\frac {d}{dr}}\left({\frac {kT_{B}(r)\rho _{B}(r)}{m_{B}}}\right)\right]=-4\pi Gr^{2}\rho _{M}(r).} If we make

SECTION 20

#1732920916866

2574-409: Is a great ring of debris similar to the asteroid belt, but consisting mainly of objects composed primarily of ice. It extends between 30 and 50 AU from the Sun. It is composed mainly of small Solar System bodies, although the largest few are probably large enough to be dwarf planets. There are estimated to be over 100,000 Kuiper belt objects with a diameter greater than 50 km (30 mi), but

2691-530: Is a measure of the total mass of the cluster, with r {\displaystyle r} being the proper distance to the center of the cluster. Using the ideal gas law p B = k T B ρ B / m B {\displaystyle p_{B}=kT_{B}\rho _{B}/m_{B}} ( k {\displaystyle k} is the Boltzmann constant and m B {\displaystyle m_{B}}

2808-428: Is a small chance that another star will pass through the Solar System in the next few billion years. Although this could destabilize the system and eventually lead millions of years later to expulsion of planets, collisions of planets, or planets hitting the Sun, it would most likely leave the Solar System much as it is today. The Sun's main-sequence phase, from beginning to end, will last about 10 billion years for

2925-495: Is dependent on the redshift z {\displaystyle z} of the cluster and is given by ρ B ( 0 ) / ρ M ( 0 ) ∝ ( 1 + z ) 2 ( θ s ) 3 / 2 {\displaystyle \rho _{B}(0)/\rho _{M}(0)\propto (1+z)^{2}\left({\frac {\theta }{s}}\right)^{3/2}} where θ {\displaystyle \theta }

3042-510: Is down to his last coin when a spaceman hires him to double for an unspecified public figure. It is only when he is on his way to Mars that he finds out he will have to impersonate one of the most prominent politicians in the Solar System (and one with whose views Smith deeply disagrees): John Joseph Bonforte. Bonforte is the leader of the Expansionist coalition, currently out of office but with

3159-683: Is equal to the area of the top or bottom, times the height – the formula for finding the volume of a cube. F weight = − ρ g A h {\displaystyle F_{\text{weight}}=-\rho gAh} By balancing these forces, the total force on the fluid is ∑ F = F bottom + F top + F weight = P bottom A − P top A − ρ g A h {\displaystyle \sum F=F_{\text{bottom}}+F_{\text{top}}+F_{\text{weight}}=P_{\text{bottom}}A-P_{\text{top}}A-\rho gAh} This sum equals zero if

3276-469: Is made plausible through Bonforte's extensive Farley files .) The central political issue in the election is the granting of the vote to Martians in the human-dominated Solar System. Lorenzo shares the anti-Martian prejudice prevalent among large parts of Earth's population, but he is called upon to assume the persona of the most prominent advocate of Martian enfranchisement. Smith takes on not only Bonforte's appearance, but some aspects of his personality. At

3393-407: Is negligible. From the time of Isaac Newton much work has been done on the subject of the equilibrium attained when a fluid rotates in space. This has application to both stars and objects like planets, which may have been fluid in the past or in which the solid material deforms like a fluid when subjected to very high stresses. In any given layer of a star there is a hydrostatic equilibrium between

3510-412: Is no "gap" as seen between the size of Earth and of Neptune (with a radius 3.8 times as large). As many of these super-Earths are closer to their respective stars than Mercury is to the Sun, a hypothesis has arisen that all planetary systems start with many close-in planets, and that typically a sequence of their collisions causes consolidation of mass into few larger planets, but in case of the Solar System

3627-618: Is stable up to a certain (critical) angular momentum (normalized by M G ρ r e {\displaystyle M{\sqrt {G\rho r_{e}}}} ), but in 1834 Carl Jacobi showed that it becomes unstable once the eccentricity reaches 0.81267 (or f {\displaystyle f} reaches 0.3302). Above the critical value the solution becomes a Jacobi, or scalene, ellipsoid (one with all three axes different). Henri Poincaré in 1885 found that at still higher angular momentum it will no longer be ellipsoidal but piriform or oviform . The symmetry drops from

Double Star - Misplaced Pages Continue

3744-464: Is strong consensus among astronomers that five members of the Kuiper belt are dwarf planets . Many dwarf planet candidates are being considered, pending further data for verification. The scattered disc, which overlaps the Kuiper belt but extends out to near 500 AU, is thought to be the source of short-period comets. Scattered-disc objects are believed to have been perturbed into erratic orbits by

3861-430: Is the Solar System's star and by far its most massive component. Its large mass (332,900 Earth masses ), which comprises 99.86% of all the mass in the Solar System, produces temperatures and densities in its core high enough to sustain nuclear fusion of hydrogen into helium. This releases an enormous amount of energy , mostly radiated into space as electromagnetic radiation peaking in visible light . Because

3978-413: Is the angular width of the cluster and s {\displaystyle s} the proper distance to the cluster. Values for the ratio range from 0.11 to 0.14 for various surveys. The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a planet , dwarf planet , or small Solar System body . According to the definition of planet adopted by

4095-432: Is the dwarf planet Ceres , which is icy, at 945 km, whereas the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. At 1,469 km Iapetus is neither spherical nor ellipsoid. Instead, it is rather in a strange walnut-like shape due to its unique equatorial ridge . Some icy bodies may be in equilibrium at least partly due to

4212-434: Is the icy moon Mimas at 396 km, whereas the largest icy object known to have an obviously non-equilibrium shape is the icy moon Proteus at 420 km, and the largest rocky bodies in an obviously non-equilibrium shape are the asteroids Pallas and Vesta at about 520 km. However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium

4329-468: Is thought to be remnants from the Solar System's formation that failed to coalesce because of the gravitational interference of Jupiter. The asteroid belt contains tens of thousands, possibly millions, of objects over one kilometer in diameter. Despite this, the total mass of the asteroid belt is unlikely to be more than a thousandth of that of Earth. The asteroid belt is very sparsely populated; spacecraft routinely pass through without incident. Below are

4446-639: The Einstein field equations R μ ν = 8 π G c 4 ( T μ ν − 1 2 g μ ν T ) {\displaystyle R_{\mu \nu }={\frac {8\pi G}{c^{4}}}\left(T_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }T\right)} and using the conservation condition ∇ μ T μ ν = 0 {\displaystyle \nabla _{\mu }T^{\mu \nu }=0} one can derive

4563-623: The International Astronomical Union in 2006, one defining characteristic of planets and dwarf planets is that they are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Such a body will often have the differentiated interior and geology of a world (a planemo ), though near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto ) have not thoroughly differentiated since their formation. Often

4680-489: The Milky Way galaxy. The Solar System formed at least 4.568 billion years ago from the gravitational collapse of a region within a large molecular cloud . This initial cloud was likely several light-years across and probably birthed several stars. As is typical of molecular clouds, this one consisted mostly of hydrogen, with some helium, and small amounts of heavier elements fused by previous generations of stars. As

4797-608: The Sweden Solar System , uses the 110-meter (361-foot) Avicii Arena in Stockholm as its substitute Sun, and, following the scale, Jupiter is a 7.5-meter (25-foot) sphere at Stockholm Arlanda Airport , 40 km (25 mi) away, whereas the farthest current object, Sedna , is a 10 cm (4 in) sphere in Luleå , 912 km (567 mi) away. At that scale, the distance to Proxima Centauri would be roughly 8 times further than

Double Star - Misplaced Pages Continue

4914-1011: The Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates: d P d r = − G M ( r ) ρ ( r ) r 2 ( 1 + P ( r ) ρ ( r ) c 2 ) ( 1 + 4 π r 3 P ( r ) M ( r ) c 2 ) ( 1 − 2 G M ( r ) r c 2 ) − 1 {\displaystyle {\frac {dP}{dr}}=-{\frac {GM(r)\rho (r)}{r^{2}}}\left(1+{\frac {P(r)}{\rho (r)c^{2}}}\right)\left(1+{\frac {4\pi r^{3}P(r)}{M(r)c^{2}}}\right)\left(1-{\frac {2GM(r)}{rc^{2}}}\right)^{-1}} In practice, Ρ and ρ are related by an equation of state of

5031-449: The asteroid belt (between Mars's and Jupiter's orbit) and the Kuiper belt (just outside Neptune's orbit). Six planets, seven dwarf planets, and other bodies have orbiting natural satellites , which are commonly called 'moons'. The Solar System is constantly flooded by the Sun's charged particles , the solar wind , forming the heliosphere . Around 75–90 astronomical units from the Sun,

5148-459: The eccentricity by ϵ , {\displaystyle \epsilon ,} with he found that the gravity at the poles is where G {\displaystyle G} is the gravitational constant, ρ {\displaystyle \rho } is the (uniform) density, and M {\displaystyle M} is the total mass. The ratio of this to g 0 , {\displaystyle g_{0},}

5265-494: The frost line , and it lies at roughly five times the Earth's distance from the Sun. The planets and other large objects in orbit around the Sun lie near the plane of Earth's orbit, known as the ecliptic . Smaller icy objects such as comets frequently orbit at significantly greater angles to this plane. Most of the planets in the Solar System have secondary systems of their own, being orbited by natural satellites called moons. All of

5382-419: The fusor stars in the Milky Way . The Sun is a population I star , having formed in the spiral arms of the Milky Way galaxy. It has a higher abundance of elements heavier than hydrogen and helium (" metals " in astronomical parlance) than the older population II stars in the galactic bulge and halo . Elements heavier than hydrogen and helium were formed in the cores of ancient and exploding stars, so

5499-528: The grand tack hypothesis suggests that a final inward migration of Jupiter dispersed much of the asteroid belt, leading to the Late Heavy Bombardment of the inner planets. The Solar System remains in a relatively stable, slowly evolving state by following isolated, gravitationally bound orbits around the Sun. Although the Solar System has been fairly stable for billions of years, it is technically chaotic , and may eventually be disrupted . There

5616-427: The heliosphere , which spans much of the Solar System. Along with light , the Sun radiates a continuous stream of charged particles (a plasma ) called the solar wind . This stream spreads outwards at speeds from 900,000 kilometres per hour (560,000 mph) to 2,880,000 kilometres per hour (1,790,000 mph), filling the vacuum between the bodies of the Solar System. The result is a thin , dusty atmosphere, called

5733-554: The interplanetary medium , which extends to at least 100 AU . Activity on the Sun's surface, such as solar flares and coronal mass ejections , disturbs the heliosphere, creating space weather and causing geomagnetic storms . Coronal mass ejections and similar events blow a magnetic field and huge quantities of material from the surface of the Sun. The interaction of this magnetic field and material with Earth's magnetic field funnels charged particles into Earth's upper atmosphere, where its interactions create aurorae seen near

5850-421: The magnetic poles . The largest stable structure within the heliosphere is the heliospheric current sheet , a spiral form created by the actions of the Sun's rotating magnetic field on the interplanetary medium. The inner Solar System is the region comprising the terrestrial planets and the asteroids . Composed mainly of silicates and metals, the objects of the inner Solar System are relatively close to

5967-441: The planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space . In general, it is what causes objects in space to be spherical. Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies , and features in astrophysics and planetary geology . Said qualification of equilibrium indicates that

SECTION 50

#1732920916866

6084-566: The pre-solar nebula collapsed, conservation of angular momentum caused it to rotate faster. The center, where most of the mass collected, became increasingly hotter than the surroundings. As the contracting nebula spun faster, it began to flatten into a protoplanetary disc with a diameter of roughly 200 AU and a hot, dense protostar at the center. The planets formed by accretion from this disc, in which dust and gas gravitationally attracted each other, coalescing to form ever larger bodies. Hundreds of protoplanets may have existed in

6201-465: The principles of equilibrium of fluids . A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities . This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. It can also be a satisfactory approximation when flow speeds are low enough that acceleration

6318-412: The 8-fold D 2h point group to the 4-fold C 2v , with its axis perpendicular to the axis of rotation. Other shapes satisfy the equations beyond that, but are not stable, at least not near the point of bifurcation . Poincaré was unsure what would happen at higher angular momentum, but concluded that eventually the blob would split in two. The assumption of uniform density may apply more or less to

6435-470: The Kuiper belt. The entire region is still largely unexplored . It appears to consist overwhelmingly of many thousands of small worlds—the largest having a diameter only a fifth that of Earth and a mass far smaller than that of the Moon—composed mainly of rock and ice. This region is sometimes described as the "third zone of the Solar System", enclosing the inner and the outer Solar System. The Kuiper belt

6552-510: The Moon is from Earth. If the Sun–Neptune distance is scaled to 100 metres (330 ft), then the Sun would be about 3 cm (1.2 in) in diameter (roughly two-thirds the diameter of a golf ball), the giant planets would be all smaller than about 3 mm (0.12 in), and Earth's diameter along with that of the other terrestrial planets would be smaller than a flea (0.3 mm or 0.012 in) at this scale. Besides solar energy,

6669-462: The Solar System is a measure of the total amount of orbital and rotational momentum possessed by all its moving components. Although the Sun dominates the system by mass, it accounts for only about 2% of the angular momentum. The planets, dominated by Jupiter, account for most of the rest of the angular momentum due to the combination of their mass, orbit, and distance from the Sun, with a possibly significant contribution from comets. The radius of

6786-545: The Solar System is home to the giant planets and their large moons. The centaurs and many short-period comets orbit in this region. Due to their greater distance from the Sun, the solid objects in the outer Solar System contain a higher proportion of volatiles such as water, ammonia, and methane, than planets of the inner Solar System because their lower temperatures allow these compounds to remain solid, without significant sublimation . The four outer planets, called giant planets or Jovian planets, collectively make up 99% of

6903-457: The Solar System stands out in lacking planets interior to the orbit of Mercury. The known Solar System lacks super-Earths , planets between one and ten times as massive as the Earth, although the hypothetical Planet Nine , if it does exist, could be a super-Earth orbiting in the edge of the Solar System. Uncommonly, it has only small terrestrial and large gas giants; elsewhere planets of intermediate size are typical—both rocky and gas—so there

7020-400: The Solar System, created by heat and light pressure from the early Sun; those objects closer to the Sun, which are more affected by heat and light pressure, are composed of elements with high melting points. Objects farther from the Sun are composed largely of materials with lower melting points. The boundary in the Solar System beyond which those volatile substances could coalesce is known as

7137-406: The Sun by the outer planets, and are expected to become comets or be ejected out of the Solar System. While most centaurs are inactive and asteroid-like, some exhibit cometary activity, such as the first centaur discovered, 2060 Chiron , which has been classified as a comet (95P) because it develops a coma just as comets do when they approach the Sun. The largest known centaur, 10199 Chariklo , has

SECTION 60

#1732920916866

7254-455: The Sun compared to around two billion years for all other subsequent phases of the Sun's pre- remnant life combined. The Solar System will remain roughly as it is known today until the hydrogen in the core of the Sun has been entirely converted to helium, which will occur roughly 5 billion years from now. This will mark the end of the Sun's main-sequence life. At that time, the core of the Sun will contract with hydrogen fusion occurring along

7371-495: The Sun fuses hydrogen at its core, it is a main-sequence star. More specifically, it is a G2-type main-sequence star , where the type designation refers to its effective temperature . Hotter main-sequence stars are more luminous but shorter lived. The Sun's temperature is intermediate between that of the hottest stars and that of the coolest stars. Stars brighter and hotter than the Sun are rare, whereas substantially dimmer and cooler stars, known as red dwarfs , make up about 75% of

7488-422: The Sun is 0.0047 AU (700,000 km; 400,000 mi). Thus, the Sun occupies 0.00001% (1 part in 10 ) of the volume of a sphere with a radius the size of Earth's orbit, whereas Earth's volume is roughly 1 millionth (10 ) that of the Sun. Jupiter, the largest planet, is 5.2 AU from the Sun and has a radius of 71,000 km (0.00047 AU; 44,000 mi), whereas the most distant planet, Neptune,

7605-403: The Sun is growing brighter; early in its main-sequence life its brightness was 70% that of what it is today. The temperature, reaction rate , pressure, and density increased until hydrostatic equilibrium was achieved: the thermal pressure counterbalancing the force of gravity. At this point, the Sun became a main-sequence star. Solar wind from the Sun created the heliosphere and swept away

7722-472: The Sun twice for every three times that Neptune does, or once for every two. The classical belt consists of objects having no resonance with Neptune, and extends from roughly 39.4 to 47.7 AU. Members of the classical Kuiper belt are sometimes called "cubewanos", after the first of their kind to be discovered, originally designated 1992 QB 1 , (and has since been named Albion); they are still in near primordial, low-eccentricity orbits. Currently, there

7839-405: The Sun, they are four terrestrial planets ( Mercury , Venus , Earth and Mars ); two gas giants ( Jupiter and Saturn ); and two ice giants ( Uranus and Neptune ). All terrestrial planets have solid surfaces. Inversely, all giant planets do not have a definite surface, as they are mainly composed of gases and liquids. Over 99.86% of the Solar System's mass is in the Sun and nearly 90% of

7956-499: The Sun; the radius of this entire region is less than the distance between the orbits of Jupiter and Saturn. This region is within the frost line , which is a little less than 5 AU from the Sun. The four terrestrial or inner planets have dense, rocky compositions, few or no moons , and no ring systems . They are composed largely of refractory minerals such as silicates —which form their crusts and mantles —and metals such as iron and nickel which form their cores . Three of

8073-496: The TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ( t , r , θ , φ ) {\displaystyle (t,r,\theta ,\varphi )} , the index i runs for the coordinates r and θ {\displaystyle \theta } ). The hydrostatic equilibrium pertains to hydrostatics and

8190-426: The action of the fluid can be derived. There are three forces: the force downwards onto the top of the cuboid from the pressure, P , of the fluid above it is, from the definition of pressure , F top = − P top A {\displaystyle F_{\text{top}}=-P_{\text{top}}A} Similarly, the force on the volume element from the pressure of the fluid below pushing upwards

8307-986: The assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density ρ D = ρ M − ρ B {\displaystyle \rho _{D}=\rho _{M}-\rho _{B}} satisfies the non-linear differential equation d d r [ r 2 ρ D ( r ) d d r ( k T D ( r ) ρ D ( r ) m D ) ] = − 4 π G r 2 ρ M ( r ) . {\displaystyle {\frac {d}{dr}}\left[{\frac {r^{2}}{\rho _{D}(r)}}{\frac {d}{dr}}\left({\frac {kT_{D}(r)\rho _{D}(r)}{m_{D}}}\right)\right]=-4\pi Gr^{2}\rho _{M}(r).} With perfect X-ray and distance data, we could calculate

8424-565: The astronomical sense (chemical compounds with melting points of up to a few hundred kelvins such as water, methane, ammonia, hydrogen sulfide , and carbon dioxide . ) Icy substances comprise the majority of the satellites of the giant planets and small objects that lie beyond Neptune's orbit. The centaurs are icy, comet-like bodies whose semi-major axes are longer than Jupiter's and shorter than Neptune's (between 5.5 and 30 AU). These are former Kuiper belt and scattered disc objects (SDOs) that were gravitationally perturbed closer to

8541-531: The axis of rotation depended only on the distance from the axis and was proportional to that distance, and the component in the direction toward the plane of the equator depended only on the distance from that plane and was proportional to that distance. Newton had already pointed out that the gravity felt on the equator (including the lightening due to centrifugal force) has to be r p r e g p {\displaystyle {\frac {r_{p}}{r_{e}}}g_{p}} in order to have

8658-610: The baryon density at each point in the cluster and thus the dark matter density. We could then calculate the velocity dispersion σ D 2 {\displaystyle \sigma _{D}^{2}} of the dark matter, which is given by σ D 2 = k T D m D . {\displaystyle \sigma _{D}^{2}={\frac {kT_{D}}{m_{D}}}.} The central density ratio ρ B ( 0 ) / ρ M ( 0 ) {\displaystyle \rho _{B}(0)/\rho _{M}(0)}

8775-421: The best of his ability. Penny (Bonforte's adoring secretary and now Smith's wife) says, "she never loved anyone else." The noted science-fiction writer and critic James Blish was no fan of Heinlein's treatment of his first-person protagonists in a number of his novels. Writing in 1957, however, Blish says that "The only first-person narrator Heinlein has created who is a living, completely independent human being

8892-402: The bodies in the Kuiper belt . Since the discovery of the Kuiper belt, the outermost parts of the Solar System are considered a distinct region consisting of the objects beyond Neptune . The principal component of the Solar System is the Sun, a G-type main-sequence star that contains 99.86% of the system's known mass and dominates it gravitationally. The Sun's four largest orbiting bodies,

9009-410: The collisions caused their destruction and ejection. The orbits of Solar System planets are nearly circular. Compared to many other systems, they have smaller orbital eccentricity . Although there are attempts to explain it partly with a bias in the radial-velocity detection method and partly with long interactions of a quite high number of planets, the exact causes remain undetermined. The Sun

9126-457: The collisions thereof) emits X-ray radiation. The absolute X-ray luminosity per unit volume takes the form L X = Λ ( T B ) ρ B 2 {\displaystyle {\mathcal {L}}_{X}=\Lambda (T_{B})\rho _{B}^{2}} where T B {\displaystyle T_{B}} and ρ B {\displaystyle \rho _{B}} are

9243-432: The core will be hot enough for helium fusion; the Sun will burn helium for a fraction of the time it burned hydrogen in the core. The Sun is not massive enough to commence the fusion of heavier elements, and nuclear reactions in the core will dwindle. Its outer layers will be ejected into space, leaving behind a dense white dwarf , half the original mass of the Sun but only the size of Earth. The ejected outer layers may form

9360-413: The descriptions of the three largest bodies in the asteroid belt. They are all considered to be relatively intact protoplanets , a precursor stage before becoming a fully-formed planet (see List of exceptional asteroids ): Hilda asteroids are in a 3:2 resonance with Jupiter; that is, they go around the Sun three times for every two Jovian orbits. They lie in three linked clusters between Jupiter and

9477-441: The early Solar System, but they either merged or were destroyed or ejected, leaving the planets, dwarf planets, and leftover minor bodies . Due to their higher boiling points, only metals and silicates could exist in solid form in the warm inner Solar System close to the Sun (within the frost line ). They would eventually form the rocky planets of Mercury, Venus, Earth, and Mars. Because these refractory materials only comprised

9594-491: The equilibrium shape is an oblate spheroid , as is the case with Earth. However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid . Also, the purported dwarf planet Haumea is scalene due to its rapid rotation, though it may not currently be in equilibrium. Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape

9711-449: The first generation of stars had to die before the universe could be enriched with these atoms. The oldest stars contain few metals, whereas stars born later have more. This higher metallicity is thought to have been crucial to the Sun's development of a planetary system because the planets formed from the accretion of "metals". The region of space dominated by the Solar magnetosphere is

9828-485: The flattening ( f {\displaystyle f} ) and the ratio at the equator of centrifugal force to gravitational attraction. (Compare with the exact relation above for the case of uniform density.) Clairaut's theorem is a special case, for an oblate spheroid, of a connexion found later by Pierre-Simon Laplace between the shape and the variation of gravity. If the star has a massive nearby companion object then tidal forces come into play as well, distorting

9945-439: The fluid's velocity is constant. Dividing by A, 0 = P bottom − P top − ρ g h {\displaystyle 0=P_{\text{bottom}}-P_{\text{top}}-\rho gh} Or, P top − P bottom = − ρ g h {\displaystyle P_{\text{top}}-P_{\text{bottom}}=-\rho gh} P top − P bottom

10062-499: The form f ( Ρ , ρ ) = 0, with f specific to makeup of the star. M ( r ) is a foliation of spheres weighted by the mass density ρ ( r ), with the largest sphere having radius r : M ( r ) = 4 π ∫ 0 r d r ′ r ′ 2 ρ ( r ′ ) . {\displaystyle M(r)=4\pi \int _{0}^{r}dr'\,r'^{2}\rho (r').} Per standard procedure in taking

10179-407: The four inner planets (Venus, Earth, and Mars) have atmospheres substantial enough to generate weather; all have impact craters and tectonic surface features, such as rift valleys and volcanoes. Asteroids except for the largest, Ceres, are classified as small Solar System bodies and are composed mainly of carbonaceous , refractory rocky and metallic minerals, with some ice. They range from

10296-441: The giant planets, account for 99% of the remaining mass, with Jupiter and Saturn together comprising more than 90%. The remaining objects of the Solar System (including the four terrestrial planets, the dwarf planets, moons, asteroids , and comets) together comprise less than 0.002% of the Solar System's total mass. The Sun is composed of roughly 98% hydrogen and helium, as are Jupiter and Saturn. A composition gradient exists in

10413-566: The gravitational influence of Neptune's early outward migration . Most scattered disc objects have perihelia within the Kuiper belt but aphelia far beyond it (some more than 150 AU from the Sun). SDOs' orbits can be inclined up to 46.8° from the ecliptic plane. Some astronomers consider the scattered disc to be merely another region of the Kuiper belt and describe scattered-disc objects as "scattered Kuiper belt objects". Some astronomers classify centaurs as inward-scattered Kuiper belt objects along with

10530-414: The gravity if the fluid is not rotating, is asymptotic to as ϵ {\displaystyle \epsilon } goes to zero, where f {\displaystyle f} is the flattening: The gravitational attraction on the equator (not including centrifugal force) is Asymptotically we have: Maclaurin showed (still in the case of uniform density) that the component of gravity toward

10647-415: The larger moons orbit their planets in prograde direction, matching the direction of planetary rotation; Neptune's moon Triton is the largest to orbit in the opposite, retrograde manner. Most larger objects rotate around their own axes in the prograde direction relative to their orbit, though the rotation of Venus is retrograde. To a good first approximation, Kepler's laws of planetary motion describe

10764-491: The largest natural satellites are in synchronous rotation , with one face permanently turned toward their parent. The four giant planets have planetary rings, thin discs of tiny particles that orbit them in unison. As a result of the formation of the Solar System , planets and most other objects orbit the Sun in the same direction that the Sun is rotating. That is, counter-clockwise, as viewed from above Earth's north pole. There are exceptions, such as Halley's Comet . Most of

10881-422: The level of cosmic-ray penetration in the Solar System varies, though by how much is unknown. The zone of habitability of the Solar System is conventionally located in the inner Solar System, where planetary surface or atmospheric temperatures admit the possibility of liquid water . Habitability might be possible in subsurface oceans of various outer Solar System moons. Compared to many extrasolar systems,

10998-443: The main asteroid belt. Trojans are bodies located within another body's gravitationally stable Lagrange points : L 4 , 60° ahead in its orbit, or L 5 , 60° behind in its orbit. Every planet except Mercury and Saturn is known to possess at least 1 trojan. The Jupiter trojan population is roughly equal to that of the asteroid belt. After Jupiter, Neptune possesses the most confirmed trojans, at 28. The outer region of

11115-400: The mass orbiting the Sun. All four giant planets have multiple moons and a ring system, although only Saturn's rings are easily observed from Earth. Jupiter and Saturn are composed mainly of gases with extremely low melting points, such as hydrogen, helium, and neon , hence their designation as gas giants . Uranus and Neptune are ice giants , meaning they are largely composed of 'ice' in

11232-406: The massive base of the tallest mountain on Earth, Mauna Kea , has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium. In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure-gradient force . The force of gravity balances this out, keeping

11349-400: The moment of electoral victory, Bonforte dies of the aftereffects of his kidnapping, and Smith has to assume the role for life. In a retrospective conclusion set twenty-five years later, Smith reveals that he wrote the first-person narrative as therapy. By this point, he views his early life and ambitions as almost those of someone else. He has applied Bonforte's ideals in his political career to

11466-642: The nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium: d P d r = − G M ( r ) ρ ( r ) r 2 = − g ( r ) ρ ( r ) ⟶ d P = − ρ ( h ) g ( h ) d h {\displaystyle {\frac {dP}{dr}}=-{\frac {GM(r)\rho (r)}{r^{2}}}=-g(r)\,\rho (r)\longrightarrow dP=-\rho (h)\,g(h)\,dh} (we have made

11583-664: The nonrelativistic limit, we let c → ∞ , so that the factor ( 1 + P ( r ) ρ ( r ) c 2 ) ( 1 + 4 π r 3 P ( r ) M ( r ) c 2 ) ( 1 − 2 G M ( r ) r c 2 ) − 1 → 1 {\displaystyle \left(1+{\frac {P(r)}{\rho (r)c^{2}}}\right)\left(1+{\frac {4\pi r^{3}P(r)}{M(r)c^{2}}}\right)\left(1-{\frac {2GM(r)}{rc^{2}}}\right)^{-1}\rightarrow 1} Therefore, in

11700-402: The orbits of objects around the Sun. These laws stipulate that each object travels along an ellipse with the Sun at one focus , which causes the body's distance from the Sun to vary over the course of its year. A body's closest approach to the Sun is called its perihelion , whereas its most distant point from the Sun is called its aphelion . With the exception of Mercury, the orbits of

11817-409: The outward-pushing pressure gradient and the weight of the material above pressing inward. One can also study planets under the assumption of hydrostatic equilibrium. A rotating star or planet in hydrostatic equilibrium is usually an oblate spheroid , that is, an ellipsoid in which two of the principal axes are equal and longer than the third. An example of this phenomenon is the star Vega , which has

11934-432: The outward-scattered residents of the scattered disc. Hydrostatic equilibrium In fluid mechanics , hydrostatic equilibrium ( hydrostatic balance , hydrostasy ) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity , are balanced by a pressure-gradient force . In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing

12051-464: The planets are nearly circular, but many comets, asteroids, and Kuiper belt objects follow highly elliptical orbits. Kepler's laws only account for the influence of the Sun's gravity upon an orbiting body, not the gravitational pulls of different bodies upon each other. On a human time scale, these perturbations can be accounted for using numerical models , but the planetary system can change chaotically over billions of years. The angular momentum of

12168-489: The poles by an amount equal (at least asymptotically ) to five fourths the centrifugal force at the equator. In 1742, Colin Maclaurin published his treatise on fluxions, in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by r e , {\displaystyle r_{e},} the polar radius by r p , {\displaystyle r_{p},} and

12285-415: The primary characteristic of the Solar System enabling the presence of life is the heliosphere and planetary magnetic fields (for those planets that have them). These magnetic fields partially shield the Solar System from high-energy interstellar particles called cosmic rays . The density of cosmic rays in the interstellar medium and the strength of the Sun's magnetic field change on very long timescales, so

12402-507: The remaining gas and dust from the protoplanetary disc into interstellar space. Following the dissipation of the protoplanetary disk , the Nice model proposes that gravitational encounters between planetisimals and the gas giants caused each to migrate into different orbits. This led to dynamical instability of the entire system, which scattered the planetisimals and ultimately placed the gas giants in their current positions. During this period,

12519-467: The remaining mass is in Jupiter and Saturn. There is a strong consensus among astronomers that the Solar System has at least nine dwarf planets : Ceres , Orcus , Pluto , Haumea , Quaoar , Makemake , Gonggong , Eris , and Sedna . There are a vast number of small Solar System bodies , such as asteroids , comets , centaurs , meteoroids , and interplanetary dust clouds . Some of these bodies are in

12636-401: The same pressure at the bottom of channels from the pole or from the equator to the centre, so the centrifugal force at the equator must be Defining the latitude to be the angle between a tangent to the meridian and axis of rotation, the total gravity felt at latitude ϕ {\displaystyle \phi } (including the effect of centrifugal force) is This spheroid solution

12753-522: The shape of the object is symmetrically rounded, mostly due to rotation , into an ellipsoid , where any irregular surface features are consequent to a relatively thin solid crust . In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System . For a hydrostatic fluid on Earth: d P = − ρ ( P ) g ( h ) d h {\displaystyle dP=-\rho (P)\,g(h)\,dh} Newton's laws of motion state that

12870-404: The solar wind is halted, resulting in the heliopause . This is the boundary of the Solar System to interstellar space . The outermost region of the Solar System is the theorized Oort cloud , the source for long-period comets , extending to a radius of 2,000–200,000 AU . The closest star to the Solar System, Proxima Centauri , is 4.25 light-years (269,000 AU) away. Both stars belong to

12987-461: The star into a scalene shape when rotation alone would make it a spheroid. An example of this is Beta Lyrae . Hydrostatic equilibrium is also important for the intracluster medium , where it restricts the amount of fluid that can be present in the core of a cluster of galaxies . We can also use the principle of hydrostatic equilibrium to estimate the velocity dispersion of dark matter in clusters of galaxies. Only baryonic matter (or, rather,

13104-834: The temperature and density of the baryonic matter, and Λ ( T ) {\displaystyle \Lambda (T)} is some function of temperature and fundamental constants. The baryonic density satisfies the above equation d P = − ρ g d r {\displaystyle dP=-\rho g\,dr} : p B ( r + d r ) − p B ( r ) = − d r ρ B ( r ) G r 2 ∫ 0 r 4 π r 2 ρ M ( r ) d r . {\displaystyle p_{B}(r+dr)-p_{B}(r)=-dr{\frac {\rho _{B}(r)G}{r^{2}}}\int _{0}^{r}4\pi r^{2}\,\rho _{M}(r)\,dr.} The integral

13221-480: The terrestrial inner planets, allowing them to grow massive enough to capture large atmospheres of hydrogen and helium, the lightest and most abundant elements. Leftover debris that never became planets congregated in regions such as the asteroid belt, Kuiper belt, and Oort cloud. Within 50 million years, the pressure and density of hydrogen in the center of the protostar became great enough for it to begin thermonuclear fusion . As helium accumulates at its core,

13338-656: The three-dimensional Navier–Stokes equations for the equilibrium situation where u = v = ∂ p ∂ x = ∂ p ∂ y = 0 {\displaystyle u=v={\frac {\partial p}{\partial x}}={\frac {\partial p}{\partial y}}=0} Then the only non-trivial equation is the z {\displaystyle z} -equation, which now reads ∂ p ∂ z + ρ g = 0 {\displaystyle {\frac {\partial p}{\partial z}}+\rho g=0} Thus, hydrostatic balance can be regarded as

13455-456: The total mass of the Kuiper belt is thought to be only a tenth or even a hundredth the mass of Earth. Many Kuiper belt objects have satellites, and most have orbits that are substantially inclined (~10°) to the plane of the ecliptic. The Kuiper belt can be roughly divided into the " classical " belt and the resonant trans-Neptunian objects . The latter have orbits whose periods are in a simple ratio to that of Neptune: for example, going around

13572-687: The trivial notation change h  =  r and have used f ( Ρ , ρ ) = 0 to express ρ in terms of P ). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads: ∂ i P P + ρ − ∂ i ln ⁡ u t + u t u φ ∂ i u φ u t = 0 {\displaystyle {\frac {\partial _{i}P}{P+\rho }}-\partial _{i}\ln u^{t}+u_{t}u^{\varphi }\partial _{i}{\frac {u_{\varphi }}{u_{t}}}=0} Unlike

13689-512: Was "simply creating an agreeably entertaining light novel, and in that task he succeeds admirably." At the 1957 Worldcon it received the Hugo Award for Best Novel (Heinlein's first). In 2012, the novel was included in the Library of America two-volume boxed set American Science Fiction: Nine Classic Novels of the 1950s , edited by Gary K. Wolfe . The cover illustration by Anthony Roberts for

#865134