What does the law of planetary distances by Titius states?What ist its major flaw?
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If you write the number sequence 0,3, 6, 12, 24, 48, 96, and add 4 to each number (4, 7, 10, etc) then divide by ten, you get the distance of each planet from the Sun, measured in astronomical units (1 a.u.=93 million miles=150 million kilometers).  This works out as Mercury 0.4, Venus 0.7, Earth 1.0, Mars 1.6, --- 2.8, Jupiter 5.2, and Saturn 10.0  This works out pretty accurately, but there was nothing at 2.8. Herschel discovered Uranus in 1781 at 19.6, right where another planet was supposed to go according to the Titius rule.   When Ceres was discovered in 1801, it was at 2.72, filling the gap.  Neptune, however is not near 38.8, but at 30.  Astronomers now believe the "law" is either a coincidence, or the result of billions of years of gravitational interactions.
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Newton's laws of motion together with his law of gravity give a relation among\n\n    * the period P of a planet's orbit.\n    * the distance a from the planet to the Sun.\n    * a constant G measured in laboratory experiments.\n    * the mass M of the Sun. \n\n(For our purposes, assume the orbits are circles. Also assume that the mass of a planet is tiny compared to the mass of the Sun.)\n\n\nUsing this relation with P and a for the Earth gives the mass of the Sun.\n\nM ~ 2 x 1030 kg.\n\nWe will use this relation later on to get the masses of other stars.\n\nIt can also be used to get the masses of galaxies!\n\nDavison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu
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After the discovery of Uranus, it was noticed that its orbit was not as it should be in accordance with Newton's laws.  It was therefore predicted that another more distant planet must be perturbing Uranus' orbit. Neptune was first observed by Galle and d'Arrest on 1846 Sept 23 very near to the locations independently predicted by Adams and Le Verrier from calculations based on the observed positions of Jupiter, Saturn and Uranus. An international dispute arose between the English and French (though not, apparently between Adams and Le Verrier personally) over priority and the right to name the new planet; they are now jointly credited with Neptune's discovery. Subsequent observations have shown that the orbits calculated by Adams and Le Verrier diverge from Neptune's actual orbit fairly quickly. Had the search for the planet taken place a few years earlier or later it would not have been found anywhere near the predicted location. \n\nMore than two centuries earlier, in 1613, Galileo observed Neptune when it happened to be very near Jupiter, but he thought it was just a star. On two successive nights he actually noticed that it moved slightly with respect to another nearby star. But on the subsequent nights it was out of his field of view. Had he seen it on the previous few nights Neptune's motion would have been obvious to him. But, alas, cloudy skies prevented obsevations on those few critical days. \n\nNeptune has been visited by only one spacecraft, Voyager 2 on Aug 25 1989. Much of we know about Neptune comes from this single encounter. But fortunately, recent ground-based and HST observations have added a great deal, too. \n\nBecause Pluto's orbit is so eccentric, it sometimes crosses the orbit of Neptune making Neptune the most distant planet from the Sun for a few years. \n\nNeptune's composition is probably similar to Uranus': various "ices" and rock with about 15% hydrogen and a little helium. Like Uranus, but unlike Jupiter and Saturn, it may not have a distinct internal layering but rather to be more or less uniform in composition. But there is most likely a small core (about the mass of the Earth) of rocky material. Its atmosphere is mostly hydrogen and helium with a small amount of methane. \n\nNeptune's blue color is largely the result of absorption of red light by methane in the atmosphere but there is some additional as-yet-unidentified chromophore which gives the clouds their rich blue tint. \n\nLike a typical gas planet, Neptune has rapid winds confined to bands of latitude and large storms or vortices. Neptune's winds are the fastest in the solar system, reaching 2000 km/hour. \n\nLike Jupiter and Saturn, Neptune has an internal heat source -- it radiates more than twice as much energy as it receives from the Sun. \n\nAt the time of the Voyager encounter, Neptune's most prominent feature was the Great Dark Spot (left) in the southern   hemisphere. It was about half the size as Jupiter's Great Red Spot (about the same diameter as Earth). Neptune's winds blew the Great Dark Spot westward at 300 meters/second (700 mph). Voyager 2 also saw a smaller dark spot in the southern hemisphere and a small irregular white cloud that zips around Neptune every 16 hours or so now known as "The Scooter" (right). It may be a plume rising from lower in the atmosphere but its true nature remains a mystery. \n\nHowever, HST observations of  Neptune (left) in 1994 show that the Great Dark Spot has disappeared! It has either simply dissipated or is currently being masked by other aspects of the atmosphere. A few months later HST discovered a new dark spot in Neptune's northern hemisphere. This indicates that Neptune's atmosphere changes rapidly, perhaps due to slight changes in the temperature differences between the tops and bottoms of the clouds. \n\n Neptune also has rings. Earth-based observations showed only faint arcs instead of complete ri
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By size and orbit, mainly.\n\nOrbit comes first. Kepler noticed that the gap between Mars and Jupiter was wider than could have been expected, Johann Titius described a systematic and J.E. Bode formulated a rule for the distances of the planetary orbits from the sun. This rule works fine for the inner planets, the missing planet at the asteroid belt, Jupiter, Saturn and Uranus, but places Neptun on a intermediary orbit (about half the distance expectedby the Titius-Bode rule).\n\nWhen Pluto was discovered, its mean distance was about the expected value for the planet behind Uranus, which is why it was classified as a planet.\n\nWith the discovery of Sedna, Pluto now is regarded as a Kuyper Belt object rather than a regular planet.\n\n\nAsteroids come as numerous bodies occupying broadly the same orbit around the sun, without a central planet.\n\n\nBTW, the Earth-Moon system is an oddball in itself, basically a binary planet with the gravity centre between earth and moon forming the planetary orbit around the sun.\n\n\nSize, or surface gravity, is the other criterium. There is no fixed value where a planet begins and planetoids end, but 1/10th of earth gravity could be a useful rule of thumb.\n\nSeveral of the larger moons (earth's, Titan and at least for of Jupiter's moons) would qualify as planets if they had their own solar orbits rather than orbiting a heavier planet. Most of the smaller moons are de facto asteroid/planetoids caught by the  planets.
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It would depend on where Earth and Jupiter are in their orbits.\n\nAt the closest point, when Earth and Jupiter are aligned, their distance may be "only" 628.7 E6 km.\nOr when Earth and Jupiter are on oposite sides of the sun, the distance may be as much as 927.9 E6 km.
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The distance between Earth and Pluto varies as the two planets move around their orbits. When they are closest, they are about 29 A.U. apart; at most, the distance is about 51 A.U. Since light travels about 300,000 kilometers each second, it would take light anywhere between 8 hours and 14 hours to make the round-trip journey to Pluto from Earth.\n\nRadio signals travel at the same speed as light. If you were using radio signals to control a robot on Pluto, you would have to be very patient. If you sent your robot a command to move, the command would arrive at least 4 hours later. Then, if your robot took a picture and sent it back to Earth, it would take at least 4 more hours before you could see that picture! \n\n\n\nAU\n\nAU, which stands for "astronomical unit", is a unit for measuring distance. One AU is the average distance from the Sun's center to the Earth's center. It is equal to 149,597,871 km (92,955,807 miles).\n\nAUs are often more convenient to use than kilometers when measuring large distances such as those in space. In this case kilometers are just too small - it would be like measuring the distance from Boston to San Francisco in inches. AUs simply make a measurement easier to understand and give you something to compare it to.\n\nFor example, Saturn's orbit around the Sun has an average radius of 9.5 AU, which means that Saturn is about ten times farther from the Sun than Earth is. The average distance from the Sun to distant Pluto is about 40 AU. Mercury, the planet closest to the Sun, orbits at an average distance of 0.39 AU.\n\nAUs are generally used for measurements of distances within our Solar System. Distances to stars are much larger, and are expressed in terms of light years. One light year is equal to more than 63,000 AUs. The nearest star, Proxima Centauri, is just over 4 light years away.\n\nAlthough Pluto was discovered in 1930, limited information on the distant planet delayed a realistic understanding of its characteristics. Today Pluto remains the only planet that has not been visited by a spacecraft, yet an increasing amount of information is unfolding about this peculiar planet. The uniqueness of Pluto's orbit, rotational relationship with its satellite, spin axis, and light variations all give the planet a certain appeal.\n\nPluto is usually farther from the Sun than any of the nine planets; however, due to the eccentricity of its orbit, it is closer than Neptune for 20 years out of its 249 year orbit. Pluto crossed Neptune's orbit January 21, 1979, made its closest approach September 5, 1989, and will remain within the orbit of Neptune until February 11, 1999. This will not occur again until September 2226.\n\nAs Pluto approaches perihelion it reaches its maximum distance from the ecliptic due to its 17-degree inclination. Thus, it is far above or below the plane of Neptune's orbit. Under these conditions, Pluto and Neptune will not collide and do not approach closer than 18 A.U. to one another.\n\nPluto's rotation period is 6.387 days, the same as its satellite Charon. Although it is common for a satellite to travel in a synchronous orbit with its planet, Pluto is the only planet to rotate synchronously with the orbit of its satellite. Thus being tidally locked, Pluto and Charon continuously face each other as they travel through space.\n\nUnlike most planets, but similar to Uranus, Pluto rotates with its poles almost in its orbital plane. Pluto's rotational axis is tipped 122 degrees. When Pluto was first discovered, its relatively bright south polar region was the view seen from the Earth. Pluto appeared to grow dim as our viewpoint gradually shifted from nearly pole-on in 1954 to nearly equator-on in 1973. Pluto's equator is now the view seen from Earth.\n\nDuring the period from 1985 through 1990, Earth was aligned with the orbit of Charon around Pluto such that an eclipse could be observed every Pluto day. This provided opportunity to col
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Kepler has three laws of planetary motion:\n\n1. The orbit of a planet about a star is an ellipse with the star at one focus.\n\n2. A line joining a planet and its star sweeps out equal areas during equal intervals of time.This is also known as the law of equal areas.\n\n3. The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits. This one has an equation tied to it:\n\nT^2 = xa^3, where T = orbital period of a planet and a = semimajor axis of orbit
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Kepler's Laws \nIllustration of elliptical orbit of a planet with the sun at the left focus. The semi-major and semi-minor axes are denoted by  and . The shaded triangular area element is needed for the discussion of Kepler's second law. Perihelion and aphelion are respectively the points on the orbit nearest and farthest from the sun. Note that at perihelion and aphelion the velocity is purely tangential, i. e., the velocity component along the radius vector is zero.  \nJohannes Kepler, using data compiled by Tycho Brahe, inferred three laws governing the motions of planets in the solar system: \nPlanets move in elliptical orbits with the sun at one focus. \nEqual areas are swept out in equal times by the line connecting the sun and the planet. \nThe square of the period of revolution of the planet around the sun is proportional to the cube of the semi-major axis of the ellipse. \nThese laws were instrumental in the development of modern mechanics and the universal law of gravitation by Isaac Newton. \nShowing that the first law is consistent with Newtonian mechanics is mathematically more difficult than we can undertake in this course. However, the second law turns out to be a simple consequence of the conservation of angular momentum. It shows an elliptical orbit with the area swept out as a planet moves from position 1 to position 2. We estimate this area as , where we have ignored the small unshaded part of the area to the right of the shaded triangle. The distance traveled by the planet in time  is , so the magnitude of the velocity is . However, in computing the angular momentum, we need the tangential component of the velocity, i. e., the component normal to the radius vector . This is simply . The angular momentum is , where  is the mass of the planet. Combining this with the formula for  results in \nSince gravitation is a central force, angular momentum is conserved, which means that  is constant. Thus, we have shown that conservation of angular momentum is equivalent to Kepler's second law. \nKepler's third law turns out to be a consequence of the universal law of gravitation. We can prove this for circular orbits. We know that a planet moving in a circular orbit around the sun is accelerating toward the sun with the centripetal acceleration , where  is the speed of the planet's motion in its orbit and  is the orbit's radius. This acceleration is caused by the gravitational force, so we can equate the force divided by the planetary mass to , resulting in where  is the mass of the sun. This may be solved for Eliminating  in favor of the period of revolution  results in ...This agrees with Kepler's third law since the semi-major axis of a circle is simply the radius .
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To be sure, the theory has a lot of gaps.  So it's not a Law.  All's it takes is one scientifically provable discovery that doesn't fit the theory to launch a search for a new theory that will explain the new information while keeping the old proven stuff too.  A good example is Einstein's Theory of Relativity.  Newtonian Mechanics fails at extreme sizes and speeds.  Relativity so far has been able to explain all the variances found to date at those extremes, but has not been proven to be 100% valid all the time, so it's not a law yet.  If you can discover something that invalidates evolutionary theory, you'll probably win a Nobel Prize!
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Kepler's laws are simply empirical rules. What really predicts planetary motion is Newton's theory of gravity, which confirms Kepler's laws. It also explains most of the deviations from those laws as due to gravitational perturbation from other planets. \n\nEinstein's general relativity adds very little to Newton's calculations for our solar system. Newton calculated that the precession of Mercury's orbit should be 531 arc-seconds per century. General relativity correctly accounted for the full 574 arc-seconds. I'm not sure if you can work time dilation per se into that, but that's the most significant modification to Newton/Kepler by general relativity that I know of. (disclaimer - I am not a physicist)\n\nRe the equivalency of time: There is a time standard based on the center of the sun that is used for these calculations, to eliminate gravitational effects on the time base.
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The distances to stars closer than about 150 light years can be measured directly by use of parallax.  The position of the star against background stars is measured at times 1/2 year apart, and then it is a simple mathematical procedure to determine the distance (you have a side and two angles of a triangle--the angular distance the star appears to move at it's distance over 1/2 year equals 186 million miles-the diameter of the orbit of the earth).  \n\nStars farther than that cannot be measured directly.  But, by use of knowledge about how bright a star should be (on average) for it's spectral type (which loosely is governed by its mass) an estimate of its intrinsic brightness can be made, and then by looking at how bright it appears, it's distance can be estimated.\n\nCepheid variables are used, as well, but mostly to determine the distances to groups of stars and of other galaxies.  Incidentally, the North Star (Polaris, or Alpha Ursa Minor) is a cepheid variable.\n\nNovae and supernovae tend to have average intrinsic brightnesses, so their apparent brightness in, say, a distant galaxy, tells us (within limits) it's distance.\n\nRed shift is used for objects outside our galaxy because the amount of red shift within our galaxy would be extremely small (it increases with distance) if it were not totally overcome by the gravity of the galaxy.
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Kepler's Third Law states that the ratio of the squares of the periods of any two  planets is equal to the ratio of the cubes of their average distances from the sun.  Here, the "period" simply means the length of time it takes for a planet to orbit the sun once.\n\nIf R1 and R1 are the orbital radii (i.e., the distance from the sun) of planets 1 and 2, and T1 and T2 are the orbital periods, then the Kepler's Thrd Law has the mathematical form:\n\n\n(T1/T2)^2 = (R1/R2)^3\n\nHere, we know that for the Earth, T1 = 1 year, and R1 = 1 AU (1 AU is one Astronomical Unit, which is defined as the average distance from the Earth to the Sun).  We want to find R2 if T2 = 5 years.  So:\n\n(1 yr /5 yr)^2 = (1 AU/R2)^3\n1/25 = (1 AU)^3/(R2)^3\nR2 = (25 AU^3)^(1/3)\nR2 = 2.924 AU
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Kepler's Laws (of planetary motion) use Calculus (first quarter/semester if that is what you were wondering about).  You can get a good understanding of them by simplifying them with geometry, trig and logic though I believe.\n\nMost descriptions of the motion of bodies (like planets and comets) use calculus, trig(for angles), and some other basic geometry, as well as good ole logic.
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Dan's result seems extremely low and the reason is that when he converted metres to inches he divided instead of multiplying so his final answer needs to be multiplied by about 1600.\n\nI don't think the earth's rotational speed around its own axis is relevant. I am unclear which Dan has taken, this or the earth's orbital speed around the sun.\n\nIf the radius of the Earth's orbit is 93 million miles, then the circumference of the orbit (assuming a circle for simplicity) is 2 pi r or 6.28 x 93 x 10^6 miles. In a fortnight (14 days out of 365) the earth will travel 14/ 365 ths of that distance (ignoring leap years for simplicity) and with 8 furlongs to a mile, that is\n\n8 x 14/365 x 6,28 x 93 x 10^6 f per f\n\nFor an approximate result, say 93 divides into 365 4 times, and divide the 4 into the 8 to leave\n\n28 x 6,28 x 10^6 furlongs per fortnight\n\n= approx 1.75 x 10^8 furlongs/fortnight\n\nOf course the sun itself is moving at about ten miles a second in the direction of Alpha Herculis, but that too is irrelevant to the calculation as is the rotational velocity of the earth on its own axis.
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So far, the laws of nature have been constant wherever we look. This includes astronomical observations of events long ago and far away. Therefore, the assumption that the laws do not change is a reasonable one and is generally accepted. If you want to argue otherwise, you need to specify what laws you think were different, in what way, and how could we tell. Otherwise, your argument is no better than "science doesn't know everything; therefore, pigs can fly".
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Jupiter is the largest planet in the solar system. Its diameter is 88,846 miles (142,984 kilometers), more than 11 times that of Earth, and about one-tenth that of the sun. It would take more than 1,000 Earths to fill up the volume of the giant planet. When viewed from Earth, Jupiter appears brighter than most stars. It is usually the second brightest planet -- after Venus.\n\nJupiter is the fifth planet from the sun. Its mean (average) distance from the sun is about 483,780,000 miles (778,570,000 kilometers), more than five times Earth's distance. Ancient astronomers named Jupiter after the king of the Roman gods.\n\nAstronomers have studied Jupiter with telescopes based on Earth and aboard artificial satellites in orbit around Earth. In addition, the United States has sent six space probes (crewless exploratory craft) to Jupiter.\n\nAstronomers witnessed a spectacular event in July 1994, when 21 fragments of a comet named Shoemaker-Levy 9 crashed into Jupiter's atmosphere. The impacts caused tremendous explosions, some scattering debris over areas larger than the diameter of Earth.\n\nPhysical features of Jupiter\n\nJupiter is a giant ball of gas and liquid with little, if any, solid surface. Instead, the planet's surface is composed of dense red, brown, yellow, and white clouds. The clouds are arranged in light-colored areas called zones and darker regions called belts that circle the planet parallel to the equator.\n\nOrbit and rotation\n\nJupiter travels around the sun in a slightly elliptical (oval-shaped) orbit. The planet completes one orbit in 4,333 Earth days, or almost 12 Earth years.\n\nAs Jupiter orbits the sun, the planet rotates on its axis, an imaginary line through its center. The axis is tilted about 3¡. Scientists measure tilt relative to a line at a right angle to the orbital plane, an imaginary surface touching all points of the orbit.\n\nJupiter rotates faster than any other planet. It takes 9 hours 56 minutes to spin around once on its axis, compared with 24 hours for Earth. Scientists cannot measure the rotation of the interior of the giant planet directly, so they have calculated the speed from indirect measurements. They first calculated the speed using an average of the speeds of the visible clouds that move with interior currents, except for a more rapid zone near the equator.\n\nJupiter sends out radio waves strong enough to be picked up by radio telescopes on Earth. Scientists now measure these waves to calculate Jupiter's rotational speed. The strength of the waves varies under the influence of Jupiter's magnetic field in a pattern that repeats every 9 hours 56 minutes. Because the magnetic field originates in Jupiter's core, this variation shows how fast the plant's interior spins.\n\nJupiter's rapid rotation makes it bulge at the equator and flatten at the poles. The planet's diameter is about 7 percent larger at the equator than at the poles.\n\nMass and density\n\nJupiter is heavier than any other planet. Its mass (quantity of matter) is 318 times larger than that of Earth. Although Jupiter has a large mass, it has a relatively low density. Its density averages 1.33 grams per cubic centimeter, slightly more than the density of water. The density of Jupiter is about 1/4 that of Earth. Because of Jupiter's low density, astronomers believe that the planet consists primarily of hydrogen and helium, the lightest elements. Earth, on the other hand, is made up chiefly of metals and rock. Jupiter's mix of chemical elements resembles that of the sun, rather than that of Earth.\n\nJupiter may have a core made up of heavy elements. The core may be of about the same chemical composition as Earth, but 20 or 30 times more massive.\n\nThe force of gravity at the surface of Jupiter is up to 2.4 times stronger than on Earth. Thus, an object that weighs 100 pounds on Earth would weigh as much as 240 pounds on Jupiter.\n\nThe atmosphere of Jupiter is composed of abou
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The Earth would immediately leave it’s orbit in a direction tangential to the current orbital plane at a velocity equal to it’s current orbital velocity, roughly 11 km/s.  The final path will be modified by the gravitaitonal force of the other solar system bodies, but since the Sun’s gravitational attraction is much greater than the others,  the solar system would just fly apart.  \n\nThere’s no delay in gravity force propagation, so the effects will be instantaneous the moment the gravity is “turned off”.\n\nEDIT:  \n\nmrjeffrey 321:  It is correct.  The information of the sun's gravitational field really does travel faster than the speed of light.  I don't have any vested interest in any particular theory, I prefer to look at the facts and the experimental data.  Ask any astronomer who performs astrometric or planetary position calculations using celestial mechanics.  The positions of the planets are always calculated using instantaneous gravity.  The positions are then corrected for aberration, the visual position error caused by the fact that light is speed limited.  So, we really calculate the actual positions of the planets, and then we correct for where we actually see the light coming from these planets, delayed by the speed of light.\n\nIn fact, if you model the solar system by adding in a delay for "gravity propagation" at the speed of light, the orbits of the planets in the solar system begin to slowly deteriorate.  This is most obvious with observations of certain binary double stars, where any delay in gravity would cause the star pairs to fly apart.  According to actual ephemeris measurements, the Earth is being accelerated to point about 20 arc-seconds ahead of where the sun appears in the sky.  This is because gravity is pulling us instantaneously towards the true position of the sun, not the apparent position we see in the sky.\n\nI'm not an expert on relativity, so I'm not going to argue fine points about what general  or special relativity either does or doesn't say or is interpreted to say.  What matters is the actual evidence, and the evidence says that the effects of gravity are instantaneous.\n\nNote that there was a paper published back in 2003 regarding the measurement of the speed of gravity, which resulted in it being very close to the speed of light.  There are several errors in this paper that were pointed out after publication.  The calculations used were shown to be incorrect.\n\nAn interesting question on this subject is black holes.  If we agree that gravity is a particle or wave, and we agree that nothing, no information, can escape a black hole, then how is it that black holes exhibit gravity? If they are truly so massive that they warp the very fabric of space-time, then how is it that gravity waves can escape when light cannot  If we accept the fact that black holes are "information holes" in the sky, how can they reveal themselves through gravity?