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On predicting planetary orbits A number of studies have shown that the inner solar system is chaotic, with a Lyapunov time scale of about 5 million years. This 5 million year time scale means that while one can somewhat reasonably create a planetary ephemeris (a time-based catalog of where the planets were / will be) that spans from 10 million years into ...

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The effective gravity inside the ISS is very close to zero, because the station is in free fall. The effective gravity is a combination of gravity and acceleration. (I don't know that "effective gravity" is a commonly used phrase, but it seems to me to be applicable here.) If you're standing on the surface of the Earth, you feel gravity (1g, 9.8 m/s2) ...

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You've used the gravitational constant with only three significant digits. So it's no surprise that your answer isn't accurate to five significant digits. Instead of $G$ and $M_\odot$ separately, you should use the product $GM_\odot$, known as the standard gravitational parameter. Its value is known very accurately: in the link, you'll find $$GM_\odot = ... 23 The main plot below shows the potential energy of a mass in the Earth-Moon system under the unrealistic assumption that the system is not rotating. i.e. This mirrors (at present) all but one of the 4 answers given, in assuming that this point is defined where the gravitational force on a mass due to the Earth and the Moon are equal and opposite (i.e. at the ... 17 This is not possible. The lowest possible mass for a main sequence star (sustaining H-1 fusion; it's the regular kind of star) is around 80 Jupiter masses. Just below this, objects are referred to as Brown Dwarfs, which are technically not stars. Whereas the highest possible mass for a terrestrial planet is about 5-10 Earth masses (as per here). Above this ... 16 This web page has a nice discussion on it: http://archive.ncsa.illinois.edu/Cyberia/NumRel/EinsteinTest.html Basically the orbit's eccentricity would precess around the sun. Classical stellar mechanics (or Newtonian gravity) couldn't account for all of that. It basically had to do with (and forgive my crude wording) the sun dragging the fabric of ... 16 Set the forces on the test particle from the Earth and Moon equal:$$F_E=F_MG\frac{M_EM_{\text{ test particle}}}{R_E^2}=G\frac{M_MM_{\text{ test particle}}}{R_M^2}$$The Gs and M_{\text{ test particle}}s cancel, leaving you with$$\frac{M_E}{R_E^2}=\frac{M_M}{R_M^2}$$but you know that R_M, the distance between the test particle and the Moon, is ... 15 If you could take from orbital energy, then it would decrease, until at some point in the future it would zero. Hence, it can't be perpetual. 15 To some extent the universe exhibits something called self-organized criticality where a dynamic, non-linear system with many degrees of freedom (the gas after the Big Bang but before the emergence of structure) eventually forms a system with a notable degree of scale invariance (moons orbiting planets, planets orbiting stars, stars orbiting galactic ... 14 This is not that there is no exact solution, only the exact solutions for x(t) and y(t) use elliptic functions. The problem whether elliptic functions (which are defined by inverse of some integrals) are "good" functions is a bit philosophical one; one can on one hand state that sine is not a real function because one must integrate or sum a infinite ... 14 The excitement behind various claims is somewhat excessive. First, the Mayan astronomers, see e.g. Mayan astronomy at this page, didn't use any armillary spheres or sextants as others did. Their observations were made with naked eye and they were depicting positions of planets with crosses. The accuracy of the Venus' position after a synodic 584-day cycle ... 13 The Moon moves at about a thousand metres per second, but it's a long way away so it only appears to move slowly. Most of the apparent movement of the Moon is actually due to the rotation of the Earth. We see it appearing to go round the Earth once a day, but it actually takes about 28 days to complete an orbit. The Wikipedia article on the Moon's orbit has ... 13 First, you state a few things that aren't quite right in your question. While the view that's generally talked about is that Phobos and Deimos are likely captured asteroids, dynamically it's a pretty difficult problem (you generally need a third (in this case fourth?) body to take away the extra energy, and it's hard to get a circular orbit around the ... 13 Here's another way of looking at it. Let M1, M2, M3 be our three masses. In the three body problem we're considering, the whole frame containing M1, M2 and M3 is rotating. You're right to think that if that frame was fixed then the points L4 and L5 would not be stable. After all if you perturb M3 from L4 or L5 then it should just roll down the potential ... 12 It's possible, but it seems like it'd be rare. The planets with the most moons are giant, and very far away from the sun. That means the moons will be very strongly bound to the planet and not get disturbed much by the sun. If our moon had a moon, it'd have to be just the right distance from it that it wouldn't collide with it (the moon's gravity is far from ... 11 There are two elements to why the universe appears to be so orderly: the physical laws of that govern the universe are the same everywhere, and astronomical objects are very, very, very far from each other. Consider two objects, one much larger than the other, and both very far from anything else. Because of gravity (which works the same everywhere), the ... 11 The horseshoe orbit shape does occur only in the reference frame of the Earth’s orbit. It is a manifestation of a third body problem, and the orbit is in an accelerated reference frame. The loop, which is this distended horseshoe shape, has no central gravitational source inside the loop. As a result the orbit is a “pseudo-orbit.” From the perspective of an ... 11 The spiral arms don't mean that the mass is getting sucked to the center. They're just wave-like density patterns. The bodies in orbit around the center of the galaxy are in stable orbit; just like the Earth around the Sun and the Moon around the Earth. What happens is that gravity accounts for the centripetal force (in the orbiting frame, gravity is ... 11 To expand on Prahar's answer, let me run some numbers to try and convince you this is reasonable. Your answer is correct to within one part in 104:$$ \frac{365.256363004}{365.2075}\approx 1.000133795. $$The main perturbing influence on Earth's orbit is the gravitational pull of Jupiter, whose mass is about 1000 times smaller than the Sun, and which orbits ... 11 We already harvest energy from the Moon. It causes the tides and stress and strain and motion throughout the Earth. As a result, the Moon keeps getting farther away. (And it causes some heating in the Earth). The Moon at one time had a spin that was not locked to the Earth, and the tidal bulges in the Moon's shape caused by the Earth generated heat in the ... 10 Is it possible for a star to have the same mass and radius as e.g. the Moon and orbit a planet like Earth at the same distance (at which Moon orbits Earth in actuality)? No. The lowest mass type of star is a Brown Dwarf, which still has a mass greater than that of Jupiter. Even brown dwarfs have too little mass to fuse light hydrogen. Neutron stars ... 10 Kepler's 3rd law assumes that the Earth travels in a perfect ellipse with the only gravitational force on it being from the Sun. Further, Kepler's laws are derived from Newtonian gravitation. In reality, the orbit of the Earth is affected by the gravitational pull of other planets, and by the effects of General Relativity and is therefore not quite ... 9 At Lagrange point L1. Specifically for Earth-Moon L1, these calculations show 326054 km. 9 Earth is about 100x more massive than the moon, and since F \propto M / r^2 , the distance from Earth to the astronaut would have to be about \sqrt{100} = 10x further than from the moon to the astronaut. Therefore, the astronaut falls "up" about 90% of the way to the moon. [The earlier answers go a lot more into detail (and are more technically ... 9 In his lecture The Cosmic Distance Ladder (video), mathematician Terence Tao describes the history of how mankind has successfully mapped the solar system and beyond. In particular, he describes why Copernicus put the sun in the center (reason: he discovered that the sun is dozens of times bigger than the earth) and how Kepler found his laws of planetary ... 9 No "large bodies" that I know of. Certainly it is physically possible for something to orbit a moon; lots of spacecraft have been orbited around the Moon and other moons in the solar system. As long as we're simply discussing hierarchies of orbits, the Sun orbits the galactic center and the Milky Way is gravitationally bound to the Local Group. [EDIT: ... 9 When you look at the dynamics in the rotating reference frame, there are 4 forces acting on the particle: the two gravitational pulls from the massive bodies, the centrifugal push away from the center of rotation (located between the massive objects) and the Coriolis force. The first three forces depend on the position of the particle, and can be derived ... 9 The Wikipedia article on Pluto has a good explanation. Basically, the inclinations of their orbits are such that they never approach each other more closely than about 17 AU (more than 1.5 billion kilometers). In fact, Pluto comes closer to Uranus (11 AU) than it does to Neptune. And since Pluto and Neptune are in a 3:2 gravitational resonance, their ... 8 The force you experience is of the form \vec{F} = - Gmr\vec{u_r}, and we also know that in the surface, r=R, it is \vec{F}=- gm\vec{u_r}, so$$\vec{F} = -gm\frac{r}{R}\vec{u_r}$$This is a conservative force that can be derived from a potential$$U = \frac{1}{2}gm\frac{r^2}{R} Because this is a central force, angular momentum will be conserved, ...

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This was previously a comment to space_cadet's answer but became long (down-vote wasn't me though). I don't understand space_cadet's talk about unstable orbits. Recall that two-body system with Coulomb interaction has an additional $SO(3)$ symmetry and has a conserved Laplace-Runge-Lenz vector which preserves the eccentricity. Because interactions between ...

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