

Subject:
earth's absolute velocity
Category: Science > Astronomy Asked by: arminiusga List Price: $10.00 
Posted:
13 Jun 2002 18:30 PDT
Expires: 13 Jul 2002 18:30 PDT Question ID: 25504 
Assuming an absolute reference point in the universe what can be said of the absolute velocity of a point on earth taking into account geographical position, altitude, earth's rotation, orbital speed, motion of the solar system, motion of the galaxy and all other speeds and "directions" involved. Has there been any mathematical formulation of how this vector changes in time? That is, what are the varying accelerations that a terrestial point might be subjected to?  


Subject:
Re: earth's absolute velocity
Answered By: eiffelga on 14 Jun 2002 08:56 PDT Rated: 
Hello arminius, and thanks for your interesting question! As others have pointed out in the comments, there is no distinguished "absolute reference point" in the universe. No doubt you understand this, because you have asked us to "assume" an absolute reference point. For the purposes of this question, I will use the cosmic microwave background radiation to supply a frame of reference, and will summarize the components of the earth's velocity relative to that frame of reference. The velocity of a point on earth's equator due to the earth's rotation is proportional to the distance of that point from the centre of the earth. The equatorial radius of the earth is 6378 km. To that radius we must add the altitude above sea level of the point in which we are interested. For example, for a 1000 meter mountain we would add 1km to the radius. We then multiply by 2 pi to get the rotational circumference, and divide by the number of seconds in the sidereal day to get the velocity of that point due to the earth's rotation. The siderial day, the time taken for the earth to present the same point towards the "fixed" stars, is 86164.10 seconds. Therefore, the velocity at the top of a 1000 meter mountain due to the earth's rotation is approximately 465 meters per second or 1675 km/hr. For a point which is not on the equator, multiply by the cosine of its latitude. For example, London is at latitude 51 degrees North, so the velocity of London is 465 times 0.629, or 293 meters per second. This is only an approximation, because the earth is not a perfect sphere. If you wish to correct for this, details can be found at Eric Weisstein's "World of Astronomy" on the "Earth" page: http://scienceworld.wolfram.com/astronomy/Earth.html There are many other corrections that can be applied to take into account peturbations of the earth's rotation, including the Chandler Wobble http://scienceworld.wolfram.com/astronomy/ChandlerWobble.html the Milankovitch Cycles http://scienceworld.wolfram.com/astronomy/MilankovitchCycles.html and a slipping about its rotation axis http://scienceworld.wolfram.com/astronomy/VariationofLatitude.html however these effects are all small. There is a tidal effect due to the moon and, to a lesser extent, the sun. In addition to the ocean tides, there is a tidal effect on solid land of about 0.2 meters approximately twice every 25 hours: http://www.henrycort.hants.sch.uk/find/science/space/ The earth's orbital speed around the sun is about 29786 meters per second (based on an average orbital distance of 149.6 million kilometers and a year of 31.56 million seconds): http://scienceworld.wolfram.com/astronomy/Year.html The earth's orbit around the sun is elliptical, and corrections can be made for this: http://www.analemma.com/Pages/EllipticalOrbit/EllipticalOrbitMath/EllipOrbitMath.html The gravitational effect of the moon and of the sun's planets also affects the earth's orbit. The axis of the earth's rotation is not the same as the axis of its revolution around the sun. The difference between these (of 23.5 degrees) causes the earth's seasons. The solar system is part of our galaxy, and is about 30,000 lightyears away from its center. It travels around that center about once every 200 million years, at an average speed of about 230 km per second: http://www.sunspot.noao.edu/PR/answerbook/motion.html Our galaxy is part of a group of galaxies known as the Local Group, which are close enough together to have a significant gravitational effect on each other. Our galaxy is moving towards the center of the Local Group at around 40 km per second: http://www.sunspot.noao.edu/PR/answerbook/motion.html Now let's consider the cosmic microwave background radiation, which is thought to be remnant radiation from the early stages in the evolution of the universe. This radiation comes from all directions, but the strength varies according to direction in a pattern that suggests we are moving relative to the matter which last scattered the background radiation. Our local group of galaxies is moving through the cosmic microwave background radiation at about 600 km per second: http://www.nobel.se/physics/laureates/1978/wilsonlecture.pdf (page 18) However, our sun is moving through the cosmic microwave background radiation at only 370 km per second, due to its relative movement within the local group. It is not possible to produce a mathematical formulation to show how the earth's overall velocity changes with time. One reason is that the earth's rotation and orbit are slowing down and will change significantly within the time of one galactic revolution. Another reason is that the various gravitational bodies interact, and this interaction will change as their positions change. As dannidinga pointed out in the comments, it is not even possible to mathematically formulate the motion of THREE gravitationallyinteracting bodies. Nevertheless, you can get a feel for the overall motion by superimposing the orbital rotation of the earth around the sun onto a 370 km per second linear motion of the sun relative to the background radiation. The other velocities are either much smaller or are changing very slowly. I hope you find this information useful. Additional link: Astronomical constants from Eric Weisstein's "World Of Astronomy": http://scienceworld.wolfram.com/astronomy/Earth.html Google search strategy: "astronomical constants" ://www.google.com/search?hl=en&lr=&q=%22astronomical+constants%22 london latitude ://www.google.com/search?hl=en&ie=UTF8&oe=UTF8&q=london+latitude tides "solid land" ://www.google.com/search?q=tides+%22solid+land%22&hl=en&lr=&start=20&sa=N universe "frame of reference" ://www.google.com/search?hl=en&lr=&q=universe+%22frame+of+reference%22 "cosmic microwave background radiation" ://www.google.com/search?hl=en&lr=&q=%22cosmic+microwave+background+radiation%22&btnG=Google+Search "hubble constant" ://www.google.com/search?hl=en&lr=&q=%22hubble+constant%22 "group of galaxies" "particular velocity" ://www.google.com/search?hl=en&lr=&q=%22group+of+galaxies%22+%22particular+velocity%22 Regards, eiffelga  

arminiusga
rated this answer:
Hello eiffelga Perhaps an explanation of how the question arose in the mind of a mathematically naive biologist. I was flying from Boston to San Francisco walking from forward to aft in a United Airlines jet when the question occurred to me: how could I describe my motion with reference to the cosmos? Starting with the pace I was walking, subtracted from the speed of the jet, adding the rotational speed of the earth at my present latitude, adding the orbital speed of the earth around the sun, taking into account the speed and direction of the solar system within our galaxy, the motion of said galaxy with respect to some fixed point in the universe, etc. In other words, in what manner (speed and direction) was I personally whizzing around and how did that change with time? What, in effect, are the accelerations that I was and am undergoing ?While I can more or less understand the concept of speed, the component of the vector, direction, eludes me. I cannot visualize how "direction" would be described in a cosmic sense, since the cardinal points of the earthly compass cannot come to the rescue. So while the first few steps might be manageable, not knowing the magnitude of the movements of galaxies boggles me. Thanks for the rapid, indeed instantaneous response. I appreciate the thoroughness of your answer and your clarity of exposition. Before you proposed the microwave background as a point of reference I was going to suggest the quasar called BR 12020725. Best regards arminiusga 

Subject:
Re: earth's absolute velocity
From: jesserudermanga on 13 Jun 2002 23:31 PDT 
I think you could take the center of mass of the universe as your fixed point and the rest frame of the center of mass of the universe as your inertial frame. I don't know how far Earth is from that point or how fast it is moving relative to that point. 
Subject:
Re: earth's absolute velocity
From: jaapga on 14 Jun 2002 02:02 PDT 
I don't think you could take the centre of mass of the universe as your fixed point. The thing is that to the best of our current cosmological knowledge, the universe is curved. Compare it to the surface of a sphere, which is 2dimensional and curved in the 3rd dimension. Now try finding the centre of the surface of a sphere. Within its own two dimensions. You cannot. Now, you may object, that doesn't mean that there isn't a centre *of mass* for that surface. However, if the mass on that surface is relatively (i.e. relative to the order of the size of the sphere) homogeneously spread out, you won't be able to find one. Now I guess that the universe's mass on such a large scale comes close to being homogeneously spread out, but I should ask a 'real' cosmologist about that some time or look it up. There are, of course, lumps, which we call galaxies, and lumps of lumps, yes indeed, but then, I never heard of these lumps of lumps lumping together in a specific "corner" of the universe. 
Subject:
Re: earth's absolute velocity
From: dannidinga on 14 Jun 2002 02:39 PDT 
I'll take up the question where thx1138 left it, that is, if we are given some point in the universe as a reference point, how to calculate the location of some given point on Earth as a function of time. This can be done, IN THEORY, that is, the answer is the solution of some differential equation describing the dynamics of motion of all the bodies of the universe under their mutual interacting forces. In Newtonian mechanics (which we know to be false, of course) one would simply write down Newton's law F=mA for each of the bodies in the universe, where F is the force, in this case the sum of the gravitational pulls of all the other bodies, m is the mass of the body, and a is the acceleration (the second derivative of the location). Once we solve this system of equations, we need to transform our system of coordinates to a system where our reference point becomes the fixed point 0. Like I said, Newtonian mechanics is unsuitable for treating problems at this scale, so really we would have to use the equations of Einstein's general relativity theory, which are much more complicated, but can equally well be written down by a competent professional (i.e. not me). So why did I mention Newtonian mechanics? To demonstrate that even in this much simplified case (not to mention that we neglected electrical forces and all sorts of other weird phenomena such as stars exploding etc.), the answer can only be computed IN THEORY, whereas in PRACTICE this becomes, well, practically impossible. Even for a problem concerning the motion of THREE celestial bodies, there is no analytical expression (that is, an explicit solution of the equations of motion given by a formula) for the motion of the bodies  this is the famous threebody problem (whose amusing history is described in detail in the book The Problems of Mathematics by Ian Stewart). Hope this helps, dannidin p.s. some potentially useful search terms: Newton's laws of motion general relativity (theory) the MichelsonMorley experiment (a physics experiment designed to measure the speed of the Earth relative to the hypothetical absolute fixed point of the universe, whose famous failure led eventually to the understanding by Einstein that there can be no such thing and to his discovery of relativity theory  see for instance http://www.drphysics.com/syllabus/M_M/M_M.html http://www.aip.org/history/einstein/emc1.htm) 
Subject:
Re: earth's absolute velocity
From: gruffgarethga on 14 Jun 2002 09:01 PDT 
Einsteins relativity does not provide a frame of reference in space (everything is relative), but recent empirical discoveries of the cosmic background radiation from the COBE satellite have established one. This microwave radiation is spread almost uniformly through space and is the cooled remnants of the heat from the ancient big bang. By measuring the temperature in different directions and finding a doppler effect creating red and blue shifts in the heat, it has been established that our galaxy is moving through space at about 1 million miles an hour (fast !) in the direction of space that we see occupied by the constellation of Leo. We also know that the sun is orbiting with our rotating galaxy  about once every 200 million years. The sun also has its own localised movement relative to the nearby stars  a kind of bouncing up and down through the plane of the galaxy  about once every 10,000 years, which may be related to the frequency of ice ages. Movements of the earth within the solar system are wellknown. I don't know the equations, but take all these movements into account and you will get your answer ! 
Subject:
Re: earth's absolute velocity
From: odyssey2001ga on 24 Jun 2002 07:15 PDT 
There is an interesting point nobody addressed yet. Arminius originally suggested using the quasar BR 12020725 as a point of reference. Doing so would give a somewhat surprising result: Taking this quasar as a reference point, the earth would be moving at 282,000 kilometers per second! This enormous speed comes from the fact that our universe is expanding. As the universe expands, the galaxies move away from one another. And the further an object is, the faster it is receeding from us. As Quasar BR 12020725 is one of the most distant objects known, it moves away from us at the incredible speed of 282,000 kilometers per second (94% the speed of light). And if we take the quasar as a point of reference, the earth will be the one moving at this mindboggling speed. 
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