The fate of the Earth?
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From: Sam Wormley on 8 Sep 2009 17:39 dow wrote: > Mass of sun = 2.707 e 7 times mass of moon (using figures in Rubber Bible) > Radius of earth's orbit = 389.4 times radius of moon's orbit. (ditto) > > Tidal effect of moon on earth = 389.4^3 / 2.707e7 = 2.181 times tidal > effect of sun. > > This assumes both orbits are circular, of course. In reality, they are > not, so the ratio varies considerably. When earth is at aphelion and > the moon is at perigee, the sun is 418.6 times further from earth than > the moon is, which makes the tidal ratio 2.709:1, so in this situation > it is closer to 3:1 than 2:1. > You seem to be missing the main points (almost on purpose)! Do the differential force on both sides of the earth for the moon at average distance. And to the same for the differential force on both sides of the earth for the sun at its average distance. http://hyperphysics.phy-astr.gsu.edu/HBASE/tide.html âF_sun = 0.00017 * F_sun = 0.03 x F_moon âF_moon = 0.068 * F_moon The tidal effect on the earth of the moon is about 2.27 times the tidal effect on the earth of the sun. Putting it another way, the tidal affect on the earth cause by the sun is about 44% that of the moon.
From: dow on 9 Sep 2009 11:10 On Sep 8, 5:39Â pm, Sam Wormley <sworml...(a)mchsi.com> wrote: > dow wrote: > > Mass of sun = 2.707 e 7 times mass of moon (using figures in Rubber Bible) > > Radius of earth's orbit = 389.4 times radius of moon's orbit. (ditto) > > > Tidal effect of moon on earth = 389.4^3 / 2.707e7 = 2.181 times tidal > > effect of sun. > > > This assumes both orbits are circular, of course. In reality, they are > > not, so the ratio varies considerably. When earth is at aphelion and > > the moon is at perigee, the sun is 418.6 times further from earth than > > the moon is, which makes the tidal ratio 2.709:1, so in this situation > > it is closer to 3:1 than 2:1. > > Â Â You seem to be missing the main points (almost on purpose)! Do the > Â Â differential force on both sides of the earth for the moon at average > Â Â distance. And to the same for the differential force on both sides of > Â Â the earth for the sun at its average distance. > > Â Â Â http://hyperphysics.phy-astr.gsu.edu/HBASE/tide.html > > Â Â Â âF_sun = 0.00017 * F_sun = 0.03 x F_moon > > Â Â Â âF_moon = 0.068 * F_moon > > Â Â Â The tidal effect on the earth of the moon is about 2.27 times the > Â Â Â tidal effect on the earth of the sun. Putting it another way, the > Â Â Â tidal affect on the earth cause by the sun is about 44% that of the > Â Â Â moon. I'm not missing the point at all. Gravitational force, f, is proportional to the inverse square of the distance. df/dx = k/x^2 The tidal gradient is df/dx, so that's proportional to 1/x^3. The tidal gradient is proportional to the inverse cube of the distance, and, of course, to the mass of the body producing it. The sun is about 2.7e7 times as massive as the moon, and is about 400 times further away from te earth, so the moon's tidal effect on the earth is (400^3)/ (2.7e7) times as great as the sun's. It really is that simple, or at least it would be if the distances were constant. However, in reality they are not, so the ratio varies. The ratio of the moon's tidal effect to the sun's is sometimes closer to 2:1, and sometimes to 3:1. When I was a kid, I used to enjoy messing about in boats near the British coast. It was a matter of common observation that the heights of the "spring" tides, at full or new moon, were about twice as great as the heights of the "neap" tides, at the moon's quarter phases. The Internet didn't exist back then, but we knew this fact anyway! From this 2:1 ratio of tide heights, it's easy to derive the ratio of the moon's tidal effect to the sun's: (m+s) / (m-s) = 2 m+s = 2m - 2s 3s = m So the moon's tidal effect is three times the sun's. Approximately, of course. However, this was during the northern summer, when the earth is near aphelion. (I wasn't keen on playing in boats in wintertime.) The sun's tidal effect was therefore near its annual minimum, so the ratio m/s was greater than average. By saying thsat the moon's tidal effect is 2.27 times the sun's, you are implying that it is constant, and that simply is not true, whatever your Internet source says. Sometimes (often during the northern summer) it is closer to 3:1 than 2:1. dow
From: Yousuf Khan on 10 Sep 2009 08:44 dow wrote: > It is now thought that the sun probably will not engulf the earth and > moon when it becomes a red giant. The loss of solar mass to the solar > wind will reduce the maximum radius of the sun and will also cause the > earth's orbit to spiral outward. Both effects will reduce the > probability of the earth beig engulfed. The solar mass loss due to the solar winds probably won't be significant *until* the Sun goes red giant. Current solar winds don't even represent a fraction of a percent of total solar mass over the billions of years of Sun's existence. Yousuf Khan
From: Yousuf Khan on 10 Sep 2009 09:21 dow wrote: > Honestly, I can't recall where I read that the earth is likely to > escape being engulfed by the sun, but I have read it somewhere. Of > course, if I am thnking it, then "it is now thought". Scientists are still going back and forth on this question. As soon as there is an announcement that the Earth *will* be engulfed, another announcement from another supercomputer simulation shows that it won't be. Latest thinking is that the Sun *will* engulf, again. The Sun Will Eventually Engulf Earth--Maybe: Scientific American http://www.scientificamerican.com/article.cfm?id=the-sun-will-eventually-engulf-earth-maybe The previous study of course found the opposite case. 'Scientists' Good News: Earth May Survive Sun's Demise in 5 Billion Years' by Dennis Overbye - RichardDawkins.net http://richarddawkins.net/article,1633,Scientists-Good-News-Earth-May-Survive-Suns-Demise-in-5-Billion-Years,Dennis-Overbye Yousuf Khan
From: dow on 10 Sep 2009 10:50
On Sep 10, 9:21 am, Yousuf Khan <bbb...(a)yahoo.com> wrote: > dow wrote: > > Honestly, I can't recall where I read that the earth is likely to > > escape being engulfed by the sun, but I have read it somewhere. Of > > course, if I am thnking it, then "it is now thought". > > Scientists are still going back and forth on this question. As soon as > there is an announcement that the Earth *will* be engulfed, another > announcement from another supercomputer simulation shows that it won't > be. Latest thinking is that the Sun *will* engulf, again. > > The Sun Will Eventually Engulf Earth--Maybe: Scientific Americanhttp://www.scientificamerican.com/article.cfm?id=the-sun-will-eventua... > > The previous study of course found the opposite case. > > 'Scientists' Good News: Earth May Survive Sun's Demise in 5 Billion > Years' by Dennis Overbye - RichardDawkins.nethttp://richarddawkins.net/article,1633,Scientists-Good-News-Earth-May... > > Yousuf Khan I also read somewhere that the earth might survive even if it is briefly engufed by the sun, i.e. the surface of the photosphere expands around it. The density of the solar material would be so low that the planet could continue in orbit for a while. If the sun shrinks back quickly enough, the planet might emerge. Of course, its surface would be drastically affected. dow |