tag:blogger.com,1999:blog-30971820.post4292337993006790193..comments2023-10-31T21:30:25.737+08:00Comments on Fresh Brainz: Counterintuitive Science: Orbital MechanicsThe Key Questionhttp://www.blogger.com/profile/05426898630563791849noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-30971820.post-44052443874495398902007-08-20T18:13:00.000+08:002007-08-20T18:13:00.000+08:00Hi John and Glendon, thanks for the encouragment. ...Hi John and Glendon, thanks for the encouragment. Truth be told my maths isn't that good, but I see the beauty of physics and try hard to make physics stories comprehensible to everyone.<BR/><BR/>I'm really busy now with work, but I'll put up a post about cancer biology soon, for the first Bayblab blog carnival.<BR/><BR/>Cheers!The Key Questionhttps://www.blogger.com/profile/05426898630563791849noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-60041120841136262042007-08-19T20:43:00.000+08:002007-08-19T20:43:00.000+08:00Excellent post Lim, thank you! I didn't know anyt...Excellent post Lim, thank you! I didn't know anything about orbital mechanics, but your explanation was clear. You really need to write books. Very engaging.Glendon Mellowhttps://www.blogger.com/profile/03582347493421110738noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-27127609923870346012007-08-17T02:10:00.000+08:002007-08-17T02:10:00.000+08:00Lim - The Biological PhysicistLim - The Biological PhysicistJohn Evohttps://www.blogger.com/profile/10868904051881865159noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-84145048241493755542007-08-16T19:45:00.000+08:002007-08-16T19:45:00.000+08:00Hi Lim,Thanks for the explanation. Looks like u r ...Hi Lim,<BR/><BR/>Thanks for the explanation. Looks like u r quite a physics pro! <BR/><BR/>Will chew on the explanation and think over it..Teckhttps://www.blogger.com/profile/14295352820509148635noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-39457971776310846142007-08-16T13:18:00.000+08:002007-08-16T13:18:00.000+08:00To Kamel:I'm pretty sure they were aware of Kepler...To Kamel:<BR/><BR/>I'm pretty sure they were aware of Kepler's work, but I'm not certain why Gemini 4 was such a struggle for them. To read original mission reports and summaries, here is a useful resource - <BR/><BR/>http://www.geocities.com/bobandrepont/geminipdf.htm<BR/><BR/>To Teck:<BR/><BR/>Thanks for checking the quoted information!<BR/><BR/>Yes, the choice of words in the article is misleading, but I believe the concept is mainly correct.<BR/><BR/>Let's discuss this.<BR/><BR/><B>"By increasing his craft’s speed, he had increased its distance from the earth."<BR/><BR/>It was really by directing the thrust away from earth that the distance from earth increased. One could direct the thrust towards earth and increase speed towards earth, thereby moving to a lower orbit.</B><BR/><BR/>Not necessarily - because there are vectors involved (Oh no! Not vectors!!! :P )<BR/><BR/>The motion of a body in orbit can be resolved into two velocity vectors, the horizontal component (along a fixed altitude) and the radial component (towards/away from Earth).<BR/><BR/>If the astronaut fired engines such that the horizontal component of velocity increases, the vehicle will climb to a higher orbit.<BR/><BR/>Of course the radial component also matters, but resultant motion depends on both vectors - pointing downwards doesn't always lead to a lower orbit.<BR/><BR/>The easiest way (and much easier to calculate too) to drop to a lower orbit is reduce the horizontal component of velocity by flipping around and firing engines horizontally. <BR/><BR/>The space shuttle does this routinely to de-orbit for re-entry.<BR/><BR/><B>"In this new, higher orbit, the craft’s linear velocity, measured in miles per hour, was greater than before."<BR/><BR/>If the new higher orbit is a stable one, the total energy is greater than before. BUT, the new KE and hence linear speed should have been lower than the original KE in the lower orbit. <BR/>[ KE = GMm/(2r) ]</B><BR/><BR/>Again vectors are involved here. Let's say the target is ahead and above. The astronaut aims at the target, tilts his spacecraft to say, 45 degrees upward and fires engines.<BR/><BR/>As his vehicle increases in altitude, the horizontal component of velocity reduces (this is governed by Kepler's 2nd Law) but the radial component must necessarily increase, otherwise the vehicle can't climb to a higher orbit.<BR/><BR/>The resultant speed of his vehicle, measured in its direction of travel, does increase.<BR/><BR/>During orbital manoeuvers, the orbits of space vehicles are not circular, so the mathematics gets rather involved.<BR/><BR/>For more details about orbital mechanics, this is a superb resource:<BR/><BR/>http://aerospacescholars.jsc.nasa.gov/HAS/cirr/ss/3/2.cfm<BR/><BR/>Hope that this information will be helpful to you and your students!The Key Questionhttps://www.blogger.com/profile/05426898630563791849noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-74444119399337952722007-08-16T10:20:00.000+08:002007-08-16T10:20:00.000+08:00Hi Lim,After discussing with a colleague, we have ...Hi Lim,<BR/><BR/>After discussing with a colleague, we have some reservations about the reasoning employed here:<BR/><BR/>"By increasing his craft’s speed, he had increased its distance from the earth. In this new, higher orbit, the craft’s linear velocity, measured in miles per hour, was greater than before.<BR/><BR/>But its angular velocity—the rate at which it was traveling around the earth, measured in revolutions per hour—was lower. As Kepler had pointed out, objects in low orbits will complete an orbit around the earth faster than those in high orbits, even though their linear velocity is lower."<BR/><BR/>--------------------<BR/><B>"By increasing his craft’s speed, he had increased its distance from the earth."</B><BR/><BR/>It was really by <I>directing the thrust away from earth</I> that the distance from earth increased. One could direct the thrust towards earth and increase speed towards earth, thereby moving to a lower orbit.<BR/><BR/>------------------------<BR/><B>"In this new, higher orbit, the craft’s linear velocity, measured in miles per hour, was greater than before."</B><BR/><BR/>If the new higher orbit is a stable one, the total energy is greater than before. BUT, the new KE and hence linear speed should have been lower than the original KE in the lower orbit. <BR/>[ KE = GMm/(2r) ]<BR/><BR/>------------------------<BR/><B>angular velocity was lower.</B><BR/><BR/>Yes. This is correct. In a higher orbit, the angular velocity is lower.<BR/>[ angular speed is <I>inversely proportional</I> to radius of orbit to the power of 3/2. - Kepler's law]<BR/><BR/>------------------------<BR/><B>"objects in low orbits will complete an orbit around the earth faster than those in high orbits, even though their linear velocity is lower."</B><BR/><BR/>The first part is correct, given Kepler's law. BUT, the linear speed is higher in a lower orbit. <BR/>[ v = (GM/r)^1/2 ]<BR/><BR/>------------------------<BR/><BR/>Hmmm... looks like some dubious reasoning employed here. Can anyone here care to check if I'm right and shed some more light on this?Teckhttps://www.blogger.com/profile/14295352820509148635noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-84155105310894089582007-08-16T04:16:00.000+08:002007-08-16T04:16:00.000+08:00So that's why I can never catch up to my friend Bo...So that's why I can never catch up to my friend Bob... he's at a different ALTITUDE than me! If only I had read Kepler...<BR/><BR/>Keep it up, Lim!John Evohttps://www.blogger.com/profile/10868904051881865159noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-53918405181717309122007-08-16T02:27:00.000+08:002007-08-16T02:27:00.000+08:00Very interesting article, though I'm a bit shocked...Very interesting article, though I'm a bit shocked that NASA engineers wouldn't have been familiar with Kepler's work.Kamelhttps://www.blogger.com/profile/15548259062576527751noreply@blogger.comtag:blogger.com,1999:blog-30971820.post-59587592832520653242007-08-16T00:52:00.000+08:002007-08-16T00:52:00.000+08:00Brilliant account of orbital motion, Lim!I think I...Brilliant account of orbital motion, Lim!<BR/><BR/>I think I can tweak this to become an application question in my exams setting for my students! haha.. 职业病 ~~Teckhttps://www.blogger.com/profile/14295352820509148635noreply@blogger.com