tag:blogger.com,1999:blog-3596550435682943926.post6883159562399188399..comments2023-01-05T02:20:45.223-08:00Comments on Hop's Blog: Lamentable Lagrange articlesHop Davidhttp://www.blogger.com/profile/12923433894475072056noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-3596550435682943926.post-79356948376904663862017-01-22T10:34:44.144-08:002017-01-22T10:34:44.144-08:00Melon, it's a 3 body problem, therefore messy....Melon, it's a 3 body problem, therefore messy. I don't know of a nice clean simple equations for figuring departure and arrival burns in this case. The best way I know of is Runge-Kutta approximations and chopping the trajectory in many small time intervals.<br /><br />I have made approximations based on more straightforward 2-body approximations. A LEO to EML1 orbit would be a 300 x 320351 km ellipse (I'm using earth altitudes here, not distance from earth's center). This transfer orbit's perigee speed is 10.81 km/s and apogee speed is .22 km/s. I used the Vis Viva equation to get these numbers.<br /><br />The LEO burn is pretty much a 2 body scenario. So I go with 10.8 - 7.7 to get 3.1 km/s TLI burn.<br /><br />But the apogee burn to park at EML1 is trickier. A circular 2 body orbit at that altitude would be moving 1.1 km/s. However EML1 is moving at the same angular velocity as the moon. So EML1 is moving more like .85 km/s. So for a long time I went with .85 -.22 or about a .63 km/s circularization burn at apogee.<br /><br />Then I grabbed some of Bob Jenkins' orbit sim JAVA code (with his permission) and did my own earth moon sims. The moon exerts an appreciable influence over a fairly large neighorbhood of the apogee. The moon lends a hand. So it's a little less than .63 km/s. Maybe around .55 to .6 km/s.<br /><br />So adding a 3.1 perigee burn to a .6 apogee burn, I usually say LEO to EML1 is about 3.7 km/s.<br /><br />And the orbit is time reversible so the same numbers going from EML1 to LEO. Although with LEO you could have the spacecraft pass through the upper atmosphere and using aerobraking to shed velocity. So the LEO circularization burn could be less than 3.1 km/s.<br /><br />I know that's not a satisfactory answer but it's the best I can give you right now.Hop Davidhttps://www.blogger.com/profile/12923433894475072056noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-35085735560701220322017-01-21T15:36:36.834-08:002017-01-21T15:36:36.834-08:00 I find the L1 position at 326000 km along the... I find the L1 position at 326000 km along the Terra-Luna line, and the <br />gravitational balance point at 346000 km, but I am not able to calculate <br />the single impulse delta-V to go from circular low earth orbit to either <br />position. Is there a straightforward way to do this, and to find the <br />position in LEO for the burn? -MBMelcon<br />Melcon37https://www.blogger.com/profile/11220458377451730966noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-28374004001887984992017-01-17T07:57:06.383-08:002017-01-17T07:57:06.383-08:00Hello, Hop! Thank you for an excellent article. ...Hello, Hop! Thank you for an excellent article. I appreciate that your crusade took you to galacticjourney.org, and I've amended the offending sentence. I also responded to your comment.<br /><br />Hope to see you around in the future. Gideon Marcushttp://galacticjourney.orgnoreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-68885260140324040982017-01-15T13:28:12.965-08:002017-01-15T13:28:12.965-08:00Lionel, nice link. Thanks. Hope I'll have some...Lionel, nice link. Thanks. Hope I'll have some time to explore that website. Yeah, presenting math and physic ideas visually is what I try to do.Hop Davidhttps://www.blogger.com/profile/12923433894475072056noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-12932373839641246362017-01-15T07:51:52.505-08:002017-01-15T07:51:52.505-08:00Hi Hop, sure, and I respect your determination for...Hi Hop, sure, and I respect your determination for correctness. <br /><br />Changing the subject, I recently came across a youtube channel with some really nicely done explanations of mathematical concepts via artwork, and it reminded me of some of the things on your website. Have you come across <a href="https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/featured" rel="nofollow">3Blue1Brown</a>? Very helpful for learning and explaining mathLionel Whttps://www.blogger.com/profile/01930963095389078741noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-64796691627452167122017-01-11T11:53:57.123-08:002017-01-11T11:53:57.123-08:00This is a particularly good explanation and illust... This is a particularly good explanation and illustration.<br /><br /> The 'short text' explanation might be that 'the Lagrange points are those points in a two-body system where the sum of forces acting on a third body balance out in a rotating frame of reference'. That's a simplification that obscures at least as much as it reveals, but might be useful as a reference note.<br /><br />@ Matter Beam:<br /> As far as posting more often, I know I've had trouble finding suitable topics. My existing posts cover pretty much all the ground I intended to cover, so now it's just incidental or forward-looking posts and occasional 'paper rocket' math adventures.<br /> Hop's body of work is so thorough that it is difficult to find an orbital-mechanics topic that isn't already covered in a clear and informative way. From this outsider's perspective it seems many recent posts here are prompted by current events and are intended to clear up misperceptions.Anonymoushttps://www.blogger.com/profile/17210444292050682322noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-56545842674875239432016-12-15T12:44:11.597-08:002016-12-15T12:44:11.597-08:00Lionel W., thanks.
Re: Fraser -- he and his crew ...Lionel W., thanks.<br /><br />Re: Fraser -- he and his crew do drum up interest for space and space exploration. And we all make mistakes, myself included.<br /><br />But sources of misinformation can prevent understanding of a topic. So long as Fraser's articles/vids on Lagrange points and Interplanetary Transit System remain uncorrected, I'll be annoyed.Hop Davidhttps://www.blogger.com/profile/12923433894475072056noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-74624479294073381792016-12-14T15:01:29.031-08:002016-12-14T15:01:29.031-08:00Great explanation Hop.
Please do cut Fraser a bi...Great explanation Hop. <br /><br />Please do cut Fraser a bit of slack though - he and the rest of the UT crew go to great lengths to inform people, misinformation does happen by accident - nobody is perfect! I'm sure Fraser will get around to making a correction, perhaps via a later video.Lionel Whttps://www.blogger.com/profile/01930963095389078741noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-42574050312242886022016-12-11T07:42:17.084-08:002016-12-11T07:42:17.084-08:00Fraser Cain, going to your Lagrange vid and articl...Fraser Cain, going to your Lagrange vid and article I see they are still wrong. Your article on the Interplanetary Transit Network is still misleading. <br /><br />Universe Today remains a source of misinformation.Hop Davidhttps://www.blogger.com/profile/12923433894475072056noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-11411979260528203282016-12-05T05:58:21.945-08:002016-12-05T05:58:21.945-08:00Very interesting explanation.
I hope you posted m...Very interesting explanation.<br /><br />I hope you posted more often...Matter Beamhttps://www.blogger.com/profile/16721504049578296529noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-46212228028242612682016-12-02T11:46:13.802-08:002016-12-02T11:46:13.802-08:00Thanks for the debunk! I'll be more careful ne...Thanks for the debunk! I'll be more careful next time I delve into this topic to get my analogies right. Fraser Cainhttp://universetoday.comnoreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-17385434193767300202016-11-28T12:59:10.355-08:002016-11-28T12:59:10.355-08:00Ah, it appears you are correct. That is a very go...Ah, it appears you are correct. That is a very good diagram, too!Ian Malletthttps://www.blogger.com/profile/00105420256087675307noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-52975432730761818372016-11-28T07:12:28.449-08:002016-11-28T07:12:28.449-08:00Ian, it is the line through Pluto's center tha...Ian, it is the line through <b>Pluto's center</b> that that crosses at 60º. Pluto's center, Charon's center and L4 or L5 form an equilateral triangle. But the barycenter does not lie on the corner of an equilateral triangle. It sits on an angle slightly greater than 60º. The top angle becomes a little less than 60º. I will try to clarify this by adding an illustration to this blog post.Hop Davidhttps://www.blogger.com/profile/12923433894475072056noreply@blogger.comtag:blogger.com,1999:blog-3596550435682943926.post-29202840504396406332016-11-27T20:54:06.562-08:002016-11-27T20:54:06.562-08:00Something has gone wrong. For the force vectors f...Something has gone wrong. For the force vectors for L4/L5, you say "The angle between these vectors is 60º", yet the angle through the barycenter needs to be 60º, and doing both is geometrically impossible.Ian Malletthttps://www.blogger.com/profile/00105420256087675307noreply@blogger.com