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 Libration on tidelocked planets (Read 10977 times)
 EDG Ultimate Member oh, crumbs!!! Posts: 611 Gender: Re: Libration on tidelocked planets Reply #15 - 09/16/07 at 17:57:21   huh. that's handy. When did amazon start doing that?! Back to top (formerly known as Mal)   IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Libration on tidelocked planets Reply #16 - 09/16/07 at 20:12:50   I don't know.  I didn't feel like looking for my copy of SSD, so I just Googled for "synchronous rotation empty focus" and that popped up.  I was surprised too. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Libration on tidelocked planets Reply #17 - 09/19/07 at 13:02:37   It seems to be possible to derive a formula , altough approximative to second order ...(M&D pg 44) Using the formulas of M&D in the pages 38-44 one can derive the "delta" angle if the anomaly (f) or the eccentric anomly (E) is known   Derivation is shown in annex .     This formula works under the assumption that the planet always is directed to the empty focus , so the angle under which the sun is seen must be "delta" .   Plugging this values into excel one can hardly distinguish the "delta" from a sine for eccentricities up to 0.25 ( Pluto ) .   ( Help : isn't it possible to reduce the size of the picture here?) Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Libration on tidelocked planets Reply #18 - 09/21/07 at 10:04:11   Applying the above formulas gives the following plot ... In abscis the E - value ( eccentric anomaly in radians) , in ordinate the longitude in degrees under which the sun is seen from the eccentric moving tital locked planet .   The plot was generated for ascending values of eccentricity starting with 0.0 ....to 0.9 with steps of 0.1.   The last picture shows the plot for e=0.95. Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Libration on tidelocked planets Reply #19 - 09/21/07 at 10:20:51   That's interesting how it deviates from a pure sine wave.   Is this mean longitude or true longitude?   What does the y-axis represent?  Is that time?  Does this represent 1 complete orbit?   0.0 to 0.9 step 0.1 = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 I can see 10 frames in the animation.  Where does 0.95 come from? Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Libration on tidelocked planets Reply #20 - 09/21/07 at 10:25:06   Quote from Tony on 09/21/07 at 10:20:51:That's interesting how it deviates from a pure sine wave. Is this mean longitude or true longitude? What does the y-axis represent?  Is that time?  Does this represent 1 complete orbit? 0.0 to 0.9 step 0.1 = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 I can see 10 frames in the animation.  Where does 0.95 come from?   The longitude is the angle of view ( see delta) in the formula , or the angle as seen from the planet between the focus and the empty focus .   This is the y-axis , in degrees .   I have 10 values :  0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 0.95.   The x-axis is the eccentric anomaly , somewhat more than one orbit ( one orbit = 6.28 ) Back to top IP Logged
 Tony YaBB Administrator Posts: 1058 Gender: Re: Libration on tidelocked planets Reply #21 - 10/10/07 at 14:42:19   Quote from Tony on 09/16/07 at 14:13:55:Quote from frankuitaalst on 09/16/07 at 13:36:17:You're right ! Is really amazing ! Is this geometrically correct if you draw lines to the focus ?   I printed the picture and tried that.  It's close but not perfect.  But I manually pieced together the image, so I wouldn't expect it to be perfect. Quoting myself     It turns out it is not quite perfect as Grant pointed out in the BAUT thread: http://www.bautforum.com/questions-answers/64727-tidelocked-planets-libration-cr eating-day-night-cycles.html#post1084211 .  I made a new image to verify.  I used Gravity Simulator to take a screen shot every 1/12th of an orbital period for an e=0.8 orbit.  Then I photoshopped in the two-tone balls, rotating them 30 degrees each time, and drawing a line perpendicular to their hemisphere dividing line.  They don't all point to the empty focus, but they're close. Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Libration on tidelocked planets Reply #22 - 10/10/07 at 14:51:27   Yes , the statement  that one side is always directed towards the empty focus is true as a first order approximation ( Murray&Dermot says ).    If also the higher order of e ( ie e^2...) are taken into consideration the statement is not true anymore .   That's a pitty .   In the other case it would have as a consquence that the position of a planet could be calculated pure from geometrics .   BTW : the evolution I pictured in the previous post is also of first order ( ie . +/-exact for small e ). Back to top IP Logged
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