A lot of this is going over my head but I thank you for having this available for us to watch. I'll probably watch it a few times after this to let it all sink in!
This lecture was great in terms of geometrical detail, some important geometrical identities were overlooked and collapsed into just an equality sign, not even a comment, by my lecturer. This video unveiled all of those collapsed details, I do however think that this lecture was unclear regarding the linear relationship between time and true anomaly, that is only satisfied for the mean anomaly, not the true one. It was not really brought up so after following your derivation for a while I was like, oh no - what is going on here. This details was better captured by my lecturer, who instead assumed a more general form of the ellipse (shifted in x) and used the notion of angular momentum after defining the mean anomaly, then getting the derivative form and conducting integration which then led to Keplers equation. Nonetheless, I am greatful that you provide us with this detailed content. I am looking forward to your intricate explanations in the other videos as well as your animations.
Thank you for the quick recap at the end, it is really helpfull. May be I am wrong but at 56:43, the formula to compute the time t seems to be wrong. To me, t should be equal to M*T / (2*pi). Since the mean anomaly is the "projection" of the true anomaly on an perfect circle, to compute the time it takes from an angle 0° to, let's say, 30°, we compute the eccentricity anomaly with the 30° thanks to the formula of E. Then compute the mean anomaly M and perform the formula I mentioned above. It seems to work for me when I want to compute the time it takes to my satellite to go from true anomaly to another. But may be I did not understand what t is.
Thank you Dr Toellner for your video. I have a quick question. When you are solving for eccentric anomaly (18:45), you state that cos E and sin E produce ambiguous solutions. To get around it, you use some trig identities to write the angle in terms of a half angle identity. Is there a reason why the half angle of tangent is picked over the half angle of cosine? Both would produce an unique solution in the domain 0 to 2pi.
When calculating true anomaly, at what condition we should add pi() to overall calculations results, which change the sign of the co-ordinates in the final calculations?
ruclips.net/video/rDQTZadS058/видео.html the formula for θ(t)/θ(T) is wrong and cannot be derived from the formula for t/T as the angle θ is not a linear function of time. This gets "corrected" in the following slide where mean anomaly is introduced.
so just replace the theta(t) with mean anomaly right, because mean anomaly treats it like a circular orbit, which in the case of circular orbit, the anomaly angle and time are linear with each other
many thanks for this. 893 subscribers, but in a parallel universe you should have 893 million subscribers. fortunately or unfortunately, this planet prefers naked women teaching them how to put make up on before going out to get knocked up. greetings from a Greek guy.
@@deniousp Don't hate on waifu's man. That's the culture lol. But thanks to this channel because it's so easy for me to review this stuff and makes it easier because without using this type of knowledge daily, you lose it. I took a spacecraft dynamics and control course a couple of years ago, and it was the best class I've ever enrolled in during my undergrad.
A lot of this is going over my head but I thank you for having this available for us to watch. I'll probably watch it a few times after this to let it all sink in!
This lecture was great in terms of geometrical detail, some important geometrical identities were overlooked and collapsed into just an equality sign, not even a comment, by my lecturer. This video unveiled all of those collapsed details, I do however think that this lecture was unclear regarding the linear relationship between time and true anomaly, that is only satisfied for the mean anomaly, not the true one. It was not really brought up so after following your derivation for a while I was like, oh no - what is going on here. This details was better captured by my lecturer, who instead assumed a more general form of the ellipse (shifted in x) and used the notion of angular momentum after defining the mean anomaly, then getting the derivative form and conducting integration which then led to Keplers equation. Nonetheless, I am greatful that you provide us with this detailed content. I am looking forward to your intricate explanations in the other videos as well as your animations.
amazingly clear and detailed explanation
it was helpfull Sir, we really gain alot
at 11:18 is theta a linear function of time? It needs to be the case for the equation to work isn't it?
Thank you for the quick recap at the end, it is really helpfull.
May be I am wrong but at 56:43, the formula to compute the time t seems to be wrong. To me, t should be equal to M*T / (2*pi).
Since the mean anomaly is the "projection" of the true anomaly on an perfect circle, to compute the time it takes from an angle 0° to, let's say, 30°, we compute the eccentricity anomaly with the 30° thanks to the formula of E. Then compute the mean anomaly M and perform the formula I mentioned above.
It seems to work for me when I want to compute the time it takes to my satellite to go from true anomaly to another.
But may be I did not understand what t is.
Thank you Dr Toellner for your video. I have a quick question. When you are solving for eccentric anomaly (18:45), you state that cos E and sin E produce ambiguous solutions. To get around it, you use some trig identities to write the angle in terms of a half angle identity. Is there a reason why the half angle of tangent is picked over the half angle of cosine? Both would produce an unique solution in the domain 0 to 2pi.
beautiful :)
Excellent! Thanks!
Glad it was helpful!
thank you Sir
When calculating true anomaly, at what condition we should add pi() to overall calculations results, which change the sign of the co-ordinates in the final calculations?
ruclips.net/video/rDQTZadS058/видео.html the formula for θ(t)/θ(T) is wrong and cannot be derived from the formula for t/T as the angle θ is not a linear function of time. This gets "corrected" in the following slide where mean anomaly is introduced.
yea I was thinking the same too
so just replace the theta(t) with mean anomaly right, because mean anomaly treats it like a circular orbit, which in the case of circular orbit, the anomaly angle and time are linear with each other
many thanks for this. 893 subscribers, but in a parallel universe you should have 893 million subscribers. fortunately or unfortunately, this planet prefers naked women teaching them how to put make up on before going out to get knocked up.
greetings from a Greek guy.
lol misogynistic physics simp, I bet the only naked women you've seen are your anime waifu and your mom
@@deniousp Where was the misogyny?
@@deniousp Don't hate on waifu's man. That's the culture lol. But thanks to this channel because it's so easy for me to review this stuff and makes it easier because without using this type of knowledge daily, you lose it. I took a spacecraft dynamics and control course a couple of years ago, and it was the best class I've ever enrolled in during my undergrad.
what's the formula you have used to calculate mean anomaly at 25:01
Kepler's formula: M = E - ε sin E
you did not prove why M=E-e sinE ??? where it came from
at 24:22 mistake in r formula, should be as 23:35
snu ece:)