Recent content by Charles Link

One thing that comes out of the scattering theory is the scattering (in the rest frame of the moon) makes two asymptotes, (incoming and outgoing), where the total scattering angle is ## 2 \arctan(GM/(v_o^2 b )) ## where ## v_o ## is the asymptotic speed and ## b ## is the impact parameter which...

and a follow-on to post 90: It appears the Nasa engineers really had to thread the needle on this one to get the rocket to do what it did. It is basically a textbook scattering problem, sending the rocket in the vicinity of the moon, but of all the possible trajectories, they needed to have...

In post 78 I mentioned the symmetry to the hyperbola that occurs in the rest frame of the moon. Further study shows the point of closest approach didn't necessarily happen directly opposite the earth, but I think the Nasa engineers worked it out so that was approximately the case. That way...

He mentions about ten minutes into the video in post 88 about the bright ring around the lower part of the earth, and he didn't seem to know what it is. I could be wrong, but I think that one is obvious=it's Rayleigh scattering from the earth's atmosphere. (about 20 or 30 miles of atmosphere...

To comment further on the above post 84: The approximate formula I have for ## v ##, (it neglects any effect from the moon), integrates to get ## t ## as a function of ## r ## for a straight line path, even though the actual path was a very flat ellipse. The closed form integration for the...

That is basically what I did, and this one did not turn out to be of the slingshot variety. Instead, in going back and forth between the two frames of reference, there was just a slight decrease in speed in the frame of reference of the earth all the way to the closest approach which was...

In post 73 I mentioned something that took me a while to figure out, and it wasn't at all obvious to me: The conservation of energies using the potential of the moon and the change in potential of the moon does not hold in the rest frame of the earth because the moon is moving, and thereby the...

It may be worth mentioning, to add to my post 78 above, (the theory is all spelled out in the Kleppner and Kolenkow text), the hyperbola rotated by 90 degrees so that it is oriented sideways has formula in polar coordinates of ## r=\frac{17.0}{1-2.33 \cos{\theta}} ##, with ## r ## in...

To comment more on my post 74 above, I dug out my Kleppner and Kolenkow mechanics textbook from college, and the path neglecting the earth in the rest frame of the moon is an unbound hyperbolic trajectory. Given the speed at the minimum point was 3140 m.ph. at a distance of 5170 miles from...

I'd also like to comment on the first photo of post 66. I think what looks like the moon's shadow is simply the earth illuminated by the sun from the side. If it were a solar eclipse, it would occur at the time of a new moon. The new moon according to a google occurred on april 17, 2026. The...

The calculation with the moon's gravitational potential does indeed work in the rest frame of the moon. To compute it, we can to a good approximation simply ignore the effect of the earth when the rocket is near the moon. For initial conditions, we can put the rocket 6000 miles from the path...

In regards to posts 60 and posts 63 above, I did a calculation assuming the total energy of the rocket stays constant using the gravitational potentials of the earth and moon, and that calculation showed the rocket should speed up considerably, up to about 2600 m.p.h. I determined that...

I do think if the nail is a permanent magnet, that the tip will be of one polarity and the head of the other polarity. That would make it so that the tip gets centered on one region of the underlying magnet and the head on the other. The alternative is that the magnetism on the head is more...

I presume you are referring to any permanent magnetism, if there is any, appears to be minimal, but why not check for it, like @Baluncore suggested, with a compass.

From the response of the nail it is likely it is not permanently magnetized, if that is what you are referring to. It is responding how one might expect to induced magnetization. If the nail permanently had one pole on the top and the opposite pole on the tail, the response would be for each...