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nowisthetime@pod.automat.click
nowisthetime

#CropCircles Are Not What You Think | Top Secret Alien UAP & #UFO News with Dr. #StevenGreer:

Source: https://youtube.com/watch?v=BTERk4se3sQ

#Crop #Circles Are Not What You Think | Top Secret Alien UAP & UFO News with Dr. Steven Greer
History of UFO Disclosure - Are crop circles messages from beyond or just another UFO anomaly? Dr. Steven Greer explores mysterious crop formations, featuring eyewitness accounts and theories of advanced technology, hinting at an extraterrestrial or transdimensional origin for authentic circles.

About Dr. Steven Greer:
Dr. Steven Greer is renowned for his dedication to disclosing classified UFO and extraterrestrial information. Over the past 30 years, he has briefed senior government officials worldwide, conducted hundreds of interviews, press conferences, and lectures. As the author of five books and the producer of documentaries seen by millions, he continues to educate people on peaceful contact with interstellar civilizations, the world of UFOs and UAPs, CE5 contact protocols, meditation techniques, and the transformative power of free energy. Dive into our discussions on Close Encounters, Unacknowledged, the Lost Century, and other documentaries, movies, and trailers. His podcasts with Joe Rogan, Patrick Bet David, Shawn Ryan, Danica Patrick, Logan Paul, Bob Lazar and other pioneers cover topics like remote viewing, ancient mysteries, Area 51, alien sightings, and advanced technology.

mkwadee@diasp.eu
Khurram Wadee

#JohannesKeppler was a brilliant #astronomer who studied the motion of #planets. Like everyone, he also had some strange ideas about the heavens, no doubt as a person in the middle ages would about the harmony of worlds and their purported relation to things like the #PlatonicSolids, which was of course bogus. He is probably best known for his famous three laws of #PlanetaryMotion which he reluctantly formulated when he had to abandon the idea that planets only orbit the #Sun in perfect #circles.

His First Law says that planets orbit the Sun in an #ellipse with the Sun at one #focus. Of course, a circle can be thought of as an ellipse where the two #foci have coalesced into one point (zero eccentricity). Here is what the orbit would look like in that case. The angular velocity of the planet is constant in this case and the areas swept out in equal times are identical.
Circular orbit

#Keppler's Second Law states that the areas swept out in equal times are always identical, even for eccentric ellipses. Here are two examples and you can show that the areas of all the sectors in each case are identical. The Sun is labelled S, the other focus is labelled S' and the centre of the orbit is labelled C.
Elliptic orbit e = 0.2
Elliptic orbit e = 0.5
The corollary of this law is that the angular velocity of the planet changes over its orbit, being faster when it is closer to the Sun and slower when it is further away. I have shown the constant-velocity position in red and you can see that it lags behind for half the orbit and leads for the other half.

These animations required me to learn the #mathematics of #CelestialMechanics and I had to find out what terms like #MeanAnomaly, #EccentricAnomaly and #TrueAnomaly are. It also requires the #NumericalSolution of one algebraic equation, which was fun to investigate. All the details are on the #Wikipedia page for Kepler's Laws here:
https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

The third law relates the orbital period to the mean distance from the Sun but that is not covered here.

#MyWork #Maxima #WxMaxima #FreeSoftware #Physics #Astronomy #AnimatedGif #Animation

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mkwadee@diasp.eu
Khurram Wadee

To construct a #ParallelLine to a given line (in blue) in 2D #EuclideanSpace, all you need to do is pick two #points and draw #circles centred at those points of a specified #radius. Draw a #perpendicular to the line at each point (in red) and then draw a new line passing through the intersection of the perpendicular with the circles and there is the line parallel to the original one. Here is the process shown in #Geogebra.

Parallel lines in Euclidean space

Using this #software, you can also explore #non-Euclidean space and here is the same action in #HyperbolicSpace (here in a #PoincaréDisc). #StraightLines are replaced by #GeodesicLines which look like #CircularArcs which intersect the #disc at #RightAngles. Circles are transformed to circles but their hyperbolic centres are not at the centre of their Euclidean centres. The boundary is analogous to infinity.

Repeating the construction for Euclidean space, you can see that the parallel lines diverge.

Parallel lines in hyperbolic space

#Mathematics #Geometry #NonEucldeanGeometry #EuclideanGeometry #FreeSoftware

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