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161 lines
11 KiB
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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Tim Good · Follow Optical Engineer at Honeywell (company) · Updated Nov 6
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I’ve been in a “discussion” with Michael Brenner recently on the topic of projectile trajectories and how that relates to orbital mechanics. He denies the accuracy of the description of an orbiting body as being in free fall, where the body is sometimes described as constantly falling but missing the planet.
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Honestly, I can understand how that description falls somewhat flat (no pun intended), but I provided a clear example to him of how the trajectory of an object moving at orbital velocity can be calculated using either a circular path or parabolic path over a short distance, and the two methods provide the exact same answer (within seven significant digits over 1 km). He refused to accept this but also refused to explain where I made a mistake. Instead he simply kept saying “what about an object 1 km high launched horizontally at 1000 m/s?” I told him the elliptical path which that would produce would result in significantly more difficult math to solve, and why can’t he just tell me what’s wrong with my simple circular orbit example? But, he thought he could just take my claim that the math is hard as some kind of victory.
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Well, I decided I needed to challenge myself. After all, I love math. So, this can’t be that hard, right? But part of me said “he doesn’t deserve the dignity conferred on him by my answering his question when he refused to answer mine.” But, it kept eating at my curiosity. So, no, he doesn’t deserve it, and he likely won’t appreciate it either, but I just had to prove (once again) to myself that the world continues to makes sense, and I can look at the work I did and feel a deep sense of satisfaction, regardless of what he thinks.
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So, here it is. I use a few basic principles:
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1. Newton’s Law of Gravity
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2. Kepler’s second law
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3. Conservation of energy
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Initial conditions are nothing more than a given altitude and horizontal velocity.
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Upvote · 29
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 1/6
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 2/6
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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The only math Michael knows how to do is captured in the Excel sheet in cells C12 and C13 which assumes constant gravity and a flat earth. That, of course, is wrong, because with a projectile range of 14 km the ground has started to drop, as can be seen, by about 16 m. But when an elliptical trajectory is calculated and compared to a parabolic trajectory, both over a sphere, the difference in the two results is only 9 mm over those 14 km, so once again (coincidentally) accurate to seven significant digits.
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To anyone who happens to cross paths with Michael, if you see him going on about Newton’s cannonball thought experiment, or ballistic trajectories, or “hammer-throw physics” (???), or saw-tooth paths, any any related nonsense, please direct him back to this derivation of the conclusive answer to his arrogant question as a reminder that math and physics doesn’t care what he thinks.
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Edit 11/5/23:
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As anticipated, Michael claimed victory in the face of defeat but for a far more compelling reason than typical flerfer excuses. He has a formula he uses that he claims calculates the trajectory of an object using “orbital mechanics.” At one point earlier in our discussion I said his formula was bogus. However, after my post to DFE, Michael showed me that his formula actually produced the same result for the [1000 m/s, 1 km] example as my derivation and to the same degree of accuracy. Admittedly, this came as a surprise, as I had not analyzed his formula in detail. So, now I have. To begin, here’s his formula, which I will say is very clean and simple:
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As Michael sees it, this equation combines orbital mechanics and simple ballistics by subtracting the centrifugal acceleration from the gravitational acceleration. As he sees it, when the two are equal, gravity is supposedly cancelled and the object no longer falls, so this should represent orbit. And, it is true that at the speed where the denominator goes to zero, the velocity is, in fact, at the traditional value for a circular orbit. On the other hand, if velocity is zero, the result is the simple parabolic range over a flat earth.
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Michael believes that if orbital mechanics are real, then at any intermediate value of velocity the range from this equation would be the same as what you find using the simple parabolic equation over a flat plane. That does not hold, so he thinks he has proven his point. His misconception supports his notion that terrestrial ballistics and orbital mechanics are not a seamless expression of a single theory of physics.
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The problem, of course, is that his understanding of this formula is flawed. He does not know how to derive it properly. His notion of subtracting centrifugal acceleration from gravity suffers from the simple fact that centrifugal force is not an actual force. Michael will
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 3/6
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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disagree, of course, and he pushed back by showing me that his formula calculates the same result as mine, as shown below.
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But, before we let him celebrate too much, let’s look at the proper derivation of his formula. At first, I thought it might be the full symbolic solution of one of my previous derivations, but at faster velocities or higher altitudes, all three formulas diverge, as seen below.
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So, that’s not the answer. As it turns out, the formula is achieved when we make another parabolic assumption, this time for the shape of the earth. With both the trajectory and the surface assumed to have parabolic shape, the solution has a simple closed form.
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So, his formula is the exact, non-approximated solution for a parabola intersecting a parabola, having nothing to do with centrifugal forces. Except there’s just one problem. If you’ve been paying close attention, you’ll have noticed that there is a slight difference between Eq. (31) above and “Michael’s formula,” that being that the former uses RE and the latter uses RA . I’m not certain if Michael even realized he betrayed his position by making that switch. Perhaps he did it knowingly, but I’ll allow that he did it by mistake. Lastly, I’ll add one last analysis showing the proper progression from terrestrial to orbital, using the elliptical equations.
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 4/6
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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When Michael revealed his finding to me, I gave him my word that I would investigate it and update my post accordingly. I have now done that. I expect that I will hear from him again. We’ll see if he has a similar commitment to integrity in how he responds.
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654 views · View 29 upvotes
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Add a comment...
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Add comment
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Adrian Fagg · Oct 29
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That’s nice work, Tim. Michael kept wanting me to ‘do the maths’ in my part of the same argument, but I was too lazy and it would have taken me quite a while. But I also felt that I didn’t want to waste time arguing on his terms, especially since (hmiso…re)
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Gert Van Der Walt · Oct 30
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Brenner believes that, if the ISS really existed, the occupants would be stuck to the roof similar to a bucket of water swung through 360 degrees. Only this reveals his inability to understand basic physics.
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Richard Adams · Oct 31
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And yet that’s precisely what a Sun and Moon whizzing around a flat disk would require; the complete denial of centrifugal forces acting on them. Flatties don’t think and that’s the problem right there. It’s like their ice wall holding in th(em…ore)
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Chris Harrington · Oct 29
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Wow. That's commitment. Of course, the flerf will probably just throw up his hands and say, “math isn't reality!” …and then crap all over the chess board, over turn the table, and flap off. But I applaud you for sticking yo your guns and giving the f(lmerof…re)
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Adrian Fagg · Oct 30
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I don’t know if you have seen Michael’s maths but he has some very strange ideas. He thinks elliptical orbits are impossible because things must orbit around a centre that is normal to the orbital trajectory. Gravitational force(cmaonr…e)
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Chris Harrington But… if he gets parabolic trajectories, why can't he get elliptical orbits……
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J HAM · Oct 31
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Bruh, are you wearing a graduation gown in your picture? I'm just curious that's all.
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Chris Harrington · Oct 29
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This is SO GREAT! Now all Michael has to do is actually fire a cannon ball from a height of 1km and then measure how far it goes! Then he'll see the Earth is a
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sphere! 🤣🤣🤣
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Tim Good · Oct 29
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 5/6
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1/1/24, 5:01 PM
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I’ve been in a “discussion” with Michael Brenner [ https://www.quora.com/profile/Michael-Brenner-13 ] recently on the topic of projec…
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I know, right? When I finished working it out and saw that the example conditions he chose only provide an accurate answer over a sphere even when using a parabola, I thought “great. Now he’ll just say something like ‘see, i(tm…ore)
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Chris Harrington Yep. Their biggest problem with math is that they just don't understand it.…
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🤣
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Neil Davies · Oct 29
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Brenner is just an arrogant, ignorant Dunning-Kruger poster boy. He consistently gets his sorry arse handed to him by Torsten Hehl, and now you’ve really exploded his tiny mind. Way to go!
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Martin Dennett · Oct 30
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“He consistently gets his sorry arse handed to him by Torsten Hehl,”
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Got, my dear friend. Got. Since he had his arse handed to him one too many times, Brenner took the only option left available to him…
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Neil Davies You’re right, of course. The dreaded “Block (insert name here)” option.
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About the Author
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Tim Good
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Optical Engineer at Honeywell (company) MS in Mechanical Engineers, Lehigh University Graduated 1995 69.6K content views 685 this month Active in 2 Spaces Joined November 2017
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Follow · 24
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View more in Debunking Flat Earth
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https://debunkingflatearth.quora.com/I-ve-been-in-a-discussion-with-Michael-Brenner-https-www-quora-com-profile-Michael-Brenner-13-recently-on-th… 6/6
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