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Flat Earth Investigations / Re: The Gravity Conundrum...

« on: January 07, 2020, 09:26:44 AM »

Gravity

Flat-earthers seem to have a lot of problems with the idea of gravity, and this is not surprising, because science has a lot of problems with it too. To understand why this is so, it is helpful to look at the history.
The idea of gravity as a force acting between bodies at some distance from each other goes back to Robert Hooke (1635-1703), the leading English scientific researcher of his time. The story starts with the Danish astronomer Tycho Brahe (1546-1601), who like his near-contemporary Galileo is known to posterity by his forename rather than his surname. Tycho spent many years observing the positions of the planets in relation to the starry background before the invention of the telescope. His data was analysed by the German mathematician Johannes Kepler (1571-1630), who spent a lifetime making sense of the data until he was able to derive his three laws of planetary motion. He did not attempt to provide a reason for the existence of his laws.
This came to some degree from Hooke’s researches, who concluded that each planet was maintained in its orbit by some unexplained force “acting at a distance” between it and the Sun, inversely proportional to the square of the distance between them. He discussed this idea with the mathematician Isaac Newton (1643-1727), who had already established his laws of rectilinear motion, and Newton used it, without acknowledgment of Hooke, mathematically to underpin Kepler’s laws on the elliptical motions of the planets. His theory, known as Newtonian mechanics, worked perfectly to predict future events in the solar system, and until Albert Einstein (1879-1955) started to consider events in which bodies moved at an appreciable fraction of the speed of light, continued to do so. Since nothing we can currently make and no massive body naturally occurring in the solar system moves at any such speed, Newtonian mechanics works for rocket scientists too. There is no need to invoke the rather difficult Einsteinian ideas in day-to-day calculations of gravitational effects: Newton’s theory gives the right answers, and that is all anyone can ask.
Newton, who as he said himself was basing his theory on the ideas of other people, wrote that he had been able to explain the motions of the planets by ascribing them to “the power of gravity” which was his name for the force proposed by Hooke. But he then said that he had not been able to discover the causes of that power, and when pressed he came up with his famous remark “hypotheses non fingo,” which means “I don’t know and I’m not going to guess.” This phrase has been used by commentators to mean that Newton never produced any hypotheses, which is just not right; it is important to restrict it, as Newton did, to an enquiry into the causes of gravity itself.
The idea of action at a distance is philosophically unsatisfactory, and repeated efforts were made to clarify the causes of gravity. We must distinguish the effects of gravity, which at the speeds encountered in ordinary motions are defined by Newtonian mechanics and so are well understood, from the causes of gravity, the essence or reality of it. These remained hidden until Einstein developed his general theory of relativity, which essentially asserted that action at a distance, including gravity as generally understood, was a fiction and was not required in a description of the motions of the world. Gravity in this theory was an effect of the curvature of spacetime; Newtonian mechanics was an approximation applicable only at lower speeds. Flat-earthers have fastened on this concept, and, finding the ideas and mathematics of relativity too hard to understand, have happily denied the existence of gravity without coherently advancing anything to take its place. They are therefore unable to explain the motions of the planets in space, but since they don’t believe in space either, they don’t see this as a problem. No flat-earther has ever suggested that Tycho’s data is all faked, but then again this is probably because they’ve never heard of Tycho.

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Flat Earth Investigations / Re: The view from my bedroom window

« on: December 15, 2019, 10:13:23 AM »

Natasha’s second post (which I’ll refer to as “N2”, hoping she won’t take offence) seems to be leading to three separate lines of thought. The most important is the identification of the light she sees. We seem to be agreed that this is not the lighthouse at Gatteville on the north coast of France, but for clarity’s sake I ought to state that this shows two very short flashes of white light – each of one-tenth of a second – separated by 2.5 seconds; the whole repeated every ten seconds. Its direction from Brighton is 210° True, or S30°W; what the mariner calls south-west by south.
   N2 now says that she thinks the light is a flash every 4 seconds, and its direction is “more to the west from her perspective” (by perspective I think she means position). Fortunately flashing 4 seconds is pretty unusual in the Brighton area, the only example shown on the chart being a buoy showing a yellow light about a mile off the west end of the Marina.
   We don’t know which tower block Natasha lives in (and we don’t want her to tell us on the Internet!) but there are not many tower blocks close to the beach and we won’t go far wrong by assuming she lives somewhere near Bedford Square. The buoy in question bears about 120° True from the I360 Tower, which the mariner would call south-east by east. If Natasha means that Gatteville is “more to the west” of the buoy, that would be right.
   If Natasha wants to find out more about the navigation lights visible from her bedroom window, she can’t do better than look at a copy of Admiralty Chart No. 1652, which shows every buoy and lighthouse along the coast from Selsey Bill to Beachy Head, with Brighton of course smack in the middle. Unfortunately there’s no chart agent close to Brighton, but there’s any amount of sellers on the Web. Each chart costs £26.40. Or of course there might be a copy in the local reference library.
   The second theme arising from N2 is Natasha’s height and her horizon distance. The statement that she’s 82 metres above mean sea level (MSL) is a bit unlikely. To achieve this she’d have be living on about the twentieth floor of Sussex Heights, the tallest building in Brighton, the only one that exceeds about 50m. On the other hand, I think there was an indication in N1 that she lives on the sixth floor of her block. This would be about 24 metres, or say 80 feet,  above the ground. We have to add on say fifteen feet for the base of the block above MSL, and five feet for her eyes above the floor when she’s standing at the window, so I expect her to be at 100 feet or 30 metres above MSL. Her horizon distance would then be about 10 miles. (You don’t need a curvature-calculator for this: for heights below about 500 feet, use the simple formula d in miles equals the square root of the height in feet. You’re not after precision to the nearest yard.)
   GPS is notoriously unreliable when it comes to heights, but it should be able to distinguish between 82m and 30m. If she puts her GPS receiver on the windowsill and lets it settle for ten minutes, it should give something like the right answer.
   Lastly, we need to look at Natasha’s ideas about the ships out at sea. She sees them as travelling in a straight line along the “horizon line.” The first thing to say here is the visible horizon is not a straight line, it’s an arc of a circle centred on the viewer. All points on it are the same distance from the viewer: that’s why we can speak of a “horizon distance.”
   Large ships travelling westwards in the Channel from the Dover Strait have to remain in a marked shipping lane about ten miles wide, which ends just south of Brighton and is more than 20 miles off the coast. Ships going eastward have to enter a similar lane about 15 miles further south still. So from Natasha’s point of view, they will probably look as though they’re all much the same distance away; and of course, since they are below her horizon, she won’t see them during the day, but the navigation lights of the larger ships will probably be visible to her at night – green lights on those going west, red lights on those further away going east.
   I hope all this is helpful to Natasha: it’s certainly fun for me!

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Flat Earth Investigations / Re: The view from my bedroom window

« on: December 12, 2019, 04:50:38 PM »

The Gatteville lighthouse is on the Pointe de Barfleur, the north-easterly corner of the Cherbourg peninsula, and thus about 100 miles from Brighton. The nominal range listed for this light is 29 miles, which is the distance it can be seen when the actual visibility is 10 miles, and so it must have a brightness of about 3.5 million candelas, brighter than any lighthouse in Britain. Even so, it's unlikely that it could be seen at a distance of 100 miles in perfect visibility. Intervisibility depends on the distance to the horizon from both the light and the viewer: if they add up to more than the distance between them, then OK; if not, not.
   The height of 72 metres is the height above Mean High Water Springs: most of the time the light will be a few metres higher than that above the water. The tidal range at Cherbourg is about 5 metres, so on average the light is 74.5 metres above the sea.
   For the light, a height of 74.5 metres or 244 feet means a horizon distance of 15 miles. So the lady's flat needs a horizon distance of 85 miles, which requires a height of over 7,000 feet. Even in Brighton, a hilly town, this seems unlikely.
   So we have to ask: how does she know she's looking at Gatteville? Can she write back and describe the character of the light -- how many flashes, how often, what colour? This is how lights are identified, in the dark, when you can’t see the tower.