Seems Kepler was a very naughty boy..

http://www.nytimes.com/1990/01/23/scien ... gewanted=1

Done in 1609, Kepler's fakery is one of the earliest known examples of the use of false data by a giant of modern science.

- Cuchulainn
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Seems Kepler was a very naughty boy..

http://www.nytimes.com/1990/01/23/scien ... gewanted=1

Done in 1609, Kepler's fakery is one of the earliest known examples of the use of false data by a giant of modern science.

http://www.nytimes.com/1990/01/23/scien ... gewanted=1

Done in 1609, Kepler's fakery is one of the earliest known examples of the use of false data by a giant of modern science.

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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- Traden4Alpha
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Here's one: http://www.astronomy.ohio-state.edu/~po ... 5/gps.htmlInteresting. Do you have a link?Kepler is not good enough for GPS -- they need Einstein to get the accuracy.

Actually, up at Myvatn was a retired American prof talking about his day with Atlas (D?) in the 50s/60s and the very issue of time synchronisation. They let the satellite broadcast the 'time'. There is no day or night up there.

The showstopper if relativity is ignored in GPS:

If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

- Cuchulainn
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Having found [$]y[$] you now need to solve for the true anomaly [$]\theta[$], How?

[$]\tan^2(\theta/2) = a \tan^2(y/2)[$] where [$] a = (1+\varepsilon)/(1 - \varepsilon)[$].

What's [$]\theta[$]?

[$]\tan^2(\theta/2) = a \tan^2(y/2)[$] where [$] a = (1+\varepsilon)/(1 - \varepsilon)[$].

What's [$]\theta[$]?

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

you keep changing this, there have been at least 3 different expressions since I started to answer itHaving found [$]y[$] you now need to solve for the true anomaly [$]\theta[$], How?

[$]\tan^2(\theta/2) = a \tan^2(y/2)[$] where [$] a = (1+\varepsilon)/(1 - \varepsilon)[$].

What's [$]\theta[$]?

[$]\tan^2(\theta/2) = a \tan^2(y/2)[$] so [$]\theta=\pm2\arctan\left[\sqrt{a \tan^2(y/2)}\right][$], with the addition of some multiple of [$]2\pi[$] if necessary for physical reasons

- Cuchulainn
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Sorry, I wanted to write the unknown on the left. Looks like a whole bunch of solutions. I suppose only one of them is physically correct?

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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- Cuchulainn
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- Cool way, isn't it? to find power series for tan (t).

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