User talk:Tweesdad
Regarding the free fall page: "Without air resistance (Parabolic Approximation): changed heading to uniform gravitational field. The solution is not an "approximation"
In nature there is no such thing as a "uniform gravitational field". Therefore all uniform gravitational fields are by definition approximations to real gravitational fields. These approximations are used so often that people easily forget that they are not the true solutions.
The equations in question were first derived by Galileo before the discovery of the inverse square law. Newton was the first to point out that these equations are only approximate.
When these equations are used to represent graviational fields, they are commonly known as to as "the parabolic approximation". (http://www.lightandmatter.com/html_books/0sn/ch02/ch02.html Section 2.3.2 Circular orbits). Since these equations have a commonly accepted name, they should be referred to by that name in the header.
Galileo's equations ARE the exact solution for free fall in an accelerating frame. In other words, the equivalence princpal is only true in the limit of infinitesimally small distances.
Since the subject of this page is freefall in a gravitational field, Galileo's equations NOT exact. In fact, over reasonable distances, they are not even close. The error in elapsed time is 27% (1-pi/4) after falling one earth radius.
My reply --------
Thanks for your interest, comments and references. The reference to "parabolic approximation" is a good one, but it does not refer to the vertical motion of a falling object but rather the parabolic trajectory (i.e. path in space) as an approximation to an elliptical orbit. Googling "parabolic approximation" produced no other relevant links. And for the general reader I think the term is confusing.
As for Galileo's equations not being "exact", we have a difference in semantics I guess. For no air drag and a uniform gravitational field, the solutions are exact. It's the Earth's field itself which isn't "exactly" uniform. in reality. (It's not exactly inverse-square either, by the way). What I tried to communicate was that the Galilean equations were an exact solution given the assumptions. But even for the record-breaking skydives mentioned in the article, g is very close to being constant. You say that "the error in elapsed time is 27% (1-pi/4) after falling one earth radius", but I'd like to meet the person who falls radially to Earth from an altitude of 6400 km!
I would rather use the term "approximation" for something like the series expansion of y(t) for an inverse-square field given later in the article. Hope that clarifies things a little, feel free to reply (and sign your reply!) Tweesdad 05:59, 27 December 2009 (UTC)
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