Re: need arbitration about a physics problem
- From: gnygaard@xxxxxxxxxx
- Date: 25 Oct 2006 06:46:03 -0700
Sorcerer wrote:
<mainargv@xxxxxxxxx> wrote in message
news:1160932313.957804.323330@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| hi
|
| I need arbitration about a physics problem. (in a book)
| I disagree with the author of the book, but would really like second
| opinions on it.
|
| The author claimed that you when stand on Jupiter's moon Io, you would
| weight the same regardless of whether you are on the point exactly
| between Jupiter and Io (let's call it A), and the diametrically
| opposite side of that (let's call it B).
| The argument given by the author was that when you are on the point B,
| the moon Io accelerates together with you so that you would weight the
| same as you were on point A. I disagree.
|
| Here are the date given in the book.
| Io's orbit around Jupiter: 4.22 * 10^8 m
| Jupiter's mass: 1.899 * 10^27 kg
| the gravitational field on Io's surface is 1.81 N/kg
| the radius of Io is small so it's negligible in calculation
| --------------------------------------------------------------------------
| when at point A:
| gravitational field due to Jupiter alone: 0.71 N/kg
| gravitational field due to Jupiter and Io: 1.81-0.71 = 1.1 N/kg
| (toward Io)
| when at point B:
| gravitational field due to Jupiter and Io: 1.81+0.71 = 2.52 N/kg
| (toward Jupiter and Io)
| take into account when you stand on a scale on Io (accelerating toward
| Jupiter together with Io):
| 2.52 - 1.81 = 0.71 N/kg.
|
| Is the auther of the book right about weighing the same on opposite
| sides of Io?
Yes, he is.
No need for numbers, you do not weigh more at noon (A) than
you do at midnight (B).
Mass of Sun 1.98892 × 10^30 kilograms
Mass of Earth 5.9742 × 10^24 kilograms
No, he is not.
Yes, you wouldn't weigh much more or less at noon than at midnight on
Io, because it is in synchronous orbit around Jupiter and is
significantly farther from the Sun than Earth is, and far enough from
Earth for its contribution to be negligible.
But on Earth, there are indeed daily variations in little _g_ at any
fixed location on Earth's surface, due to the changing directions in
which the Moon and the Sun are pulling you (sometimes towards the
center of the Earth, sometimes away from it, usually somewhere in
between, and only when they are aligned are they pulling in either the
same direction or the opposite direction).
That difference would be much more pronounced on Io.
For example, see
http://www.space-electronics.com/Literature/Precise_Measurement_of_Mass.PDF
"1.5 Tidal variations An object on the surface of the earth is
attracted to every celestial body. Most of these masses are too far
away to have any significance on weight, but the sun and the moon do
have a significance. If you have a scale whose accuracy is 0.003 % or
better, you will notice that the weight of an object varies as a
function of the time of day. This effect is most pronounced during
spring and fall when the sun and moon align. This produces the "neap
tides" that often cause flooding of marinas at these critical dates."
Gene Nygaard
.
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