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Cell["A little jaunt brought on by a seemingly reasonable claim", "Subtitle",
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 "    ... the premise behind astrology is ridiculous ... the doctor or \
midwife or taxi driver who helped deliver you exerted a greater gravitational \
pull on you at your moment of birth than did the sun, the moon, or any of the \
planets.\n\nfrom ",
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 " by Natalie Angier\n\nLet us calculate.\n\nThe gravitational force between \
two objects varies with their masses and inversely with the square of the \
distance between them"
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Cell["\<\
While the quote addresses a person and a baby, we'll consider two adults, \
each weighing, say, 100 kg.  If they're 1/2 meter apart, the force between \
them is\
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which is actually pretty large.  For instance, this is equivalent to an \
amount of, say, salt, of mass\
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 "or, since there are 1,000 millimeters per meter, 0.126 ",
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 ", which is a cube about 1/2 mm on a side.\n\nWhich means that the person \
sitting across the table from you is exerting a gravitation force on you \
equivalent to the weight of a grain or two of salt in the palm of your hand.\n\
\nSo, back to the planets.  First, the Earth is clearly a planet and also \
clearly exerts quite a bit of force on you, far more than any taxi driver or \
midwife.  But ignoring that, what about the other celestial bodies?\n\nLet's \
consider Jupiter.  Jupiter is pretty big, but it's also pretty far away, so \
just knowing the form of the force law won't let us figure out if the force \
between you and Jupiter is large (we've got two competing effects, ",
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Jupiter's mass is easy to get"
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Cell["\<\
But how far away is it?  This value is changing all the time, of course, but \
we can get a good idea of what it is by calculating the maximum, so whatever \
result we get, we'll know that the real answer is at least that but almost \
always more.

The maximum occurs (approximately, since Jupiter and Earth move around the \
Sun in ellipses and not circles) when Jupiter is directly opposed to Earth, \
i.e. directly opposit with the Sun in the middle.  We can estimate how far \
this is by taking the sum of the maximum distance of both Jupiter and the \
Earth from the Sun\
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Cell["So what's the force between you and Jupiter?", "Text",
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Cell["Comparing to the force between you and a taxi driver", "Text",
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Cell["\<\
Oops!  Jupiter's force is five times as large.  And since we took the largest \
distance, this is the lower limit.

This raises the issue of what forces the other heavenly bodies exert on you.  \
First, though, let's simplify the math we have to do.

We're eventually going to be taking a ratio of two forces and some things are \
common to both numerator and denominator.  Specifically, G appears in both as \
does the mass of the person, so these both cancel, leaving\
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Just to check, we can calculate the answer for Jupiter and a taxi driver \
again\
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",
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So now all we need to do is calculate the forces.\
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Cell["\<\
Looks like the Earth, the Moon, and Jupiter all exert more force than your \
average taxi driver.  But the taxi driver clearly 'out gravity's everything \
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Though, we seem to be missing a rather large heavenly body\
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 "Bigger than anything but the Earth itself.\n\nWhich raises another issue, \
why does the Moon contribute more to the ocean tides than the Sun?  The Sun's \
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Moon's.\n\nI leave that as an exercise for the reader.  A hint: considering \
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Big difference.  Venus now wins over the taxi driver and Jupiter doubled its \
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Cell["\<\
We can conclude from this that Mercury's, Venus', and Mar's gravitational \
effect is dominated by its distance from us, while the force due to the \
larger planets depends mostly on their mass.

But we're not done yet.  Other things that vary a lot are the mass of the \
person and their distance from us. Looking at the equation, we can easily see \
that a 50kg (110lb) person will exert half the force. But what about, say, \
the taxi driver's hands holding a new born baby?  Here the distance is quite \
a bit closer.  Will that change anything?
 
I think a good estimate of the mass of a person's hand is about a pound, so \
two hands is about a kilogram.   What of the distance?  Before we could be \
cavalier about that since the planets are so far away, any little change we \
make at human scales is irrelevent to the final answer.  Now however, we have \
to be more careful.  The distance isn't zero, since the distance in the force \
equation is the distance between two centers of mass.  For a baby's head \
that's about 5cm from the surface and for your hand about another centimeter, \
for six centimeters total.\
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Cell["\<\
Not much change. How about one more: a car passing you on the freeway.\
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Jupiter still wins.  OK, I can't resist, one more:  you're visiting an \
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the mass of an Essex class WWII aircraft carrier is 27200 tons and it's width \
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OK, we finally overcame Jupiter but only by a factor of five. If you're 110 \
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Its gravitational force on you is equivalent to Jupiter's.  Note also that \
we're closing in on the Moon.  One might consider doing the calculation for \
the Sears Tower.

As a final observation, all this is relevent to why G, the gravitational \
constant, is the least well measured fundamental constant.  There's so much \
mass around that it's hard to know where it all is.\
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