Space Forum / Space Science / August 2008

Yes.  After I posted my question I realized that I'd left out an
important part which is that any trend after the 1968 Olympics to
recognize that performing at altitude may have influenced the outcomes
of events is a trend that was taking into account both wind resistance
and gravity.  Both are reduced at altitude, as is the amount of
available air for endurance event participants to breathe.

So, I was accustomed to thinking of the outfall of the '68 Olympics as
an air resistance thing, but I guess it would also be a recognition of
gravitational efffect upon performance?

I've been taught most of my life that the tides are, for the most
part, a result of the interaction of the moon with the Earth, so even
granting your equations, the effect of the Earth-moon interaction at
sea level seems to be palpable for bodies of water, and perhaps also
palpable for elite athletic competition.  Now, it may not be a simple
matter of the Moon's pull so much as that plus some aspects of the
Earth's rotation and orbit that are harder to understand?

-> I've been taught most of my life that the tides are, for the most
-> part, a result of the interaction of the moon with the Earth, so even
-> granting your equations, the effect of the Earth-moon interaction at
-> sea level seems to be palpable for bodies of water, and perhaps also
-> palpable for elite athletic competition.  Now, it may not be a simple
-> matter of the Moon's pull so much as that plus some aspects of the
-> Earth's rotation and orbit that are harder to understand?
 
Along most coasts, tides are quite small, less than a metre high. In
many places they are too small to be easily noticeable. Only in a few
places where there is an accidental resonance between the "sloshing"
frequency of the water in a semi-confined space and the roughly
twice-daily frequency of the tides does the amplitude become high.
 
Tides are produced by the interaction of (principally) the moon's
gravity with oceans of water that are thousands of kilometres in size.
Smaller bodies of water such as the Mediterranean Sea or Lake Superior
do not have perceptible tides. Even the largest athletes do not have
bodies large enough to be measurably affected.
 
                    dow

-> Thanks.  I'll concentrate on the altitude and its effect on weight and
-> the effect this might have on sports performance.
 
Well, in an extreme case, altitude might alter the weight (but not the
mass) of an athlete by about 0.1 percent. So suppose in the long-jump
the distance a jumper can go is inversely proportional to the force of
gravity pulling him down, then if he can jump about 5 metres, he might
go 5 millimetres further at high altitude than at sea level, from this
cause. Also, there would be less air resistance slowing him down, so he
should be able to jump further still.
 
5 mm is a significant distance in this sport.
 
While we're on this line of thought, have you ever considered the
effect the earth's rotation has on the trajectory of something like a
golf ball? The Coriolis effect pushes it sideways, in opposite
directions in the northern and southern hemispheres. When a golfer gets
a "hole in one", he must (purely by accident) have compensated for the
sideways force on the ball, which would otherwise have moved it several
centimetres from the hole.
 
                       dow

-> Gravity would be of such a small effect that it can be ignored.  To get a  
-> difference of 5 mm average, you'd have to be at an altitude where you  
-> couldn't breathe.
 
You'd have to be about 3 km above sea level. Sure, that's high, but not
high enough to prevent breathing. People live that high in places. It's
only about one-third as high as Everest.
 
                      dow

-> ....to make a measureable difference in gravity, with the earths mass? - and
-> diameter of just short of 8000 miles?
-> I'd like to see the math.
 
I've already posted it, but here it is again.
 
The earth's radius is 6000 km (to one dignificant digit). 3 km is
therefore 1/2000 of the radius. The force of gravity is inversely
proportional to the *square* of the distance from the earth's centre,
so changing this distance by 1 part in 2000 will cause a change in
gravity by 1 part in 1000. In the long jump, the distance jumped is
proportional to the time in the air which is omversely proportional to
the force of gravity pulling the jumper down. So if a jumper can jump
about 5 metres, which good jumpers can, then at an altitude of 3 km he
should be able to jump about 5 mm further than at sea level, from this
cause.
 
-> Above that, and especially on Everest, where more than a third of the people
-> die in the attempt, oxygen is carried in tanks.
 
Not always. Nowadays a lot of climbers get to the summit just breathing
the ambient air.
 
                      dow

My figures make more sense than yours, with your mixture of kilograms
and miles.
 
My estimate of a decrease of gravitational force, and therefore of the
weight of an athlete, of 0.1 percent per 3000 metres of height is close
to what you quote from Wiki, 0.28 percent for a height of 8000 metres.
Thanks for confirming my result.
 
There is nothing inaccurate in my calculation, or in the way I did it,
except that I slightly underestimated the distances that long jumpers
jump. In the Olympic Games a few days ago, the best jumpers were going
more than 6 metres. I estimated 5. So the increase in distance at a
height of 3000 metres would be more than 6 millimetres, compared with
at sea level. In the sport, distances are measured to the nearest
centimetre, so 6 millimetres would often change a measured result.
 
                       dow
 
-> Use some figures that make sense.  Your answer is a small percentage of your
-> error in estimation.  The earths mass is grossly estimated at 5.97 x 10^24  
-> kg, (note the error in the 10^21 kg range) and the diameter, depending on  
-> how you take it, about 7926 miles. (error in miles)  How do you justify an  
-> answer in mm. or the weight of an athlete or his equipment?

-> 'Wiki' has an article that I skimmed, and shows a difference in wieght of  
-> ..28% with over 8000 m in height.  I doubt any measurable difference in an  
-> athletes performance could be measured that finely.

-> http://en.wikipedia.org/wiki/Earth's_gravity 

-> "David Williams" <david.williams@bayman.org> wrote in message  
-> news:1219246633.873.1219237249@bayman.org...
-> >-> ....to make a measureable difference in gravity, with the earths mass? -
-> >and
-> > -> diameter of just short of 8000 miles?
-> > -> I'd like to see the math.
-> >
-> > I've already posted it, but here it is again.
-> >
-> > The earth's radius is 6000 km (to one dignificant digit). 3 km is
-> > therefore 1/2000 of the radius. The force of gravity is inversely
-> > proportional to the *square* of the distance from the earth's centre,
-> > so changing this distance by 1 part in 2000 will cause a change in
-> > gravity by 1 part in 1000. In the long jump, the distance jumped is
-> > proportional to the time in the air which is omversely proportional to
-> > the force of gravity pulling the jumper down. So if a jumper can jump
-> > about 5 metres, which good jumpers can, then at an altitude of 3 km he
-> > should be able to jump about 5 mm further than at sea level, from this
-> > cause.
-> >
-> > -> Above that, and especially on Everest, where more than a third of the  
-> > people
-> > -> die in the attempt, oxygen is carried in tanks.
-> >
-> > Not always. Nowadays a lot of climbers get to the summit just breathing
-> > the ambient air.
-> >
-> >                       dow

You seem to have a doltish obsession with making an easy problem seem
difficult. I showed a calculation, so simple that it can be done in the
head, that showed that, *from the effect of altitude on gravity*, a
long jumper wouold be able to jump the better part of a centimetre
further at an altitude of 3000 metres than at sea level, *all other
things being equal*. Since distances are measured to the nearest
centimetre, this would have a practical effect, making it easier to
break records at high altitudes,
 
You keep throwing out unnecessary numbers, such as the oblateness of
the earth. Certainly, there are other factors that affect how far an
athlete can jump, most significantly the wind, and latitude would be
one of these factors too. But my calculation was specifically about the
effect of altitude. Everything else is irrelevant.
 
Keep It Simple, Stupid.
 
If you want to argue that athletic records are meaningless because of
all the other factors, besides an athlete's ability, that can affect
results, then I would agree that you have a point. But if that's what
you mean, then that's what you should say.
 
                          dow
 
-> The units are irrelavent, and easily converted.  I could supply specific  
-> numbers, but you'd pick on those, too.  -doesn't matter.  All the figures I  
-> quoted are more accurate, and you still can't use them to make your math any
-> better.

-> Your guesses at numbers with errors on the order of (corrected) kilometers,  
-> with answers in millimeters, are the nonsense here.
-> Math can't be accurate unless the answer is  greater than (you don't seem to
-> comprehend this) the error in the original numbers.
-> Since your answer is orders of magnitude LESS than your errors in guessed-at
-> figures, your original statements and math are invalid.

-> The math from Wiki gives estimates for a model of gravity for a planet with  
-> ideal condition of even density, and all other factors the same.  It's  
-> stated in the article.
-> In that *theoretical* world, using your estimates, a .1% difference would  
-> change the weight of a 100 kg. athete by 100 grams.
-> Had a sandwich lately?  It weighs more.
-> Realistically, that's neglible.  All the other factors, including the mood  
-> of the athlete, the weather that day, and lots more I'm sure an actual  
-> athlete could name better than I, would be more notable than any change in  
-> gravity.
-> That's why gravity is such a hot topic in physics.  It's only recently that  
-> equipment has been designed to work on such small differences.  -on the  
-> order of 10^-20 g.
-> Go for any numbers you make up and believe.  I'll stick with the measured  
-> results.
-> Have fun.


-> "David Williams" <david.williams@bayman.org> wrote in message  
-> news:1219592763.873.1219549891@bayman.org...
-> > My figures make more sense than yours, with your mixture of kilograms
-> > and miles.
-> >
-> > My estimate of a decrease of gravitational force, and therefore of the
-> > weight of an athlete, of 0.1 percent per 3000 metres of height is close
-> > to what you quote from Wiki, 0.28 percent for a height of 8000 metres.
-> > Thanks for confirming my result.
-> >
-> > There is nothing inaccurate in my calculation, or in the way I did it,
-> > except that I slightly underestimated the distances that long jumpers
-> > jump. In the Olympic Games a few days ago, the best jumpers were going
-> > more than 6 metres. I estimated 5. So the increase in distance at a
-> > height of 3000 metres would be more than 6 millimetres, compared with
-> > at sea level. In the sport, distances are measured to the nearest
-> > centimetre, so 6 millimetres would often change a measured result.
-> >
-> >                        dow
-> >
-> > -> Use some figures that make sense.  Your answer is a small percentage of
-> > your
-> > -> error in estimation.  The earths mass is grossly estimated at 5.97 x  
-> > 10^24
-> > -> kg, (note the error in the 10^21 kg range) and the diameter, depending  
-> > on
-> > -> how you take it, about 7926 miles. (error in miles)  How do you justify
-> > an
-> > -> answer in mm. or the weight of an athlete or his equipment?
-> >
-> > -> 'Wiki' has an article that I skimmed, and shows a difference in wieght  
-> > of
-> > -> ..28% with over 8000 m in height.  I doubt any measurable difference in
-> > an
-> > -> athletes performance could be measured that finely.
-> >
-> > -> http://en.wikipedia.org/wiki/Earth's_gravity 
-> >
-> > -> "David Williams" <david.williams@bayman.org> wrote in message
-> > -> news:1219246633.873.1219237249@bayman.org...
-> > -> >-> ....to make a measureable difference in gravity, with the earths  
-> > mass? -
-> > -> >and
-> > -> > -> diameter of just short of 8000 miles?
-> > -> > -> I'd like to see the math.
-> > -> >
-> > -> > I've already posted it, but here it is again.
-> > -> >
-> > -> > The earth's radius is 6000 km (to one dignificant digit). 3 km is
-> > -> > therefore 1/2000 of the radius. The force of gravity is inversely
-> > -> > proportional to the *square* of the distance from the earth's centre,
-> > -> > so changing this distance by 1 part in 2000 will cause a change in
-> > -> > gravity by 1 part in 1000. In the long jump, the distance jumped is
-> > -> > proportional to the time in the air which is inversely proportional  
-> > to
-> > -> > the force of gravity pulling the jumper down. So if a jumper can jump
-> > -> > about 5 metres, which good jumpers can, then at an altitude of 3 km  
-> > he
-> > -> > should be able to jump about 5 mm further than at sea level, from  
-> > this
-> > -> > cause.
-> > -> >
-> > -> > -> Above that, and especially on Everest, where more than a third of  
-> > the
-> > -> > people
-> > -> > -> die in the attempt, oxygen is carried in tanks.
-> > -> >
-> > -> > Not always. Nowadays a lot of climbers get to the summit just  
-> > breathing
-> > -> > the ambient air.
-> > -> >
-> > -> >                       dow

You're revealing yourself as an idiot.
 
If you think that calculations done as you think they should be done
will produce a conclusion different from mine, then let's see them. Put
up, or shut up.
 
I don't include the earth's mass in my calculation because I can see in
advance it will cancel out. In order to calculate a jumper's takeoff
velocity, I will have to start with the distance he can jump, since
that's a measured quantity, and work backward, using the earth's mass.
Then I'll work forward again, using the mass again, and it will simply
cancel out! So I might as well just use the distance a jumper can
jump in the calculation, and not worry about the earth's mass.
 
But I guess you're too stupid to see that.
 
Ken Tucker has known me for decades. If he criticizes my logic, I take
the criticism seriously. But criticism from you is clearly of no
consequence.
 
                   dow

-> Very good.
-> Go to the head of the class!

-> "Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message  
....
-> > So is that why high jumpers and pole-vaulters do
-> > better when the moon is full, because of tidal force?
-> > Ken
-> > PS:Usually Daves "guestimates" are as accurate
-> > as my calculator!
-> > "all other things being equal" is a partial derivative.  
 
So you're praising Ken for saying that my "guesstimates" are often very
good. Yet you seem to think the opposite.
 
Consistent you're not.
 
                                dow

-> Thanks:-). Your discussion got to me to thinking
-> if we launched a rocket (all other things being equal)
-> at high tide (full or new moon) if less propellant
-> would be required to achieve the same orbit if we
-> launched at neap tide.

-> I'm hoping for a simple answer, otherwise I'll need to
-> enter the Riemann Christoffel "tidal tensor",  R_abcd
-> into the geodesic.
-> Regards
-> Ken
 
My first guess is that it would be better (require less fuel) to have
the spacecraft travel to the moon at approximately new moon than at
other times of the month. Full moon would be the worst time. The
rotating vector of the sun's gravity (rotating because of the earth's
orbital motion) would add momentum to the craft at new moon and remove
it at full moon - I think. Both new and full moon are spring tide
situations, so the situation doesn't match the tides.
 
To be sure of this, I think a simulation should be done. I know you
already have most if not all of the necessary software, so you should
be the person to do it.
 
                       dow

-> LOL, you never did before, but really, the equation is
-> acceleration = GM/r, with a minor variance on "r",
-> should I Rubber Bible G,M,r and dr ?
-> Regards
-> Ken
 
No need. If the athlete's takeoff velocity can be resolved into a
horizontal component, Vh, and a vertical component, Vv, then at landing
he will be going downward at Vv, so the total change in velocity is
2Vv. The time this will take is 2Vv/g, so the distance he will travel
is 2.Vh.Vv/g. As you say, g=GM.r^2, so the distance the jumper travels
is 2.Vh.Vv.r^2/(GM). If the value of r changes from r1 to r2, then the
two distances the athlete jumps are:
 
d1 = 2.Vh.Vv.r1^2/(GM)
d2 = 2.Vh.Vv.r2^2/(GM)
 
So d2/d1 = (r2/r1)^2
 
Behold! The V's, G, and M have cancelled out! I could see that coming.
The twit obviously couldn't.
 
So if r2/r1 = 1.0005, which will be true if r1 = 6000 and r2 = 6003 (in
kilometres), then d2/d1 qill be 1.0005^2, which is almost precisely
1.001. If d1 = 6 (metres), d2 will be 6.006 metres. In other words, at
an altitude of 3000 metres, a good long-jumper who can jump 6 metres at
sea level will be able to jump 6 millimetres further. Since distances
are measure to the nearest centimetre, his jump distance will probably
be conted as 1 cm further than at sea level.
 
Ken, I'm sure this was obvious to you. Apparently at least one other
person here lacks your insight.
 
                    dow

-> It's obvious now! 1 part in 1000 outputs 1 cm yeah(?).
-> Regards
-> Ken
 
In the marathon last week, plenty of athletes' times were within 1 part
in 1000 of each other.
 
In the final of the women's 100 metre hurdles, the favourite to win,
who was ahead at the time, just touched the second-last hurdle with her
foot. She stumbled and lost the lead. Quite likely, if her foot had
been 1 mm higher, i.e. about 1/1000 of the height of the hurdle, she
wouldn't have touched the hurdle and would have won the gold medal.
Such tiny differences can have huge effects.
 
                     dow

-> I think that same distance would ratio in Pole-Vault
-> as well (?). We can turn that (1.001) around to a
-> reduction of 1gm / Kg of the jumpers weight, so
-> an 80Kg athelete would jump 1/cm further for each
-> 80 gms of weight loss.
 
Not if the loss is muscle.
 
                     dow