Assume everything in this world is all homogeneous gold and there are 10kg of it altogether.
Volume of Gold: (10 kg)(1 000 g/1kg)(1 cm^3/19.32g)(1 m^3/ 1000000 cm^3) =5.18 E-4 m^3
Assuming the world is a sphere of pure gold of uniform density,
Volume = (4/3) pi r^3
r = cube root [ 5.18 E-4 m^3 (3/4 pi) ]
r = 4.98 E-2 m
Then assuming the man to be perpetually standing, with his center of mass to be at 1m above his feet when he is standing:
Gravitational Attraction = (G M1 M2)/s^2
Gravitational Attraction = (6.6742 E-11 N m^2 kg^-2)(10kg)(M2)(1/(1 m+4.98 E-2 m)^2)
Gravitational Attraction = M2 (6.06 E-10 N kg^-1)
F=MA
A=F/M
Acceleration due to gravity, g = (6.06 E-10 m s^-2)
That is around 0.606 nanometers per second square, which means that any money dropping from above our world would be moving down towards our poor guy on the surface at an impossibly languid pace, and if the money were to drop down, it would be a dreadfully long time before the two poor men can manage to catch it.
Luckily, our friend Shida was very clever, and used the word “sky”, which according to prestigious dictionaries refers to “The expanse of air over any given point on the earth; the upper atmosphere as seen from the earth's surface.” Therefore the money must have been teleported somehow, through dimensional gateways or other nifty devices we find in science fiction, onto the surface of our golden world, from the familiar skies of planet earth.
There are few ways money can appear in the middle of the sky of planet earth, and here we reduce the possibilities to
1. Dropped from a passing aircraft
2. Miraculous gift from heaven
Since aircraft generally do not fly more than 30km above the sea level, we can safely assume the money to be teleported from a part of the sky with at least 1kilopascal of air pressure, which is the atmospheric pressure at that height.
I do not know for exact the height of heaven, but from religious artworks it is apparent that deities or gods are often portrayed as resting on or hiding behind large, white fluffy clouds. The tallest of white fluffy clouds are the Cumulonimbus clouds, which form at altitudes of 2km – 15km. Hence we can assume that whether it is the case of our first or second alternative, the “money” in question must be from a height with an air pressure of greater than or equal to 1 kilo pascals.
Next, we are all well aware of the saying “money is the root of all evil”, and hence the money must not have been conjured in the heavens from nothing, and must have come from somewhere else. Since hell is associated with evil, then we must understand that money must have come from the center of the earth. We have no idea how hot the center of the earth really is, but most scientists agree that the value lies on a scale of a few thousand degrees. Regardless of what the exact temperature the center of the earth (where our money came from) is, we can be sure it is definitely far higher than the ignition temperature of paper, which is 233 degrees Celsius. This means that the instant the money is teleported or transported through some other means from the center of the earth to a certain height in heaven, it would combust readily with the oxygen in the atmosphere. Since paper is made from wood pulp, which is essentially cellulose, which is for a most part a hydrocarbon, we can put forward the assumption that shortly after the money appears in the sky it would have been reduced to carbon dioxide and water vapor.
Applying the conservation of kinetic energy to individual particles of carbon and hydrogen, the carbon dioxide and water vapor that would be teleported to our golden world would still retain a high temperature even after it reaches the golden world. As we all should already know, gases tend towards ideal gas behavior at high temperatures, and hence it should be reasonable to use the ideal gas laws to describe our “money”.
P1V1=k, at constant temperature, where k is a constant
A planet of 10 kg mass would have an extremely thin atmosphere due to the low gravity, one that is negligible. Observing a PV graph, with V as the y axis and P as the x axis, it is not difficult to see that as P tends towards 0, V would tend towards infinity. In other words, our “money”/mixture of carbon dioxide and water vapor, once appearing on the surface of the golden world, would immediately increase in volume drastically, with the final volume tending towards infinity.
Such an increase in volume is often referred to by laymen as “Inflation”.
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