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Re: [Phys-L] Falling - the tale of a simple 1st degree non-linear ODE

On 1/16/2019 10:44 AM, David Bowman wrote:

On the topic of long falls, it seems that a bowling ball dropped at Space Station altitudes (220 km) might well linger in the vicinity.
According to the ESA at this moment the ISS' current altitude is about 416 km. According to Wikipedia the ISS' orbit decays about 2 km/month. When it gets too low it is given a boost. The space agencies apparently like to keep its altitude in the range of 330 to 435 km according to Wikipedia.:
Oops! I transposed Metric and American Customary units for altitude!
Though g may only drop a few percent the atmospheric density drops much more dramatically at 100 km to perhaps  ~ 1 millibar.
According to the Standard Atmosphere (1976) @ 100 km g = 9.505 m/s^2 (about a 3.1 % drop from the sea level official value), the atmospheric density is 5.604 x 10^-7 kg/m^3, and the air pressure is 32.01 mPa = 0.0003201 mb.

David Bowman
I found these data for pressure and density more difficult to reconcile.
The ISA values which I can readily find go to 86 km where I find a temperature of 196.65K is given, with pressure 0.886 Pa and density 1.57 x 10^-5 kg/m^3

The American Meteorological Society claims the ISA posits a constant g and a dry gas column here:

This glossary offers a rather puzzling paragraph:

1. TheARDC Model Atmosphere
1959, extended the above [1976/ bw] standard approximately as follows:
The lapse rate from 11 to 25 km is 0°C km^-1 .
The lapse rate from 25 to 47 km is +3.0°C km^-1 ; temperature at 47
km is +9.5°C.
The lapse rate from 47 to 53 km is 0°C km^-1 .
The lapse rate from 53 to 75 km is -3.9°C km^-1 ; temperature at 75
km is -76.3°C.
The lapse rate from 75 to 90 km is 0°C km^-1 .
The lapse rate from 90 to 126 km is +3.5°C km^-1 ; temperature at
126 km is +49.7°C (molecular-scale temperatures).

Not sure how an ARDC Model of 1959 can modify an ideal atmosphere of 1976. In any event, this ARDC specification suggests the ambient temperature has risen to ~232K at 100km

Perhaps it would be simpler for me to ask for your source for the 1976 ISA data?

Regards Brian W