by neufer » Fri Oct 17, 2008 5:58 pm
Henning Makholm wrote:tbirchar wrote:So, why hasn't TIROS2 succumb to this drag over its 48 years in orbit?
Compare the orbits - TIROS is about 350 km higher than the ISS, even given the lower orbit of 700-750 km reported by Wikipedia. For back-of-the-envelope purposes, assume a scale height of 10 km for the atmosphere. Thus the density at TIROS heights should be about e^-35 ~ 10^-15 of what it is around the ISS. I have no good idea how the speed of orbital decay varies with atmospheric density, but let's be conservative and imagine it's goes as the fifth root. Even then, the TIROS satelite should be able to orbit for about 1000 times as long as the ISS between needing artificial boosts. I.e., about a century!
(Actually, one can probably not extend the exponential scaling law that high without significant correction, but any way you slice it there'll be many orders of magnitude of difference between 350km and 700km).
Indeed:
The exosphere hydrogen gas scale height ~ 500 km. ~ 4 x 14 x 8.5 km.
http://apod.nasa.gov/apod/ap000701.html
------------------------------------------------
scale height: H = kT/Mg
with:
T(exosphere) ~ 1200 ~ 4 x room temperature
M(hydrogen) ~ 1 ~ 1/14 x Nitrogen
------------------------------------------------
http://upload.wikimedia.org/wikipedia/c ... sphere.svg
<<The exosphere is the uppermost layer of the atmosphere. On Earth, its lower boundary at the edge of the thermosphere is estimated to be 500 km to 1000 km above the Earth's surface, and its upper boundary at about 10,000 km. It is only from the exosphere that atmospheric gases, atoms, and molecules can, to any appreciable extent, escape into space. The main gases within the exosphere are the lightest gases, mainly hydrogen, with some helium, carbon dioxide, and atomic oxygen near the exobase. The exosphere is the last layer before space.>>
-----------------------------------------------------------
With such large exosphere hydrogen gas scale heights
the real comparison here is not between Tiros & the ISS
but between both such heavy/dense exosphere satellites
and the "fluff ball" that was
Echo 2
which lasted 5+ years in the exosphere:
<<Echo 2, a 41.1 m diameter metallized PET film balloon with an improved inflation system to improve the balloon's smoothness and sphericity, was launched January 25, 1964 on a Thor Agena rocket. It was used for more passive communications experiments, and also to investigate the dynamics of large spacecraft and for global geometric geodesy. NASA abandoned passive communications systems in favor of active satellites following Echo 2. Echo 2 reentered on June 7, 1969.>>
[quote="Henning Makholm"][quote="tbirchar"]So, why hasn't TIROS2 succumb to this drag over its 48 years in orbit?[/quote]
Compare the orbits - TIROS is about 350 km higher than the ISS, even given the lower orbit of 700-750 km reported by Wikipedia. For back-of-the-envelope purposes, assume a scale height of 10 km for the atmosphere. Thus the density at TIROS heights should be about e^-35 ~ 10^-15 of what it is around the ISS. I have no good idea how the speed of orbital decay varies with atmospheric density, but let's be conservative and imagine it's goes as the fifth root. Even then, the TIROS satelite should be able to orbit for about 1000 times as long as the ISS between needing artificial boosts. I.e., about a century!
(Actually, one can probably not extend the exponential scaling law that high without significant correction, but any way you slice it there'll be many orders of magnitude of difference between 350km and 700km).[/quote]Indeed:
The exosphere hydrogen gas scale height ~ 500 km. ~ 4 x 14 x 8.5 km.
http://apod.nasa.gov/apod/ap000701.html
------------------------------------------------
scale height: H = kT/Mg
with:
T(exosphere) ~ 1200 ~ 4 x room temperature
M(hydrogen) ~ 1 ~ 1/14 x Nitrogen
------------------------------------------------
http://upload.wikimedia.org/wikipedia/commons/1/18/Atmosphere_with_Ionosphere.svg
<<The exosphere is the uppermost layer of the atmosphere. On Earth, its lower boundary at the edge of the thermosphere is estimated to be 500 km to 1000 km above the Earth's surface, and its upper boundary at about 10,000 km. It is only from the exosphere that atmospheric gases, atoms, and molecules can, to any appreciable extent, escape into space. The main gases within the exosphere are the lightest gases, mainly hydrogen, with some helium, carbon dioxide, and atomic oxygen near the exobase. The exosphere is the last layer before space.>>
-----------------------------------------------------------
With such large exosphere hydrogen gas scale heights
the real comparison here is not between Tiros & the ISS
but between both such heavy/dense exosphere satellites
and the "fluff ball" that was [b]Echo 2[/b]
which lasted 5+ years in the exosphere:
[img]http://www.arsastronautica.com/inflatables/echo2.jpg[/img]
<<Echo 2, a 41.1 m diameter metallized PET film balloon with an improved inflation system to improve the balloon's smoothness and sphericity, was launched January 25, 1964 on a Thor Agena rocket. It was used for more passive communications experiments, and also to investigate the dynamics of large spacecraft and for global geometric geodesy. NASA abandoned passive communications systems in favor of active satellites following Echo 2. Echo 2 reentered on June 7, 1969.>>