Calculating Altitude Of Nominal Burst - Orbital Decay

[LaurieAG]

Does anybody know how to calculate an incoming satellites Altitude of Nominal Burst (not balloon burst altitude)?

 

I have summarised (bastardised it to make it readable) an Orbital Decay program/text from the following link as the program has 180km hard coded as its Altitude of Nominal Burst. While any Altitude of Nominal Burst modifications would have to use the variables and calculations shown below the only one I'm not really sure about is the variable re. The 300 km start height would have to be changed to a variable but everything should work ok. 

 

I suspect the recent increase in solar activity has also increased the total solar X-ray flux as well as the particle precipitation rate and therefore this has impacted the atmospheric density that TIANGONG I is flying into increasing the temperature/friction and caused it to drop faster.

 

http://www.sws.bom.gov.au/Category/Educational/Space%20Weather/Space%20Weather%20Effects/SatelliteOrbitalDecayCalculations.pdf

 

Re-entry is assumed to occur when the satellite has descended to an altitude of 180 km. In all but the heaviest satellites (those with a mass to area ratio well in excess of 100 kilogram per square metre), the actual lifetime from an altitude of less than 180 km is only a few hours. 

...

This implementation does not allow for variations in the space environment, and as a result is only suitable for short time periods, or during longer times when solar and geomagnetic activity do not show significant variation. This generally only occurs around the years of solar minimum.

 

Variables

RE-ENTRY = FALSE

Re = 6378000!  

Me = 5.98E+24 'Earth radius and mass (all SI units)

G = 6.67E-11 'Universal constant of gravitation

pi = 3.1416: T = 0: dT = .1 'time & time increment are in days

D9 = dT * 3600 * 24 'put time increment into seconds

H1 = 10: H2 = H 'H2=print height, H1=print height increment

R = Re + H * 1000 'R is orbital radius in metres

P = 2 * pi * SQR(R * R * R / Me / G) 'P is period in seconds

 

Data Input

Satellite mass    (kg) = M

Satellite area   (m^2) = A

Starting height   (km) = H

Solar Radio Flux (SFU) = F10

Geomagnetic A index    = Ap

 

Basic Algorithm

WHILE RE-ENTRY = FALSE
   SH = (900 + 2.5 * (F10 - 70) + 1.5 * Ap) / (27 - .012 * (H - 200))
   DN = 6E-10 * EXP(-(H - 175) / SH) 'atmospheric density
   dP = 3 * pi * A / M * R * DN * D9 'decrement in orbital period
   IF H <= H2 THEN 'test for print
      Pm = P / 60: MM = 1440 / Pm: nMM = 1440 / ((P - dP)) / 60 'print units
      Decay = dP / dT / P * MM 'rev/day/day
      PRINT P / 60; MM; Decay 
      H2 = H2 - H1 'decrement print height
   ENDIF 
   IF H < 180 THEN  '******************** CORRECT RE-ENTRY TEST HERE 
      EXIT ' re-entry    
   ENDIF
   P = P - dP: T = T + dT 'compute new values
   R = (G * Me * P * P / 4 / pi / pi) ^ .33333 'new orbital radius
   H = (R - Re) / 1000 'new altitude (semimajor axis)
LOOP 'keep flying satellite

 

[spartan45]

 

Does anybody know how to calculate an incoming satellites Altitude of Nominal Burst (not balloon burst altitude)?

 

I have summarised (bastardised it to make it readable) an Orbital Decay program/text from the following link as the program has 180km hard coded as its Altitude of Nominal Burst. While any Altitude of Nominal Burst modifications would have to use the variables and calculations shown below the only one I'm not really sure about is the variable re. The 300 km start height would have to be changed to a variable but everything should work ok. 

 

I suspect the recent increase in solar activity has also increased the total solar X-ray flux as well as the particle precipitation rate and therefore this has impacted the atmospheric density that TIANGONG I is flying into increasing the temperature/friction and caused it to drop

 

I am not so sure that cross-sectional area should be used as a variable as the object could be tumbling or start tumbling so perhaps it is better to use object density instead. The 300 km for low density and 240 km for high density height at which objects appear to start experiencing a sharp 10 fold increase in orbit decay is too vague because it is dependent on varying solar wind and environmental conditions;

Earth orbital velocity of satellites could be reduced by the solar wind in various ways. It is well documented how the solar wind pushed balloon satellites around during their life in space. Pageos had a near polar orbit unlike Echo 1 and 2, so perhaps the solar wind, being less affected by Earth’s magnetic field at the poles caused the Pageos orbit to decay the quickest. See below:

The Echo 1, Echo 2, and Pageos balloon satellites:

Echo 1 mass = 66kg, r = 15.25m, Alt = 1,600km, re-entry 8years, decay 0.5km per day.

Echo 2 mass = 68kg, r = 20.50m, Alt = 1,200km, re-entry 5 years, decay 0.5km per day.

Pageos mass = 57kg, r = 15.25m, Alt = 4,000km, re-entry 9 years, decay 1.2km per day,

(Decay rate assumes re-entry occurs below 200km)

The balloon satellites obviously had similar densities:

Volume (sphere), Echo 1 = 4/3πr³ = 14856m³ Density Echo 1 = m/v = 66kg/14856m³ = 4.443x10^-3kg/m³  

Volume (sphere), Pageos = 4/3πr³ = 14856m³ Density Echo 1 = m/v = 57kg/14856m³ = 3.837x10^-3kg/m³

I wonder if anyone will ever be able to accurately calculate incoming satellites breakup time/altitude; certainly not according to the fascinating book referenced below!   

Janos People: A Close Encounter of the Fourth Kind, by Frank Johnson ISBN  9780854353743

The latest news on the Tiangong-1 space lab re-entry is sometime in March 2018.

https://www.space.com/38573-china-space-lab-tiangong-1-re-entry-2018.html

 

[LaurieAG]

I am not so sure that cross-sectional area should be used as a variable as the object could be tumbling or start tumbling so perhaps it is better to use object density instead. The 300 km for low density and 240 km for high density height at which objects appear to start experiencing a sharp 10 fold increase in orbit decay is too vague because it is dependent on varying solar wind and environmental conditions;

...

The latest news on the Tiangong-1 space lab re-entry is sometime in March 2018.

https://www.space.com/38573-china-space-lab-tiangong-1-re-entry-2018.html

 

Thanks spartan45 that's interesting. 

 

The latest forecast is 5th of April 2018. http://www.satview.org/?sat_id=37820U