Differences between revisions 6 and 50 (spanning 44 versions)
Revision 6 as of 2019-03-31 02:54:05
Size: 924
Comment:
Revision 50 as of 2020-08-28 05:24:41
Size: 4207
Comment:
Deletions are marked like this. Additions are marked like this.
Line 3: Line 3:
 . http://hitran.org keithl@keithl.com on kao3
 
 . https://www.sciencedirect.com/science/article/pii/0022407372900052
-------
Line 7: Line 5:
H density versus altitude: === H density versus altitude ===
Line 9: Line 7:
||<|6> {{ attachment:geocoronaMarkup.png | | width=600 }} || alt || /m3 ||
|| || 2000 km || 1e6 ||
|| || 10000 km || 1e6 ||
||<|16> {{ attachment:geocoronaMarkup.png | | width=600 }} ||<)> '''alt km''' ||<)> '''radius km''' ||<)> '''#/m3''' ||
||<)> 1000 ||<)> 7378 ||<)> 21000e6 ||
||<)> 2000 ||<)> 8378 ||<)> 12000e6 || Constr. perigee ||
||<)> 5000 ||<)> 11378 ||<)> 3100e6 ||
||<)> 10000 ||<)> 16378 ||<)> 820e6 ||
||<)> 20000 ||<)> 26378 ||<)> 180e6 ||
||<)> 30000 ||<)> 36378 ||<)> 67e6 ||
||<)> 35786 ||<)> 42164 ||<)> 45e6 || GEO circular ||
||<)> 40000 ||<)> 46378 ||<)> 35e6 ||
||<)> 50000 ||<)> 56378 ||<)> 22e6 ||
||<)> 60000 ||<)> 66378 ||<)> 14e6 ||
||<)> 69572 ||<)> 75950 ||<)> 11e6 || Constr. apogee ||
||<)> 70000 ||<)> 76378 ||<)> 10e6 ||
||<-3> [[attachment:geocoronaMarkup.png | image source ]] ||
Line 13: Line 22:
from [[ https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/Collisional_Cross_Section | libretexts ]]: . https://www.sciencedirect.com/science/article/pii/0022407372900052
Line 15: Line 24:
||<-3> Cross section ||
|| Gas || (nm)² || (nm)² H₂ ||

||<-12> Estimated hydrogen mass per 1000 km height, 1.67e-27kg/H ||
|| Altitude km || 1000 || 2000 || 10000 || 20000 || 30000 || 35786* || 40000 || 50000 || 60000 || 69572* || 70000 ||
|| Radius km || 7378 || 11378 || 16378 || 26378 || 36378 || 42164* || 46378 || 56378 || 66378 || 75950* || 76378 ||
|| Volume km³ || 6.8e11 || 1.6e12 || 3.4e12 || 8.7e12 || 1.7e13 || 2.2e13 || 2.7e13 || 4.0e13 || 5.5e13 || 7.2e13 || 7.3e13 ||
|| #H / m³ || 2.1e10 || 1.2e10 || 8.2e8 || 1.8e8 || 6.7e7 || 4.5e7 || 3.5e7 || 2.2e7 || 1.4e7 || 1.1e7 || 1.0e7 ||
|| H kg || 240000 || 32000 || 4700 || 2600 || 1900 || 1700* || 1000 || 1500 || 1300 || 1300* || 1200 ||

Less than 20 tonnes of hydrogen (and almost nothing else) above GEO, out to the bow shock.

=== Collision cross section table ===

|| Gas || (nm)² || (nm)² with H₂ ||
Line 25: Line 45:

The second column is the combined collision cross section with an H₂ molecule ... the square of the sum of the square roots.

from [[ https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/Modeling_Reaction_Kinetics/Collision_Theory/Collisional_Cross_Section | libretexts ]]

-----

 . http://hitran.org . . . . . . . . . k*l at k*l dot com on kao3

-----

=== 24 hour "Construction" Orbit ===
'''Note:''' 75950 km radius is the apogee of a "24 hour" geosynchronous (but NOT geostationary) orbit with a 8378 km radius (2000 km equatorial altitude) perigee. The same 42164 km semimajor axis as a circular geostationary orbit. This is a High Eccentricity Earth Orbit (HEEO), suggested by space scientist John Lewis at the University of Arizona. Given the high perigee velocity of a launch loop, this orbit is easier to achieve with much less apogee insertion ΔV than a GEO orbit. The perigee velocity of this HEEO orbit is high, and that is an excellent place for a high ΔV thrust into an interplanetary trajectory.

'''Subnote 1:''' due to the J₂ nonlinearity of the Earth's gravity field, this orbit will precess, so an exact synchronous orbit will have a slightly smaller semimajor axis.

'''Subnote 2:''' launchloop launches slows portions of the rotor; restoring rotor position and velocity requires enormous power. Larger vehicles would slow the rotor more, requiring more peak electrical power generation capacity. It is cheaper to assemble large interplanetary vehicles at a permanent orbiting construction station from dozens, perhaps hundreds of daily launches, then launch the propellant to fuel them after they are assembled.

Since a launch to an interplanetary Hohmann must occur at a specific sun-relative angle for a particular mission, the perigee angle of the construction orbit for a Mars mission at one Hohmann opportunity will differ from the next opportunity. This is an annoying constraint for infrequent Mars missions, but less so for missions to many different asteroids.

Propellant Plume Gas Scattering


H density versus altitude

geocoronaMarkup.png

alt km

radius km

#/m3

1000

7378

21000e6

2000

8378

12000e6

Constr. perigee

5000

11378

3100e6

10000

16378

820e6

20000

26378

180e6

30000

36378

67e6

35786

42164

45e6

GEO circular

40000

46378

35e6

50000

56378

22e6

60000

66378

14e6

69572

75950

11e6

Constr. apogee

70000

76378

10e6

image source

. https://www.sciencedirect.com/science/article/pii/0022407372900052

Estimated hydrogen mass per 1000 km height, 1.67e-27kg/H

Altitude km

1000

2000

10000

20000

30000

35786*

40000

50000

60000

69572*

70000

Radius km

7378

11378

16378

26378

36378

42164*

46378

56378

66378

75950*

76378

Volume km³

6.8e11

1.6e12

3.4e12

8.7e12

1.7e13

2.2e13

2.7e13

4.0e13

5.5e13

7.2e13

7.3e13

#H / m³

2.1e10

1.2e10

8.2e8

1.8e8

6.7e7

4.5e7

3.5e7

2.2e7

1.4e7

1.1e7

1.0e7

H kg

240000

32000

4700

2600

1900

1700*

1000

1500

1300

1300*

1200

Less than 20 tonnes of hydrogen (and almost nothing else) above GEO, out to the bow shock.

Collision cross section table

Gas

(nm)²

(nm)² with H₂

H₂

0.27

1.02

He

0.21

0.99

Ar

0.36

1.06

O₂

0.40

1.07

N₂

0.43

1.08

CH₄

0.46

1.09

CO₂

0.52

1.11

Cl₂

0.93

1.22

The second column is the combined collision cross section with an H₂ molecule ... the square of the sum of the square roots.

from libretexts



24 hour "Construction" Orbit

Note: 75950 km radius is the apogee of a "24 hour" geosynchronous (but NOT geostationary) orbit with a 8378 km radius (2000 km equatorial altitude) perigee. The same 42164 km semimajor axis as a circular geostationary orbit. This is a High Eccentricity Earth Orbit (HEEO), suggested by space scientist John Lewis at the University of Arizona. Given the high perigee velocity of a launch loop, this orbit is easier to achieve with much less apogee insertion ΔV than a GEO orbit. The perigee velocity of this HEEO orbit is high, and that is an excellent place for a high ΔV thrust into an interplanetary trajectory.

Subnote 1: due to the J₂ nonlinearity of the Earth's gravity field, this orbit will precess, so an exact synchronous orbit will have a slightly smaller semimajor axis.

Subnote 2: launchloop launches slows portions of the rotor; restoring rotor position and velocity requires enormous power. Larger vehicles would slow the rotor more, requiring more peak electrical power generation capacity. It is cheaper to assemble large interplanetary vehicles at a permanent orbiting construction station from dozens, perhaps hundreds of daily launches, then launch the propellant to fuel them after they are assembled.

Since a launch to an interplanetary Hohmann must occur at a specific sun-relative angle for a particular mission, the perigee angle of the construction orbit for a Mars mission at one Hohmann opportunity will differ from the next opportunity. This is an annoying constraint for infrequent Mars missions, but less so for missions to many different asteroids.

GasScatter (last edited 2020-08-28 17:21:33 by KeithLofstrom)