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| ||<-4>Hohmann orbit from moon to GEO - $ r_a = a_m ~ ~ ~ r_p = r_{GEO} || || $ a_{m-GEO}$ || Lunar-GEO semi-major axis || || $ e_{m-GEO}$ || Lunar-GEO eccentricity || || $v_{a-m-GEO}$|| Lunar-GEO apogee velocity || || $v_{l-m-GEO}$|| Lunar-GEO launch velocity || || $v_{p-m-GEO}$|| Lunar-GEO perigee velocity || || $v_{i-m-GEO}$|| Lunar-GEO insertion velocity || |
||<-4>Hohmann orbit from moon to GEO - $ r_a = a_m ~ ~ ~ r_p = r_{GEO} $ || || $ a_{m-GEO}$ || Lunar-GEO semi-major axis || 213281586 || m || || $ e_{m-GEO}$ || Lunar-GEO eccentricity || 0.8023075 || || || $v_{a-m-GEO}$|| Lunar-GEO apogee velocity || 452.7650 || m/s || || $v_{l-m-GEO}$|| Lunar-GEO launch velocity || -2442.6935 || m/s || || $v_{p-m-GEO}$|| Lunar-GEO perigee velocity || 4127.7325 || m/s || || $v_{i-m-GEO}$|| Lunar-GEO insertion velocity || -1053.0725 || m/s || |
Lunar Material and Momentum Supply
I am skeptical about high tech manufacturing in space, especially in the dusty lunar environment. Factories are big, and need a lot of PhDs to keep them running. 100 years from now, there will be many such factories in space, but for now, we have problems locating them in most countries around the world, where there is air and water and food and FedEx.
That said, there are plenty of uses for deadweight mass in space, as ballast and as a source of momentum. Earth launch is expensive, and is deficient in angular momentum compared to destination orbits.
Assuming we can get material launched from the moon ( 4.5% of the escape energy and launch loop track length )
Earth and Moon and interesting orbits |
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Earth and earth orbits |
|||
\mu_e |
Earth gravitational parameter |
3.986004418e+14 |
m3/s^2 |
r_E |
Earth equatorial radius |
6378137 |
m |
E_e |
Earth escape energy |
62.494807 |
MJ/kg |
\omega_e |
Earth angular frequency |
7.29211515e-5 |
radians/s |
r_{GEO} |
Geosynchronous radius |
42164172.4 |
m |
v_{GEO} |
Geosynchronous velocity |
3074.66 |
m/s |
Moon |
|||
\mu_m |
Lunar gravitational parameter |
4.9027779e+12 |
m3/s^2 |
r_m |
Lunar equatorial radius |
1738140 |
m |
E_m |
Lunar escape energy |
2.8207037 |
MJ/kg |
a_m |
Lunar orbit semi-major axis |
384399000 |
m |
v_m |
Lunar orbit velocity |
1023.155 |
m/s |
t_m |
Lunar orbit period |
2360591.5 |
seconds |
\omega_m |
Lunar orbit angular frequency |
2.66169954e-6 |
radians/s |
Hohmann orbit from moon to GEO - r_a = a_m ~ ~ ~ r_p = r_{GEO} |
|||
a_{m-GEO} |
Lunar-GEO semi-major axis |
213281586 |
m |
e_{m-GEO} |
Lunar-GEO eccentricity |
0.8023075 |
|
v_{a-m-GEO} |
Lunar-GEO apogee velocity |
452.7650 |
m/s |
v_{l-m-GEO} |
Lunar-GEO launch velocity |
-2442.6935 |
m/s |
v_{p-m-GEO} |
Lunar-GEO perigee velocity |
4127.7325 |
m/s |
v_{i-m-GEO} |
Lunar-GEO insertion velocity |
-1053.0725 |
m/s |