🧑🏾‍🤝‍🧑🏾 🤜🏽 🙋🏼 Chemical fuel exchange between ascending and descending spacecraft 🈳 🧛🏼 🌟

Suppose that in the not so distant future, the production of water on an industrial scale is organized on the Moon and the production of oxygen / hydrogen rocket fuel from it is established.

After that, the question of the possibility of delivering this fuel to the Earth's low reference orbit (LEO) for its subsequent use for transporting cargo from LEO to the lunar surface (PL) arises quite reasonably.

We will conventionally call the Moon-Earth direction ascending, and Earth-Moon descending.

The economic feasibility of delivering fuel to LEOZ from submarines is confirmed by a simple comparison of the first cosmic speed for the Earth 7.920 /

and the second cosmic speed for the moon, 2.376 /,

and taking into account the possibility of laying a trajectory through the Langrage-1 point, the speed for a translunar flight can be reduced to2.264 /.

Taking the oxygen / hydrogen fuel outflow rate, we I_sp = 4.650 /,

find the relative fuel M_F21

consumption for moving a spacecraft (SC) of a unit mass along the PL-LEO route by the formula:

$M_ {F21} = e ^ \ frac {V_ {21}} {I_ {sp}} - 1 = e ^ \ frac {2.264} {4.650} -1 = 0.62723 = 62.72 \%$

Taking the speed of the transition to the trans lunar orbit V_2=3.128 /

, we find the relative fuel M_F12

consumption for moving a spacecraft of unit mass along the LEO-PL route by the formula:

$M_ {F12} = e ^ \ frac {V_ {12} + V_ {21}} {I_ {sp}} - 1 = e ^ \ frac {3.128 + 2.264} {4.650} -1 = 2.18856 = 218.86 \%$

Assuming a reasonable assumption that an equal cargo flow goes in both directions, and therefore the mass of the spacecraft remains constant for all maneuvers, that is, upon reaching the end point of the route, the spacecraft unloads / loads a load of the same mass, we find the relative fuel M_F212

consumption for moving a spacecraft of unit mass along the PL-LEO route. PL by the formula:

$M_ {F212} = e ^ \ frac {V_ {21} + V_ {12} + V_ {21}} {I_ {sp}} - 1 = e ^ \ frac {2.264 + 3.128 + 2.264} {4.650} -1 = 4.18885 = 418.89 \%$

Assuming a reasonable assumption about the mass of the spacecraft of 100.0 tons and the mass of the transported cargo also 100.0 tons, we obtain a fuel mass of 837.78 tons for a full flight. It should be noted again that during this voyage the spacecraft will move 100.0 tons from the submarine to the LEO and another 100.0 tons from the LEO to the submarine. Quite reasonable weight and size characteristics for a hypothetical single-stage rocket equipped with a heat shield for aerodynamic braking.

, :

$M_ {F313} = e ^ \ frac {V_ {31} + V_ {12} + V_ {31}} {I_ {sp}} - 1 = e ^ \ frac {0.591 + 3.128 + 0.591} {4.650} -1 = 1.52661 = 152.66 \%$ $M_ {F23} = e ^ \ frac {V_ {23}} {I_ {sp}} = e ^ \ frac {1.674} {4.650} = 0.43333 = 43.33 \%$ $M_ {F1} = (1 + M_ {F313} + M_ {F23}) \ cdot (1 + M_ {F23}) - 1$ $M_ {F1} = (1 + 1.5266 + 0.4333) \ cdot (1 + 0.4333) -1 = 3.2424 = 324.24 \%$

418,89% 324,24%, 22,6%, 837,78 648,48 . , .

, -1, , :

$M_ {F12} = e ^ \ frac {V_ {12}} {I_ {sp}} - 1 = e ^ \ frac {3.128} {4.650} -1 = 0.95950 = 95.95 \%$ $M_ {F31} = e ^ \ frac {V_ {31}} {I_ {sp}} - 1 = e ^ \ frac {0.591} {4.650} -1 = 0.13553 = 13.55 \%$ $M_ {F2} = \ big ((1 + M_ {F12} + M_ {F31}) \ cdot (1 + M_ {F31}) + M_ {F23} \ big) \ cdot (1 + M_ {F23})$ $M_ {F2} = \ big ((1 + 0.9595 + 0.1355) \ cdot (1 + 0.1355) +0.4333 \ big) \ cdot (1 + 0.4333) -1 = 3.0307 = 303.07 \%$

- 27,6% , 606,14 .

, -1 , , , :

$M_ {F12 / 2} = e ^ \ frac {V_ {12/2}} {I_ {sp}} - 1 = e ^ \ frac {3.128 / 2} {4.650} -1 = 0.39982 = 39.98 \%$ $M_ {F2} = \ big ((1 + 0.3998 \ cdot 2) \ cdot (1 + 0.1355) +0.4333 \ big) \ cdot (1 + 0.4333) -1 = 2.54991 = 254.99 \%$

39,1%, 2/5, 510,0 . 100,0 100,0 510,0 / .

/ .

It should be noted that the spacecraft are not obliged to meet "in person" at these points, fuel depots equipped for receiving / transmitting and long-term storage of fuel can be located. Powerful solar panels and shadow screens will allow cryogenic components to be stored for much longer and with significantly lower losses.

Chemical fuel exchange between ascending and descending spacecraft

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