8.3.6 - Spinning Tether

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```					Landing Alternatives Considered – Spinning Tether                                     Section 8.3.6, Page X

8.3.6 - Spinning Tether
Yet another alternative we explored for placing our Lander on the lunar surface was the
idea of a spinning tether. In this alternative, the Lander and dry OTV are connected by a
tether and begin to spin. If the tether spins so that the Lander is traveling at the orbital
velocity of 1.7 km/s, then when the Lander moves toward the Moon it travels with a
speed of 2v and when it moves away it has a speed of zero (this only occurs when the
tether is exactly perpendicular to the velocity vector of the entire system). To capitalize
on this effect, we ignite a charge exactly when the Lander is at or near the lunar surface
and has zero relative speed to the Moon. The dry OTV is lost, but we place the Lander
on the surface of the Moon with little or no propellant. Figure 8.3.6.1 below illustrates
the setup. For simplicity, the figure shows the center of mass of the system to be in the
center of the tether, this is obviously not the case in the actual analysis.

w
2v
v
v=0

Fig. 8.3.6.1: The system of the dry OTV with the Lander move toward the Moon at a rate v while rotating at a
rate w. The goal is that the Lander moves with a net speed of zero relative to the Moon at some point along its
trajectory.
(Kristopher Ezra)

We observe that this alternative is subject to the same constraints as the others in that the
maximum acceleration sustained by the Lander cannot exceed 10 Earth g’s, the system
must travel at 1.7 km/s initially, and for the system to be viable it must have a mass less
than the propellant mass to lower the system to the lunar surface. With these constraints
in mind, we assume that the dry OTV and Lander are connected with a length of Kevlar
(whose safety factor is 1.25 in all cases observed) and use a work/force/energy model to
recreate the scenario. At the point in time this alternative was considered, the dry OTV

Author: Kristopher Ezra
Landing Alternatives Considered – Spinning Tether                                                                          Section 8.3.6, Page X

had a mass of 251 kg, the Lander had a mass of 138.3 kg, and the descent propellant mass
was 75 kg. Figure 8.3.6.2 shows the required length of tether for a 1.7 km/s orbital
velocity to be about 50 km.

Linear Velocity vs Tether Length
2

1.8

1.6
Magnitude of Linear Velocity (km/s)

1.4

1.2

1

0.8

0.6

0.4

0.2

0
0       10          20           30         40         50          60
Tether Length (km)

Fig. 8.3.6.2: Plot of the magnitude of the orbital velocity versus the tether length required to spin the Lander at
this rate without exceeding the 10 Earth g's constraint.
(Kristopher Ezra)

Given this tether length, we compute the net mass savings if the tether replaces the
descent propellant. The density of the tether remains constant and so does its cross
section (1.3 mm radius with 1.25 safety factor), but as the length of the tether increases so
does its total mass. Figure 8.3.6.3 shows the mass savings as a function of tether length
and it is clear to us that, even if we could support a tether with a length that is half of the
orbital height above the moon, the mass of the tether is too large. A mass savings of -325
kg indicated on the plot corresponds to a tether with a mass 325 kg greater than the
descent propellant. This equates to a tether with a weight of 400 kg. This is not feasible.
For this reason, the spinning tether alternative was discarded. Because of the very low
accelerations sustainable by the communications equipment (10 g limit), the Lander and
payload cannot be placed on the Lunar surface by means of a spinning tether system.

Author: Kristopher Ezra
Landing Alternatives Considered – Spinning Tether                                                   Section 8.3.6, Page X
Mass Savings
100

50

0

-50

Mass Savings (kg)
-100

-150

-200

-250

-300

-350

-400
0      10         20           30         40        50         60
Tether Length (km)

Fig. 8.3.6.3: This figure shows the total mass savings obtained when the tether replaces the descent propellant.
The function decreases with tether length and rapidly becomes negative.
(Kristopher Ezra)

Author: Kristopher Ezra

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