Interplanetary Transfers using Low Thrust

Much like the Low Earth to Geosynchronous transfer orbits, the Hohmann Transfer is almost always the most efficient way for conventional rockets to transfer between two planetary orbits. The following table shows some characteristics about each Hohmann Transfer from Earth’s orbit to the orbits of the other planets in the solar system. These values were determined by assuming circular coplanar orbits with the sun’s gravity as the only force. The second column shows the first impulse (ΔV) necessary to place the spacecraft onto the transfer orbit and the third column shows how much ΔV is required to circularize the spacecraft’s orbit at that radius. A negative ΔV indicates a thrust in the opposite direction of the velocity vector.

Some interesting things to note:

1. The initial ΔV used to get on the transfer orbit steadily approaches the solar system’s escape velocity of 12.337 km/s from Earth’s orbit.
2. The circularization ΔV gets smaller for the distant planets because the orbital velocity of a planet with respect to the sun decreases with distance.
3. Neptune and Pluto require less total ΔV in a pure Hohmann Transfer because of the combination of the (1) and (2).
4. The time to complete the transfer increases dramatically with distance.

Low-Thrust Transfers

We have developed a program, Low-Thrust Propagator, that propagates a spacecraft’s orbit while the spacecraft produces a small, constant force. Similar to the LEO2GEO algorithm, the program assumes the following:

• The only forces are the sun’s gravity and the spacecraft’s thrust;
• Earth’s orbit and the target’s orbit are coplanar and circular;
• The spacecraft produces a constant ΔV over time;
• The spacecraft’s initial position is 1AU from the sun;
• The spacecraft’s initial velocity is equal to the orbital velocity of Earth about the sun.

See the notes in the Software Section for a full explanation of the algorithm’s procedures as it propagates the spacecraft from Earth's orbit to the other planetary orbits. The program essentially determines the orbit of a perturbed spacecraft with the above assumptions.

Results

We have produced results for each planet in the solar system, each implementing constant-thrust values from T = 100 cm/s² to 10 μm/s² (1x10^-1 - 1x10^-5 m/s). Since Pluto was so far from Earth we extended the range of T to Pluto to include values down to 1 μm/s². In each run, we calculate the following orbital characteristics:

• The duration of time that the engine was active,
• The total ΔV produced by the engine,
• The impulse ΔV required to circularize the orbit once the target radius had been reached,
• The total ΔV required for the transfer,
• The amount of fuel used,
• The total duration of time required for the transfer.

These plots show very simply that the lower the thrust of the engine, the more the orbit spirals outward before reaching an elliptical cruise orbit. When we analyze the third plot, "Entire Orbit," in each case we see that as the thrust is reduced, the transfer ellipse becomes more circular. Furthermore, the transfer ellipse's apoapse shrinks in the case of Mercury and Venus and the transfer ellipse's periapse grows outward in the case of the outer planets as the engine's thrust is reduced. This helps to explain why it takes less energy to circularize the spacecraft's orbit at the target radius as the engine's thrust is reduced..

We have additionally plotted various features of these transfer orbits in comparison with each other.

Figure 7 shows a plot of the burn duration for each transfer orbit as a function of orbital thrust for each planet. One can see that as the transfer thrust is reduced, more time is required to obtain the velocity needed to reach the goal planet. This assumes an engine capable of producing the respective levels of thrust.

Figure 8 shows a plot of the burn duration for each transfer to a terrestrial planet as a function of orbital thrust. This is the same plot as shown in Figure 7, except concentrating on the terrestrial planetary transfers.

Figure 9 shows a plot of the burn duration for each transfer to a Jovian planet as a function of orbital thrust. This is the same plot as shown in Figure 7, except concentrating on the outer Jovian planetary transfers.

Figure 10 shows a plot of the fuel consumption for each transfer as a function of orbital thrust. When the transfer thrust is reduced, more of the total ΔV is produced by the low-thrust engine than by the impulsive maneuver at the end of the transfer (the impulse needed to circularize the orbit at the final radius). Since the low-thrust propulsion is more efficient than the final impulse, less fuel is required if the low-thrust engine does more of the work. Thus, as the thrust is reduced, less fuel is required to perform the transfer.

Figure 11 shows a plot of the total time of transfer as a function of orbital thrust for each planet on a linear scale. One can see that as the thrust level is reduced, the spacecraft spends more time traveling slower and thus requires more time to reach the necessary velocity to obtain the target radius.

Figure 12 shows a plot of the total time of transfer as a function of orbital thrust for each planet on a logarithmic scale.

After analyzing the data and the plots we were able to conclude the same things about low-thrust transfer orbits as we did for LEO to GEO transfer orbits. We see very clearly that there are certain advantages and disadvantages with using lower thrusts in these orbital transfers, as listed below:

Advantages of Lower Thrusts

• Much less fuel consumption (less fuel mass)
• Energy efficient
• Lots of time to correct for an orbital error

Disadvantages of Lower Thrusts

• Greater Mission Durations

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