Solar Sails for Polar Observation

Solar Sails for Polar Observation

FinalProject for ASEN5050 by Mark Silver

Introduction

According to most people, solar sailing is only the subject of science fiction books. However, solar sailing is a very real focus of research in aerospace engineering. The technology involves many non-conventional ideas in structural design, material science and electromagnetism, all of which make the field an attractive avenue of research. It is not very often that engineers get the chance to make the subject of many science fiction novels a reality.

The first discussion of solar sailing began in the 1920's by Russian scientists KonstantinTsiolkovsky and Fridrickh Tsander. In the mid 1950's, solar sailing became a topic of discussion among various scientists around the United States. Richard Garwin coined the term solar sailing in the first western technical publication on the subject in 1958. The possibility of propelling spacecraft with no propellant raised enthusiasm about the subject. Today there is a significant amount of research in the different technologies contributing to solar sailing [1].

Solar sails are comprised of a large reflective surface, support structure and payload. The radical structural requirements for solar sails have given birth to many interesting deployment techniques and configurations. An artist rendition of a 3-Axis stabilized geometry is shown in Figure 1.

Figure 1 - 3-Axis Stabilized Solar Sail [2]

Solar Sail Physics

Solar sail propulsion uses the fact that energy can be related to mass by Einstein's special theory of relativity. From this it can be shown that the force exerted by light is the power of the light divided by the speed of light [2]. The large reflective surface collects the force from incident light particles and transfers it to the spacecraft, thus giving the spacecraft motion. When related to the specific impulse used to compare current propellants, solar sails are found to have an infinite specific impulse (if the mission time is infinite) [2]. The standard performance metric for comparing solar sails is characteristic acceleration. Characteristic acceleration is derived from the solar radiation pressure, the mass per unit area of the sail, and the efficiency of the sail material reflectivity. This is converted to a pressure that varies with the solar luminosity and the sail distance from the sun. This relation can be seen in Equation 1, where c is the speed of light, R_s is the radius of the sun and r_d is the distance from the sun [2].

Eq. 1

The solar pressure is independent of sail area. However the total force acting on the sail is linearly related to the area of the reflective surface. For a non-ideal reflecting surface, Equation 2 relates the solar pressure to the tangential and normal forces [3]. The reflectivity of the sail material is represented by the six additional coefficients.

Eq. 2

From this force, knowing the mass of the solar sail, the magnitude of the acceleration can be determined. This acceleration (k) is used in the equation of motion found from the two-body problem to determine the orbit.

Orbit Determination

The equation of motion for a solar sail orbiting the earth's center is shown in Equation 3 [2].

Eq. 3

In this equation, r is the vector from the earth to the sail, n is the unit normal to the solar sail m is the earth gravitational constant and l is the unit vector along the sun-line. The unique thrusting abilities of solar sails allow orbits about planets that are not centered on the planet's center of mass. This form of orbit must constantly counteract the gravitational potential of a typical two-body orbit (ÑV). There are also other constant effects requiring correction such as centripetal acceleration (w´(w´r)) and coriolis effect. This expanded form of the equation of motion is given in Equation 4.

Eq. 4

This off-center equation of motion can be manipulated to find the required solar sail pitch anglea and acceleration k can be found as functions of offset center z, offset radius r, offset orbit angular velocity w and Keplerian orbit angular velocity . These relations are shown in Equation 5. Figure 2 shows the offset center and offset radius for a non-Keplerian orbit.

Eq. 5

Figure 2 - Non-Keplerian Orbit Geometry

Equation 5 can be used for various types of non-Keplerian orbits. However, the relations can be simplified by choosing between three families of orbits. The first family of non-Keplerian orbits uses a fixed value for angular velocity for all values of offset radius and offset center. The second family uses an orbital period that is a function of offset radius r. This allows the orbit to be synchronous to a Keplerian orbit of the same radius. The third family, or Type III, is the focus of this paper. In this group the offset orbit angular velocity is equal to the Keplerian angular velocity with standard orbit radius equal to z. This is an optimal family of orbits because it minimizes the required solar sail acceleration. It can also be shown that this family of orbits does not require that the orbit vector k be aligned with the sun line l. This type of orbit is referred to as a halo orbit. The only requirement for a halo orbit is that the scalar product of k and l be greater than zero. A Type III orbit requires that the sail surface normal n be aligned with the orbit vector k. This requirement increases the acceleration required for a halo orbit in proportion to the inverse square of the scalar product of k and l [3].

The halo orbit is academically interesting because it is so different than standard Keplerian orbits. An orbit that hovers over a specified range of latitude can replace multiple satellites that would be needed to collect constant data in the same range. The limitation on the scalar product of k and l limits the halo orbit to the nadir side of the planet. However, given the right sail and orbit parameters, a halo orbit can pass over the sun side of the planet. Being limited for the most part to the nadir side, halo orbits are especially inclined to make night-only observations. Night observations are more difficult for standard satellites because they must run off of battery power because the solar panels cannot create power.

Type III orbits open up many possibilities for research. As will be shown in this paper, halo orbits are not very practical for Earth observation because of the large accelerations required. However, the orbit becomes much less demanding for other planets that are smaller distances from sun or have less planetary mass, e.g. Mercury.

Example Orbits

A halo orbit derivation around Earth will now be presented. The specific solar sails used were the High-Performance Solar Sail (HPSS) and the Micro Solar Sail (m-SS). The geometries for these cases were taken from McInnes, p. 96. The HPSS is an example of the current goal for solar sail structural design. Large-scale solar sail designs are compared by total loading which is the mass per unit area of the entire structure. The HPSS has a total loading of 1.31 gm^-2, a mass of 41 kg and an area of 31,400 m². Current advances in MEMS have allowed for the development of the m-SS. The m-SS has a total loading of 15 gm^-2, a mass of 0.24 kg and an area of 16 m². Microelectronics allow for smaller size and mass for science instruments. Smaller sails can be used for more delicate missions including asteroid investigation and MEMS payload delivery.

The Mathematica^Ò calculations for halo orbits using these two geometries are included in the Appendix. The solar sail acceleration k was found independent of the sail geometry. In these calculations, orbital parameters z and r are compared by factors of Earth radii where z is h (R_Å) and r is b (R_Å). Figure 3 shows the variation in k with respect to the orbit parameters b and h.

Figure 3 - Variance of k with respect to b and h

The offset between l and k was chosen to be a rotation about the negative x-axis by 67.5°. A theoretical application for this kind of orbit is continuous polar ozone observation. It will be shown that a halo orbit is not well suited for this mission because of the aforementioned problems with planetary mass and distance from the sun.

First, the total mass allowed for varying orbital parameters is calculated for each sail geometry. The only sail mass parameter used is the total loading. The results are shown in Figure 4. It can be seen that the amount of mass allowed increases with offset center and offset radius.

Figure 4 - Allowed mass versus b and h for HPSS and m-SS respectively

As can be seen from Figures 3 and 4, the orbit parameters can vary over large ranges for various required accelerations and total masses. The ground track diameter of the orbit is of interest because orbits with large ground tracks are not using the technology efficiently for the proposed polar observation mission. The plot of the solar sail ground track diameter versus orbital parameters b and h is shown in Figure 5.

Figure 5 - Ground track diameter versus b and h

To compare the orbits, a ground track diameter of 24,600 km is used. The HPSS requires an offset center of 50 R_Å and an offset radius of 53 R_Å. The m-SS requires an offset center of 169.5 R_Å and an offset radius of 179.5 R_Å. The periods of these orbits were found to be 36.5 and 227.7 days respectively. It can be seen from these numbers that solar sail orbits for this mission are not the best choice. The orbits are very high, which would make high-spatial-resolution data acquisition difficult.

Conclusion

An overview of non-Keplerian halo orbits using solar sails was presented and two cases were analyzed. In doing so, the general physics behind solar sailing was presented. Solar sails allow for planetary and interplanetary mechanics which were previously not possible. One type of these interesting orbits is the halo orbit. A sample application of this orbit is continuous polar observation. Two radically different sail geometries were studied for use in an Earth polar observation orbit. It was shown that the mass of Earth and its position in the solar system make it and unlikely candidate for this sort of halo orbit. As we learn more about planetary observation, non-Keplerian orbits may be become a very significant tool. This fact and the difficult structural requirements of solar sails have made the area an academically interesting research area. Solar sail research is truly making scientific fact out of science fiction.