1. Elena Ancona & Roman Ya Kezerashvili Polytechnic University of Turin, Italy New York City College of Technology, USA Satellite & Space Missions Berlin, Germany July 21-23, 2016 Orbital dynamics of a solar sail accelerated by thermal desorption of coatings

2. Concepts of acceleration using thermal desorption Sail’s temperature dependence on heliocentric distance Proposed scenarios Conclusions and future development Outline Elena Ancona 2

3. “tremendous mirrors of very thin sheets” (F. Tsander, 1924). large sheets of low areal density material (Kapton, Mylar) whose only source of energy is the Sun photons flux. unlimited duration (in theory) thanks to the “ever-present push of sunlight”; no propellant is needed; acceleration is slow but continuous. Solar sail Elena Ancona 3 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

4. physical process of mass loss; dominates above temperatures of 300–600 °C; provides additional thrust as heating liberates atoms, embedded on the surface of a solar sail; suggested by Benford & Benford, 2005 using beam- powered microwave pulse for heating (from Earth or from orbit) ; For extrasolar space exploration it might be very convenient to take advantage of space environmental effects such as solar radiation heating; The solar sail naturally gains temperature through the absorption of solar radiation. Acceleration of sails by thermal desorption is not a new idea, but it is new to apply this idea to the solar sail that naturally gains temperature through the absorption of solar radiation. Thermal desorption Elena Ancona 4 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

5. Sun-Heating Desorption-Assisted Solar Sail Elena Ancona 5 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results Atoms liberated by heating provide additional thrust

6. Thermal desorption: the chemical process Elena Ancona 6 If N particles of molecular mass m p leave the sail surface at velocity v th, for the law of conservation of total momentum, the sail of mass m will move in the opposite direction with velocity v: The thermal velocity can be found with the Maxwell speeds distribution: And, finally, the acceleration due to desorption a D is: Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results k B =1.38*10 -23 J/K t = time of desorption

7. Take advantage of space environmental effects such as solar radiation heating to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. The temperature of a solar sail increases as r - 2/5 when the heliocentric distance r decreases because of temperature dependence of the emissivity and conductivity of the sail’s material. Temperature dependence on heliocentric distance Elena Ancona 7 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

8. Proposed scenarios Elena Ancona 8 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

9. 1 st scenario: Hohmann transfer plus thermal desorption acceleration Elena Ancona 9 Hohmann transfer from Earth’s orbit to an orbit very close to the Sun (almost at 0.1 AU) with a conventional chemical propulsion. The sail is deployed at the perihelion. It has one coat of the material that undergoes desorption at the temperature reached at the perihelion of the transfer orbit. The sail then escapes the Solar System with the conventional acceleration caused by the solar radiation pressure. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

10. 2 nd scenario: Elliptical transfer plus Slingshot plus thermal desorption Elena Ancona 10 The transfer occurs from Earth’s orbit to Jupiter’s orbit. A Jupiter’s fly-by leads to the orbit close to the Sun. Then as in first scenario: The sail is deployed at the perihelion. It has one coat of material that undergoes desorption at the temperature reached at the perihelion of the transfer orbit. The sail then escapes the Solar System with the conventional acceleration caused by the solar radiation pressure. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

11. 3 rd scenario: Two stage acceleration of sail through thermal desorption Elena Ancona 11 The sail has two coats of materials that undergo thermal desorption at different solar sail temperatures, that means at different heliocentric distances. The sail is deployed. The first desorption occurs at the Earth orbit and provides the thrust needed to propel the solar sail toward the Sun. Then as in first scenario: The other coat undergoes desorption at the temperature reached at the perihelion of the transfer orbit. The sail then escapes the Solar System with the conventional acceleration caused by the solar radiation pressure. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

12. Elena Ancona 12 1 st scenario: Hohmann transfer plus thermal desorption acceleration Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

13. Elena Ancona 13 2 nd scenario: Elliptical transfer plus Slingshot plus thermal desorption Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

14. The first scenario is always convenient from a time point of view, but as the heliocentric distance to reach decreases, its cost gets very high. The Jupiter flyby allows to reach 0.1 AU with an acceptable fuel cost. Depending on the material, the scenario which guarantees the best performance can be considered. Comparison: 1 st and 2 nd scenario Elena Ancona 14 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

15. Elena Ancona 15 3 rd scenario: Two stage acceleration of sail through thermal desorption Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results Sail deployed from the beginning: spiral logarithmic trajectory β relative to the coat that will desorb at perihelion (and not to the sail!); If β increases, the transfer would require less time but higher DV.

16. Elena Ancona 16 3 rd scenario: Two stage acceleration of sail through thermal desorption Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results with β = 0.1 DV of only 2.5 km/s (if the sail is already on LEO); If β increases? less time but higher DV: e.g. with β = 0.4, t f = 107 days instead of 474 days for r P = 0.1

17. Elena Ancona 17 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results Scenarios comparison Our choice: 2 nd scenario best cruise speed and distance covered in time! Also less DV than 1 st scenario (7 instead of 12 km/s) thanks to the fly- by maneuver. … but more time required! However, 3 rd scenario could be a good way to reduce time and DV required

18. Elena Ancona 18 Conclusions and future development The comparison of the scenarios shows that the second one is the best in terms of cruise speed and distance covered per year. In fact, for the heliocentric distance of 0.1 AU the cruise speed obtained is almost 327 km/s, corresponding to 69 AU travelled per year. For all the scenarios, however, the great advantage of thermal desorption is clearly evident. The natural prosecution of this work would be a detailed research on materials, in order to find out their characteristics, performances and desorption temperature suitable for solar sailing.

19. Thank you for your attention Questions? Elena Ancona 19

20. Back-up Slides Elena Ancona 20

21. Thermal desorption: the chemical process Elena Ancona 21 Comparison with the acceleration due to photon pressure a P, function of emissivity ζ, absorptivity and reflectivity : The rate of desorption corresponds to the time reduction of atoms present on surface: The rate of mass loss under heating, dNA/dt, is the desorbed flux in atoms/m 2 s. Exponential factor suggests desorption will have a sudden onset after the surface gets warm. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results SB = 5.67*10 -8 W m -2 K -4 v 0 = frequency factor q = order of desorption N A = surface concentration of adsorbed species E A = activation energy for desorption

22. Thermal desorption: the propulsion mechanism Elena Ancona 22 The acceleration due to desorption is of the order of m/ s 2, whereas that of photon pressure is few mm/ s 2 ; With an approach so close to the Sun, we get velocity increment of hundreds of km/ s. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

23. Why do we need it? Elena Ancona 23 To get as far as possible in the shortest time Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

24. Force due to solar radiation pressure acting on the sail is function of its reflectivity and the solar irradiance (energy flux coming from the Sun) at a particular distance (c is the speed of light). Acceleration of the sail: Sail loading factor: Characteristic acceleration: Lightness number: Solar sail Elena Ancona 24 maximum acceleration that can be experienced from the sail if normal to the Sun at a distance of r = 1 AU. solar radiation pressure over solar gravitation at same distance. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

25. Take advantage of space environmental effects such as solar radiation heating to accelerate a solar sail coated by materials that undergo thermal desorption at a particular temperature. The temperature of a solar sail increases as r - 2/5 when the heliocentric distance r decreases because of temperature dependence of the emissivity and conductivity of the sail’s material. Temperature dependence on heliocentric distance Elena Ancona 25 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results ENERGY BALANCE Solar electromagnetic radiation can be reflected, absorbed or transmitted Once that energy has been absorbed, it can also be emitted from the surface, as a secondary process.

26. Proposed scenarios Elena Ancona 26 Solar sail coated with materials that undergo thermal desorption at a particular temperature, as a result of heating by solar radiation at a particular heliocentric distance. Three different scenarios for extra-solar space exploration with a solar sail: 1 st scenario: Hohmann transfer plus thermal desorption acceleration. Hohmann transfer from Earth’s orbit to an orbit very close to the Sun (almost at 0.1 AU) with chemical propulsion. Sail deployed and the coat undergoes desorption at the temperature reached at the perihelion of the transfer orbit. The sail escapes the Solar System having in addition the conventional acceleration caused by solar radiation pressure. 2 nd scenario: Elliptical transfer plus Slingshot plus thermal desorption acceleration. Generic transfer from Earth to Jupiter and Jupiter’s fly-by leads to the orbit close to the Sun. Then as in 1 st scenario at the perihelion the sail is deployed and the coating undergoes desorption. The sail escapes the Solar System with the acceleration due to solar radiation pressure. 3 rd scenario: Two stage acceleration of the solar sail through thermal desorption. The sail has two coats of the materials that undergo thermal desorption at different solar sail temperatures depending on the heliocentric distance. First desorption at the Earth orbit leads the sail toward the Sun (spiral trajectory). Second desorption as in the other scenarios. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

27. Proposed scenarios Elena Ancona 27 We are considering a solar sail coated with materials that undergo thermal desorption at a particular temperature, as a result of heating by solar radiation at a particular heliocentric distance. We focus on the orbital dynamics of three different scenarios that could be considered for extra-solar space exploration by solar sail. 1 st scenario: Hohmann transfer plus thermal desorption acceleration. In this scenario a Hohmann transfer is performed from Earth’s orbit to an orbit very close to the Sun (almost at 0.1 AU). The sail would be carried to the perihelion with a conventional chemical propulsion system and then be deployed there. The sail has one coat of the material that undergo desorption at the temperature reached at the perihelion of the transfer orbit. The sail then escapes the Solar System having the conventional acceleration caused by the solar radiation pressure. 2 nd scenario: Elliptical transfer plus Slingshot plus thermal desorption acceleration. In this scenario the transfer occurs from Earth’s orbit to Jupiter’s orbit; then a Jupiter’s fly-by leads to the orbit close to the Sun, where the sail is deployed and thermal desorption accelerates it to the escape velocity. As in the previous case, the sail has one coat of the material that undergo desorption at the temperature reached at the perihelion and, after desorption, continues its acceleration due to the solar radiation pressure. 3 rd scenario: Two stage acceleration of the solar sail through thermal desorption. The proposed sail has two coats of the materials that undergo thermal desorption at different solar sail temperatures depending on the heliocentric distance. The first desorption occurs at the Earth orbit and provides the thrust needed to propel the solar sail toward the Sun. When the solar sail approaches the Sun, its temperature increases, and the second coat undergoes desorption at the perihelion of the heliocentric escape orbit. This provides a second thrust and boosts the solar sail to its escape velocity. Backup slide

28. After desorption: sail cruise speed Elena Ancona 28 Once desorption has occurred at perihelion, one can evaluate what the cruise speed of the sail will be with the law of energy conservation. Orbital mechanics of solar sail depends on sail lightness number: in order to escape β>1/2 is required. Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

29. Elena Ancona 29 1 st scenario: Hohmann transfer plus thermal desorption acceleration Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

30. Elena Ancona 30 2 nd scenario: Elliptical transfer plus Slingshot plus thermal desorption Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

31. First and second scenario compared Elena Ancona 31 Thermal desorption - Solar sail - Temperature dependence on distance - Scenarios - Results

32. Due to the gravitational field of a body, an object is forced to move along a well defined trajectory, that corresponds to a conic section. Orbital dynamics: basic concepts Elena Ancona 32 Backup slide

33. Trajectory equation Conservation of Energy Conservation of angular momentum Orbital dynamics: basic concepts Elena Ancona 33 Backup slide

34. Transfer between coplanar circular orbits Elena Ancona 34 In order to perform a transfer from an orbit to another, a change in velocity is required. The most desirable maneuver could be the one that requires less time or the one that requires less fuel consumption (so minimum V ), depending on the mission needs. The considered maneuvers are executed by impulsive shots, so the analysis holds for maneuvers with traditional chemical rocket propulsion systems and definitely not for low-thrust propulsion systems (such as electric propulsion or solar sail). Backup slide

35. The Hohmann transfer Elena Ancona 35 The Hohmann transfer is defined as the “optimum” two-burn transfer between coplanar circular orbits, meaning that it is the transfer with minimum velocity change required. It is an ellipse tangent to both circular orbits. Note: in our scenario only one delta V is required! Backup slide

36. The Hohmann transfer Elena Ancona 36 The Hohmann transfer is defined as the “optimum” two-burn transfer between coplanar circular orbits, meaning that it is the transfer with minimum velocity change required. It is an ellipse tangent to both circular orbits. Note: in our scenario only one delta V is required! Backup slide

37. Heliocentric Hohmann transfers Elena Ancona 37 Backup slide

38. The cost of a variation in velocity’s direction Elena Ancona 38 Velocity is inversely proportional to the distance from the attracting body; The cost of a change in the velocity’s direction is proportional to the velocity itself; The more the spacecraft is close to the Sun, the more changing velocity’s direction will be expansive. Backup slide

39. The cost of a variation in velocity’s direction Elena Ancona 39 Velocity is inversely proportional to the distance from the attracting body; The cost of a change in the velocity’s direction is proportional to the velocity itself; The more the spacecraft is close to the Sun, the more changing velocity’s direction will be expansive. Backup slide

40. Method of patched conics Elena Ancona 40 The patched conics approach suggests that the gravity field of a multi-body system can be locally approximated about a single body. In other words, at any instance of time, the gravitational attraction acting on the spacecraft is assumed to be originating solely from the local dominant gravitational influence. Within the sphere of influence of the Earth, the trajectory is considered as a geocentric hyperbola that is solely determined by the gravity field of the Earth; The interplanetary part of the trajectory is considered to be a heliocentric conic section that is solely determined by the Sun’s gravity field; Within the sphere of influence of the target planet the trajectory is considered as a planetocentric hyperbola that is solely determined by the gravity field of that planet. Although the radius of a planetary sphere of influence is quite large, both in an absolute sense and in relation to the radius of that planet, the radius of the sphere of influence is always small when measured on the scale of the solar system. corresponds to 145 Earth radii, as Earth radius is 6378 km; is only about 0.6%, as the Sun-Earth distance is about 23460 Earth radii. Earth’s sphere of influence radius: Backup slide

41. Solar System Planets Elena Ancona 41 Backup slide

42. Interplanetary transfers Elena Ancona 42 At the time when the spacecraft leaves the sphere of influence of the Earth, its position is almost that of the Earth - when measured on the scale of the solar system - while it has a hyperbolic excess velocity (v_inf_e) with respect to the Earth. The direction of this velocity vector relative to v_e (that is the velocity vector of the Earth relative to the Sun) depends on the time of launch from the Earth’s surface, or on the position in the parking orbit (PO) where injection takes place in case the spacecraft is injected into its interplanetary trajectory from a PO about the Earth. When the spacecraft enters the sphere of influence of the target planet, the same computation scheme can be applied. The hyperbolic trajectory of the spacecraft within the sphere of influence of the target planet is completely determined by the point where the sphere of influence is entered and by the magnitude and direction of v_inf_t. Backup slide

43. Strategy: get to an easy-to-reach nearby planet using a chemical rocket propulsion system, and pass that planet on a precise trajectory such that the planet’s gravity field would change the vehicle’s orbital energy relative to the Sun and catapult it to another more distant planet or let it escape the Solar System. In this concept, the energy required for exploring the solar system is taken from the solar system itself! The ‘propulsive force’ automatically increases in direct proportion to the mass of the spacecraft. Hence, after the spacecraft is injected onto the first ‘leg’ of its interplanetary trajectory, the acceleration experienced by the spacecraft in a swingby maneuver is independent of its mass. No other propulsion system has this unique operating characteristic. Planetary Flyby Elena Ancona 43 Backup slide

44. The modern heavy-lift launchers Delta 4050H-19 and Atlas 551 can inject a payload of about 2900 kg and 2250 kg, respectively, into an escape trajectory with V4e = 7.5 km/s after a launch due east from Cape Canaveral; this velocity corresponds to V0 = 13.3 km/s and )V0 = 5.5 km/s when injection takes place at 185 km altitude. The Ariane 5 ECA launcher can inject a payload of about 4100 kg into an escape trajectory with V4e = 3.5 km/s after a launch due east from Kourou; this velocity corresponds to V0 = 11.6 km/s and )V0 = 3.8 km/s when injection takes place at 185 km altitude. Comparing these values with the ones listed in Table 18.2, we conclude that even these heavy-lift launchers cannot launch a payload with a mass of more than 2 ton to Jupiter and beyond along a minimum-energy Hohmann trajectory. So, additional so-called kick stages, more-powerful launchers or swingby techniques are needed to launch appreciable payloads to the outer planets. Planetary Flyby Elena Ancona 44 Backup slide

45. The first spacecraft to make use of the flyby strategy was NASA’s Pioneer 10: launched in 1972, in December 1973, it approached Jupiter, traveling at 9.8 km/s. The spacecraft passed Jupiter at a minimum altitude of 130350 km on December 3, 1973, and, as a result, it sped off into deep space at 22.4 km/s. On December 2005 the spacecraft was 89.7 AU away from the Sun, heading in the direction of the star Aldebaran in the constellation Taurus at roughly 2.6 AU per year. If Aldebaran had zero relative velocity, it would take Pioneer about 2 million years to reach it. Planetary Flyby Elena Ancona 45 Backup slide

46. Thrust is required to change the spacecraft velocity Tsiolkowski’s equation: the change in velocity (DV) is equal to the velocity with which mass is expelled (gas exhaust velocity, c), times the natural logarithm of the mass of the vehicle before the mass expulsion (mi) divided by the mass of the vehicle after the mass expulsion (mf). Specific Impulse describes the efficiency of a rocket in producing thrust with a particular propellant combination. It can be interpreted as being the number of seconds that 1 unit mass of propellant will burn when it produces one unit force of thrust. Space propulsion concepts Elena Ancona 46 Backup slide

47. Limits of chemical propulsion Elena Ancona 47 The relatively low exhaust velocity of chemical propellants only allow the launch of relatively small payloads, in particular to the more distant planets. Therefore, one had to accept that only a small fraction of the solar system could ever be reached and explored by instrumented spacecraft, or one had to develop more powerful propulsion systems, such as thermal-nuclear or nuclear-electric propulsion systems. For a given mission the characteristic velocity DV is approximately constant; For chemical propulsion the specific impulse is limited by the intrinsic energy of the chemical reaction; For electric propulsion the specific impulse can grow by reducing the propellant mass flow rate (dm/dt) and the thrust or by increasing the electric power. Backup slide

48. “For flight in interplanetary space I am working on the idea of flying, using tremendous mirrors of very thin sheets, capable of achieving favorable results” (F. Tsander, 1924). Solar sails are large sheets of low areal density material whose only source of energy is the Sun photons flux. At least in theory, a solar sail mission could be of unlimited duration, thanks to the “ever-present gentle push of sunlight”. Also a remarkable advantage is that no propellant is needed. Solar sail Elena Ancona 48 Unlike chemical rockets that provide short, powerful bursts of acceleration (very high thrust with low specific impulse), solar sail acceleration is slow but continuous — and, if wisely driven, this device can reach much higher speeds. Backup slide

49. The thrust vector of a solar sail is constrained on a “bubble” surface (green in the Figure) directed away from the Sun. The sail can lose or gain orbital angular momentum and change its orbit by controlling its orientation relative to the Sun: Solar sail Elena Ancona 49 Backup slide

50. Solar sail Elena Ancona 50 Backup slide

51. Absorbed Radiation Emitted Thermal Radiation Transmitted Radiation Reflected Radiation W Solar EM Radiation Energy Balance Absorbed Energy Emitted Thermal Energy Absorbed Radiation Elena Ancona 51 Backup slide

52. Dependence of the temperature of the solar sail material on the heliocentric distance When a radiation absorption coefficient and emissivity do not depend on temperature Radiation absorption coefficient and emissivity are the major parameters governing the solar sail’s surface temperature and its serviceability. When a radiation absorption coefficient and emissivity depend on temperature Elena Ancona 52 Backup slide