Lesson 17: Spacecra/ Thermal Control I. 11/1/2016 Robin Wordsworth ES/EPS 160: Space Science and Engineering: Theory and ApplicaFons

Transcription

1 Lesson 17: Spacecra/ Thermal Control I 11/1/2016 Robin Wordsworth ES/EPS 160: Space Science and Engineering: Theory and ApplicaFons

2 ObjecFves Learn Kirchoff s Law Study thermal equilibrium of an idealized spherical planet / spacecra/ Calculate satellite eclipse Fme in a circular orbit

3 Why do we care about the space thermal environment? Planetary science Climate and radiafve balance Link with atmospheric and surface composifon (remote sensing) Satellite engineering Most electronic equipment is designed for Earth surface T range Structural requirements (minimizafon of thermal distorfon)

4 Quick quiz: What is the temperature of space? A physicist s answer: It s complicated! CMB temperature is 2.7 K. Temperature of neutrals, ions and electrons depends on the populafon in quesfon, collision rates, exchange processes, magnefc effects, solar wind interacfon. A satellite thermal engineer s answer: I don t care. A spacecra/ s temperature is determined by the balance of internal heafng and radiafve exchange with the Sun and the body it orbits, not the local temperature of space.

5 Spacecra/ thermal balance in one slide ON EARTH IN SPACE radiafon convecfon radiafon conducfon

6 Blackbody Revision WAVENUMBER [cm -1 ]: = /100c FREQUENCY [Hz] SPEED OF LIGHT [m/s] B( ) = 2h 3 c 2 1 e h /k BT 1 Spectral radiance [W/m 2 /sr/hz] = 10 4 / WAVELENGTH [μm] angular and spectral integrafon B = c 2 B flux [W/m 2 ] hap://hyperphysics.phy-astr.gsu.edu/hbase/wien.html Stefan-Boltzmann Law

7 Greybody RadiaFon Blackbody (T = T 0 )

8 Greybody RadiaFon T 4 0 Blackbody (T = T 0 )

9 Greybody RadiaFon Greybody (T = T 1, emissivity ε, absorpbvity α) T 4 0 Blackbody (T = T 0 )

10 Greybody RadiaFon Greybody (T = T 1, emissivity ε, absorpbvity α) T 4 1 T 4 0 Blackbody (T = T 0 )

11 Greybody RadiaFon + T0 4 Greybody (T = T 1, emissivity ε, absorpbvity α) T1 4 T 4 1 T 4 0 Blackbody (T = T 0 )

12 Kirchoff s Law + T0 4 Greybody (T = T 1, emissivity ε, absorpbvity α) T1 4 T 4 0 The two regions evolve towards thermal equilibrium (2 nd Law of TD) In thermal equilibrium, T 0 = T 1 (0 th Law) Hence α = ε T 4 1 Blackbody (T = T 0 )

13 Kirchoff s Law + T 4 0 Greybody (T = T 1, emissivity ε, absorpbvity α) True independently at every wavelength! T 4 1 T 4 0 α λ = ε λ WAVELENGTH-SELECTIVE FILTER Blackbody (T = T 0 )

14 IN VISIBLE IN INFRARED Fortescue, Spacecra/ Systems Engineering

15 KAPTON VISIBLE Note: In the infrared, white paint is black! INFRARED Pisacane, Fundamentals of Space Systems hap://

16 The Planetary Thermal Environment RadiaFve heat exchange dominates conducfon for satellites in LEO and above External heat sources: Sun Planetary albedo (visible) Planetary thermal radiafon and sinks: Deep space (2.7 K blackbody) Internal sources RTGs Electrical power dissipafon Humans Fin = Fout hap://wallpapersinhq.com/images/big/earth_orbit jpg hap://apod.nasa.gov/apod/ap html

17 Example: The equilibrium temperature of the Moon Lunar visible albedo is approx. A = 0.12 (12% of incoming solar radiafon reflected) So visible absorpfvity here is α = 1 - A = 0.88 Thermal emissivity for lunar silicate minerals is approx. ε = 0.9 hap://

18 Example: The equilibrium temperature of the Moon α = 0.88 ε = 0.9 AssumpFons: Absorbed solar flux balances thermal emission Internal heat and Earthshine (visible and IR) can be neglected Global mean can be applied Is this a good approximafon to the true surface temperature? F s = L = 1366 W/m2 4 d2 SOLAR CONSTANT 4 r 2 F ir = r 2 F s 4 T 4 = F s T = Fs 4 T = K 1/4

19 hap://

20 Spacecra/ equilibrium temperature in LEO A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION

21 Spacecra/ equilibrium temperature in LEO A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION EARTHSHINE (VISIBLE) EARTHSHINE (IR) INTERNAL FLUX

22 Spacecra/ equilibrium temperature in LEO Earth visibility factor Earth albedo A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION EARTHSHINE (VISIBLE) EARTHSHINE (IR) INTERNAL FLUX

23 Earthshine: visibility factor and thermal IR scaling In the visible, can assume Earth is a diffuse reflecfng sphere: For IR radiafon, F E,IR 230 W/m 2 at top of the atmosphere (by energy conservafon) MulFply this by factor r E2 /(r E +z) 2 to get approximate value at orbital alftude z VISIBLE (REFLECTED/SCATTERED) SOLAR RADIATION f Fortescue, Spacecra/ Systems Engineering

24 Equilibrium temperature in LEO Earth visibility factor Earth albedo A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION EARTHSHINE (VISIBLE) EARTHSHINE (IR) INTERNAL HEATING Spherical satellite case (e.g. Sputnik): 4 r 2 T 4 = r 2 F s + r 2 ff s A E + r 2 F E,IR + Q i

25 Equilibrium temperature in LEO Earth visibility factor Earth albedo A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION EARTHSHINE (VISIBLE) EARTHSHINE (IR) INTERNAL HEATING Spherical satellite case (e.g. Sputnik): 4 r 2 T 4 = r 2 F s + r 2 ff s A E + r 2 F E,IR + Q i 4 T 4 = F s + ff s A E + F E,IR + Q i / r 2

26 Equilibrium temperature in LEO Earth visibility factor Earth albedo A 1 T 4 = A 2 F s + A 3 ff s A E + A 3 F E,IR + Q i THERMAL EMISSION SOLAR RADIATION EARTHSHINE (VISIBLE) EARTHSHINE (IR) INTERNAL FLUX Spherical satellite case (e.g. Sputnik): T 4 = 1 4 ( / )F s(1 + fa E )+ 1 4 F E,IR + Q i /4 r 2

27 Satellite Eclipse Time (Circular Orbit) solar radiafon

28 Satellite Eclipse Time (Circular Orbit) solar radiafon

29 Satellite Eclipse Time (Circular Orbit) r E r solar radiafon f

30 Satellite Eclipse Time (Circular Orbit) r r E solar radiafon r sin f = r E f =sin 1 [r E /(r E + z)] R dark = f/ t dark = R dark t orb f QuesFons: What is t dark for LEO with zero inclinafon? How does t dark vary with z?

31 Summary RadiaFve fluxes (determined by Stefan- Boltzmann Law) dominate thermal balance in a vacuum Kirchoff s Law means α = ε at a single wavelength [but α = α(λ) in general] Satellite eclipse Fme in a circular planar orbit can be calculated simply from geometry. In ellipfcal case, we need to use Kepler s equafon (Lesson 9).