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ASEN 5050 SPACEFLIGHT DYNAMICS Solar Radiation Pressure Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP 1 Announcements • Mid-Term due now! – CAETE due date next week – After which I’ll talk through all of the answers! – I’ll be grading the mid-terms this Friday – about the earliest I can. I’ll hand them back after the CAETE due date. • Homework #6 is due Friday 10/24 – CAETE by Friday 10/31 • Concept Quiz 13 after lecture! If you pay attention to the lecture today, it’ll be easy. • Reading: Chapters 8 and 9 • I have to leave my office hours early today – if you need something, please come by 2 – 2:30. Lecture 22: SRP 2 Final Project • Get started on it! • Worth 20% of your grade, equivalent to 6-7 homework assignments. • Find an interesting problem and investigate it – anything related to spaceflight mechanics (maybe even loosely, but check with me). • Requirements: Introduction, Background, Description of investigation, Methods, Results and Conclusions, References. • You will be graded on quality of work, scope of the investigation, and quality of the presentation. The project will be built as a webpage, so take advantage of web design as much as you can and/or are interested and/or will help the presentation. Lecture 22: SRP 3 Final Project • Instructions for delivery of the final project: • Build your webpage with every required file inside of a directory. – – – • Name your main web page “index.html” – • Name the directory “<LastName_FirstName>” there are a lot of duplicate last names in this class! You can link to external sites as needed. i.e., the one that you want everyone to look at first Make every link in the website a relative link, relative to the directory structure within your named directory. – We will move this directory around, and the links have to work! • Test your webpage! Change the location of the page on your computer and make sure it still works! • Zip everything up into a single file and upload that to the D2L dropbox. Lecture 22: SRP 4 Space News • Comet Siding Spring images • Partial solar eclipse tomorrow, at sunset • Cassini is flying by Titan on Friday for the 107th time. – This time its doing a bistatic radar observation of Titan’s lakes. – Altitude of closest approach: 629 miles (1013 km) – Speed: 13,000 mph (5.6 km/s) Lecture 22: SRP 5 Comet Siding Spring Opportunity’s image from the Martian surface Lecture 22: SRP 6 Comet Siding Spring MRO’s view of the nucleus – smaller than estimates indicated! 138 m/pixel – maybe 500 meters in size Lecture 22: SRP 7 ASEN 5050 SPACEFLIGHT DYNAMICS Perturbations Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP 8 Perturbation Discussion Strategy ✔• Introduce the 3-body and n-body problems – We’ll cover halo orbits and low-energy transfers later ✔• Numerical integration ✔• Introduce aspherical gravity fields – J2 effect, sun-synchronous orbits • Solar radiation pressure • Atmospheric drag – Atmospheric entries • Other perturbations • General perturbation techniques • Further discussions on mean motion vs. osculating motion. Lecture 22: SRP 9 Solar Radiation Pressure • SRP is the effect of solar photons striking the spacecraft and imparting a force on it. • Many things can and do happen – Photons are absorbed by the spacecraft and transmit energy to the spacecraft. – Photons are reflected off of the spacecraft, imparting more energy to the spacecraft. – Photons heat up the spacecraft, which can change the thermal radiative characteristics of the spacecraft. – Photons act on average through the center of pressure; if that isn’t aligned or coincident with the center of mass then a torque is applied to the spacecraft. Lecture 22: SRP 10 Solar Radiation Pressure • If we treat the spacecraft as a uniform sphere, SRP may be perceived as merely an offset of the Sun’s gravity. Why? Force of Gravity: Net Force of SRP: •Originates from the Sun’s center of mass; •Falls off as the square of the distance; •Is transmitted at the speed of light (if the Sun moved, we’d perceive a change in the gravitational acceleration some 8 minutes later) •Originates from the Sun’s optical center; •Falls off as the square of the distance; •Is transmitted at the speed of light (if the Sun moved, we’d perceive a change in SRP some 8 minutes later) • When/Why/How is SRP any different than gravity? Lecture 22: SRP 11 Solar Radiation Pressure • SRP differs from gravity in several key ways: – Gravity attracts mass, SRP acts on a surface – Absorption, diffuse reflection, specular reflection, refraction, torques applied to a real spacecraft – Variations in the solar flux over time – Shadow / eclipse passages Lecture 22: SRP 12 Solar Radiation Pressure • 8 x 1017 photons / cm2 with λavg = 556 nm at 1 AU • Intensity, irradiance, solar flux (different names for the same thing): ~1367 W/m2 – Computed by estimating the total output of the Sun and dividing it by the surface area at our radius from the Sun 3.823 x 1026 Watts / 4πr2 – You can use a varying flux based on radius to be more accurate! • We can relate this solar flux to a pressure (i.e., a change in momentum) by measuring the momentum of the energy being transferred using Einstein’s famous relationship: • The force of solar pressure per unit area (change in momentum) is: Lecture 22: SRP 13 Solar Radiation Pressure The acceleration due to solar radiation pressure is: Unit vector from satellite to Sun Lecture 22: SRP 14 Solar Radiation Pressure • Absorption • Reflection: diffuse and specular The light is either absorbed, reflected diffusely, or reflected specularly. Depends on the material, wavelength, and surface! Lecture 22: SRP 15 Solar Radiation Pressure Fully absorbed Fully diffusely reflected Fully specularly reflected Net force All light is either absorbed, diffusely reflected, or specularly reflected! Lecture 22: SRP Net force Net force 16 Different SRP Models • Flat-Plate Model – Assume you have a flat plate that is pointed at the Sun • CR defines how much reflection the plate generates • 0 = no force, 1 = absorbed, 1.5 = combination of absorption, diffuse reflection, and specular reflection, 2 = specular To Sun Lecture 22: SRP Normal 17 Different SRP Models • Flat-Plate Model – NOT pointed at the Sun To Sun θ θ θ Normal Lecture 22: SRP 18 Different SRP Models • Flat-Plate Model – NOT pointed at the Sun To Sun θ θ θ Net Force Normal 1.0 Lecture 22: SRP 0.0 0.0 19 Different SRP Models • Flat-Plate Model – NOT pointed at the Sun To Sun θ θ Net Force θ Normal 0.0 Lecture 22: SRP 1.0 0.0 20 Different SRP Models • Flat-Plate Model – NOT pointed at the Sun To Sun Net Force θ θ θ Normal 0.0 Lecture 22: SRP 0.0 1.0 21 Different SRP Models • Flat-Plate Model – NOT pointed at the Sun To Sun θ θ Net Force θ Normal 0.33 Lecture 22: SRP 0.33 0.33 22 Different SRP Models • Cannonball Model To Sun Lecture 22: SRP 23 Different SRP Models • Cannonball Model To Sun Lecture 22: SRP Fully Absorbed Net Force 24 Different SRP Models • Cannonball Model To Sun Lecture 22: SRP Fully Diffusely Reflected Net Force 25 Different SRP Models • Cannonball Model To Sun Lecture 22: SRP Fully Specularly Reflected Net Force 26 Different SRP Models • Cannonball Model To Sun Lecture 22: SRP 1/3 absorbed, 1/3 diffused, 1/3 specular Net Force 27 Earth Albedo • Earth reflects sunlight • Earth emits IR radiation • Moon does too. Spacecraft Sunlight Earth Lecture 22: SRP 28 Earth Albedo • Earth reflects sunlight • Earth emits IR radiation • Moon does too. Spacecraft Direct SRP Emitted Radiation Reflected Radiation Sunlight Earth Lecture 22: SRP 29 Earth Albedo • Earth reflects sunlight • Earth emits IR radiation • Moon does too. 1367 Watts/m2 energy arrives at the Earth Earth’s albedo is ~0.3 239 W/m2 is reflected away, as a diffuse/specular cannonball The rest eventually gets emitted. Spacecraft Direct SRP Emitted Radiation Reflected Radiation Sunlight Earth Lecture 22: SRP 30 Earth Albedo • Earth reflects sunlight • Earth emits IR radiation • Moon does too. 1367 Watts/m2 energy arrives at the Earth Earth’s albedo is ~0.3 239 W/m2 is reflected away, as a diffuse/specular cannonball The rest eventually gets emitted. Spacecraft Direct SRP Emitted Radiation Reflected Radiation Sunlight Earth 31 Lecture 22: SRP Credit: NASA/GSFC Solar Radiation Pressure Shadow analysis aSRP = 0 in shadow Cylindrical Shadow Model (Sun infinite distance from Earth) Lecture 22: SRP 32 Solar Radiation Pressure More complicated models take into account umbra/penumbra Annular Lecture 22: SRP 33 Solar Radiation Pressure The scale illustrates how narrow the penumbra is. Lecture 22: SRP 34 Shadow Is satellite in sunlight? Cylindrical model: rSAT rSUN b rSHADE rSHADE = 6378 km cos b = rSAT × rSUN rSAT rSUN If b > 90° then If rSATsinb > rSHADE ® In Sunlight Lecture 22: SRP 35 Yarkovsky Effect Lecture 22: SRP 36 YORP Effect Lecture 22: SRP 37 Poynting Robertson Effect Lecture 22: SRP 38 Announcements • Mid-Term due now! – CAETE due date next week – After which I’ll talk through all of the answers! – I’ll be grading the mid-terms this Friday – about the earliest I can. I’ll hand them back after the CAETE due date. • Homework #6 is due Friday 10/24 – CAETE by Friday 10/31 • Concept Quiz 13 after lecture! If you pay attention to the lecture today, it’ll be easy. • Reading: Chapters 8 and 9 • I have to leave my office hours early today – if you need something, please come by 2 – 2:30. Lecture 22: SRP 39 ASEN 5050 SPACEFLIGHT DYNAMICS Atmospheric Drag Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP 40 Atmospheric Drag • Atmospheric drag is a touch more familiar, since we experience it all the time. • Force experienced by any body that travels through a gaseous medium, acting against the relative velocity. • The force passes through the center of pressure. – If the center of mass is not aligned with the center of pressure, then a torque is introduced. Lecture 22: SRP 41 Atmospheric Drag Drag tends to change a and e the most. The drag acceleration can be written as: 1 CD A 2 Vrel adrag = - 2 m r Vrel Vrel C D = coefficient of drag, dimensionless, susceptibility to drag forces, ~ 2 CD A m = ballistic coefficient ( ) m CD A r = atmospheric density A = cross - sectional area normal to the sat' s velocity vector é dx ù + w x Å ú ê dt Þ need attitude ê dy ú dr Vrel = velocity relative to a rotating atmosphere = - wÅ ´ r = ê - wÅ y ú dt ê dt ú dz ê ú êë dt úû Lecture 22: SRP 42 Atmospheric Drag • How does this relationship impact a satellite in orbit? 1 CD A 2 Vrel adrag = r Vrel 2 m Vrel Lecture 22: SRP 43 Atmospheric Drag Density varies due to: – Changes in the magnetic field (charged particles) – geomagnetic index – Changes in the solar flux (F10.7 – flux at 10.7cm wavelength) Many models (Jacchia, MSIS, DTM, etc.). Simplest is Exponential: h -h r = r0 e - ellp 0 H where r0 = ref density, h0 = ref. altitude, hellp = altitude, H = scale height Lecture 22: SRP 44 Atmospheric Drag r = r0 Lecture 22: SRP hellp -h0 e H 45 Atmospheric Drag Variability • Latitudinal Variations – Earth’s oblateness; the actual height of the satellite varies even in a circular orbit! • Longitudinal Variations – Those darn mountains cause weather variations. • Time-Varying – – – – – – – Diurnal 27-day solar cycle 11-year cycle of sunspots Seasonal variations Winds Magnetic storms Tides Lecture 22: SRP 46 Atmospheric Drag Lecture 22: SRP 47 Atmospheric Drag Lecture 22: SRP 48 Atmospheric Models Lecture 22: SRP 49 Measuring Atmospheric Density Using Satellite Data Lecture 22: SRP 50 The CHAMP Mission Along-track The end-of-mission altitude, after 5 years, will be 250 km. This objective will be attained by natural decay and orbit corrections (function of solar activity). Lecture 22: SRP • Initial mass: 522 kg • Attitude control: (2 ± 0.1)° • STAR sampling rate: 1 Hz • STAR resolution: 3·10-9 m/s2/Hz0.5 • Tracking: GPS and SLR • 87° orbit inclination • LST precession 5.44 min/day • 24-hr local time sampling in 133 days • Altitude range: 460-250 km 51 Accelerometers - ONERA http://www.onera.fr Lecture 22: SRP 52 The STAR Reference Frame Lecture 22: SRP 53 Champ Along-Track Accelerations Lecture 22: SRP 54 STAR Accelerations vs Models Lecture 22: SRP 55 April 15-24, 2002 Lecture 22: SRP 56 CHAMP Total Density at 410 km Lecture 22: SRP 57 CHAMP Density at 410 km Lecture 22: SRP 58 Density versus Latitude/Time Lecture 22: SRP 59 Day/Night Animation Lecture 22: SRP 60 North Pole Animation Lecture 22: SRP 61 South Pole Animation Lecture 22: SRP 62 CHAMP Coverage, Sept 1-15, 2002 Lecture 22: SRP 63 Total Density: September 1-14, 2002 Lecture 22: SRP 64 Total Density: September 1-14, 2002 Lecture 22: SRP 65 Total Density: September 1-14, 2002 Lecture 22: SRP 66 Wave Structures Observed Lecture 22: SRP 67 CHAMP Density at 400 km, Ascending 304 305 303 302 Lecture 22: SRP 68 CHAMP Density at 400 km, Ascending 323 324 Lecture 22: SRP 69 Zonal Winds Observed Lecture 22: SRP 70 Density Ratios: May 14 - Aug 15, 2001 Density Ratio: Observed / DTM2000, May 14 - Aug 15, 2001 90 60 60 30 30 Latitude 90 DTM2000 0 Jacchia 70 0 -30 -30 -60 Density Ratio: Observed / MSIS86 -60 -90 90 Density Ratio: Observed/DTM94, May 14 - Aug 15, 2001 Observed / MSIS86, May1614 - Aug20 15, 2001 24 0Density Ratio: 4 8 12 0 4 8 12 16 20 24 Local Time 90 60Time 90 Local DTM94 -90 MSIS86 0.5 0.7 0 30 60 0 0.8 1.0 1.2 Density -30 Ratio -30 -60 -60 -90 1.3 0 4 8 0.7 0 -60 12 Local Time 1 3 16 20 0.5 Lecture 22:0.5 SRP 0.5 0.6 0.8 0.9 1.1 1.2 1.4 1.5 time1_doc_14 30 -30 0 -90 1.5 Latitude 30 Latitude 60 0.8 1.0 1.2 Density Ratio 1.3 1.5 0.7 -90 24 Kp 4 6 0 0.8 1.0 1.2 Density Ratio 4 1.3 7 8 12 Local Time 16 20 24 1.5 0.5 0.7 0.8 1.0 1.2 Density Ratio 1.3 1.5 71 Density Ratio: Observed / DTM2000 Density Ratio: May 14, 2001 - May 1, 2002 90 90 DTM2000 60 30 30 Latitude 60 0 Jacchia 70 0 -30 -30 Density Ratio:-60 Observed / MSIS86 -60 90 Density Ratio: Observed / DTM94 0 1 3 4 6 60 90 Kp DTM94 30 60 -90 -90 0 0 0.70 0.90 1.10 1.30 -30 Density Ratio -30 -60 -60 -90 Latitude 0.50 1 3 3 3 30 4 6 0.70 7 0 -60 4 6 1 6 7 0.90 1.10 1.30 Density Ratio 7 3 4 Kp 0.5 0.50 6 0.5 0.6 0.8 0.9 1.1 1.2 1.4 all_dat1_14_md Kp Lecture 22: SRP 4 Kp MSIS86 -90Kp 0 7 -90 1 1 -30 0 0 90 60 Latitude 30 7 Density Ratio: Observed / MSIS86 0 0.7 0.8 1.0 1.2 Density Ratio 1.3 1.5 0.5 0.7 0.8 1.0 1.2 Density Ratio 1.3 1.5 72 Announcements • • Mid-term due Tuesday for CAETE students No HW7 yet, maybe Thursday. • Next week: STK Lab 2 Tuesday and Thursday (2 sessions) – • Lecture 22: SRP I’ll be out of town so Josh will run the lab. Reading: Chapters 8 and 9 73