ASEN 5050 SPACEFLIGHT DYNAMICS Solar Radiation Pressure Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP

Announcements Mid-Term due now! Homework #6 is due Friday 10/24 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

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

Final Project Instructions for delivery of the final project: Build your webpage with every required file inside of a directory. Name the directory “<LastName_FirstName>” there are a lot of duplicate last names in this class! You can link to external sites as needed. Name your main web page “index.html” 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

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

Comet Siding Spring Opportunity’s image from the Martian surface Lecture 22: SRP

Comet Siding Spring MRO’s view of the nucleus – smaller than estimates indicated! 138 m/pixel – maybe 500 meters in size Lecture 22: SRP

ASEN 5050 SPACEFLIGHT DYNAMICS Perturbations Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP

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

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

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? When/Why/How is SRP any different than gravity? Force of Gravity: 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) Net Force of SRP: 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) Lecture 22: SRP

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

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

Solar Radiation Pressure The acceleration due to solar radiation pressure is: Unit vector from satellite to Sun Lecture 22: SRP

Solar Radiation Pressure Absorption Reflection: diffuse and specular incident light The light is either absorbed, reflected diffusely, or reflected specularly. Depends on the material, wavelength, and surface! Lecture 22: SRP

Solar Radiation Pressure Fully absorbed Fully diffusely reflected Fully specularly reflected incident light Net force All light is either absorbed, diffusely reflected, or specularly reflected! Net force Net force Lecture 22: SRP

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 Normal Lecture 22: SRP

Different SRP Models Flat-Plate Model NOT pointed at the Sun θ θ To Sun θ Normal Lecture 22: SRP

Different SRP Models Flat-Plate Model NOT pointed at the Sun θ θ To Sun θ Net Force Normal 1.0 0.0 0.0 Lecture 22: SRP

Different SRP Models Flat-Plate Model NOT pointed at the Sun θ Net Force θ To Sun θ Normal 0.0 1.0 0.0 Lecture 22: SRP

Different SRP Models Flat-Plate Model NOT pointed at the Sun Net Force θ θ To Sun θ Normal 0.0 0.0 1.0 Lecture 22: SRP

Different SRP Models Flat-Plate Model NOT pointed at the Sun θ Net Force θ To Sun θ Normal 0.33 0.33 0.33 Lecture 22: SRP

Different SRP Models Cannonball Model To Sun Lecture 22: SRP

Different SRP Models Cannonball Model Fully Absorbed To Sun Net Force Lecture 22: SRP

Different SRP Models Cannonball Model Fully Diffusely Reflected To Sun Net Force Lecture 22: SRP

Different SRP Models Cannonball Model Fully Specularly Reflected To Sun Net Force Lecture 22: SRP

Different SRP Models Cannonball Model 1/3 absorbed, 1/3 diffused, 1/3 specular To Sun Net Force Lecture 22: SRP

Earth Albedo Earth reflects sunlight Earth emits IR radiation Moon does too. Spacecraft Earth Sunlight Lecture 22: SRP

Earth Albedo Earth reflects sunlight Earth emits IR radiation Moon does too. Spacecraft Direct SRP Emitted Radiation Reflected Radiation Earth Sunlight Lecture 22: SRP

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 Earth Sunlight Lecture 22: SRP

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 Earth Sunlight Lecture 22: SRP Credit: NASA/GSFC

Solar Radiation Pressure Shadow analysis in shadow Cylindrical Shadow Model (Sun infinite distance from Earth) Lecture 22: SRP

Solar Radiation Pressure More complicated models take into account umbra/penumbra Annular Lecture 22: SRP

Solar Radiation Pressure The scale illustrates how narrow the penumbra is. Lecture 22: SRP

Shadow Is satellite in sunlight? Cylindrical model: b Lecture 22: SRP

Yarkovsky Effect Lecture 22: SRP

YORP Effect Lecture 22: SRP

Poynting Robertson Effect Lecture 22: SRP

Announcements Mid-Term due now! Homework #6 is due Friday 10/24 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

ASEN 5050 SPACEFLIGHT DYNAMICS Atmospheric Drag Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 22: SRP

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

Atmospheric Drag Drag tends to change a and e the most. The drag acceleration can be written as: Lecture 22: SRP

Atmospheric Drag How does this relationship impact a satellite in orbit? Lecture 22: SRP

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: where r0 = ref density, h0 = ref. altitude, hellp = altitude, H = scale height Lecture 22: SRP

Atmospheric Drag Lecture 22: SRP

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

Atmospheric Drag Lecture 22: SRP

Atmospheric Drag Lecture 22: SRP

Atmospheric Models Lecture 22: SRP

Measuring Atmospheric Density Using Satellite Data Lecture 22: SRP

The CHAMP Mission Initial mass: 522 kg Attitude control: (2 ± 0.1)° Along-track 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 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

Accelerometers - ONERA http://www.onera.fr Lecture 22: SRP

The STAR Reference Frame Lecture 22: SRP

Champ Along-Track Accelerations Lecture 22: SRP

STAR Accelerations vs Models Lecture 22: SRP

April 15-24, 2002 Lecture 22: SRP

CHAMP Total Density at 410 km Lecture 22: SRP

CHAMP Density at 410 km Lecture 22: SRP

Density versus Latitude/Time Lecture 22: SRP

Day/Night Animation Lecture 22: SRP

North Pole Animation Lecture 22: SRP

South Pole Animation Lecture 22: SRP

CHAMP Coverage, Sept 1-15, 2002 Lecture 22: SRP

Total Density: September 1-14, 2002 Lecture 22: SRP

Total Density: September 1-14, 2002 Lecture 22: SRP

Total Density: September 1-14, 2002 Lecture 22: SRP

Wave Structures Observed Lecture 22: SRP

CHAMP Density at 400 km, Ascending 303 305 304 302 Lecture 22: SRP

CHAMP Density at 400 km, Ascending 323 324 Lecture 22: SRP

Zonal Winds Observed Lecture 22: SRP

Density Ratios: May 14 - Aug 15, 2001 DTM2000 Jacchia 70 DTM94 MSIS86 Lecture 22: SRP

Density Ratio: May 14, 2001 - May 1, 2002 DTM2000 Jacchia 70 DTM94 MSIS86 Lecture 22: SRP

Announcements Mid-term due Tuesday for CAETE students No HW7 yet, maybe Thursday. Next week: STK Lab 2 Tuesday and Thursday (2 sessions) I’ll be out of town so Josh will run the lab. Reading: Chapters 8 and 9 Lecture 22: SRP