ASEN 5050 SPACEFLIGHT DYNAMICS Atmospheric Drag Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 23: Drag 1

Announcements Homework #6 is due right now –CAETE by Friday 10/31 Homework #7 will be released either today or soon. Due date depends on when I get it out –Pretty easy homework – practice with numerical integration. Comparing it to Kepler. Reading: Chapters 8 and 9 Lecture 23: Drag 2

Concept Quiz 13 Lecture 23: Drag 3

Concept Quiz 13 Lecture 23: Drag 4

Concept Quiz 13 Lecture 23: Drag 5

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 23: Drag 6

Final Project Instructions for delivery of the final project: Build your webpage with every required file inside of a directory. –Name the directory “ ” –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 23: Drag 7

Space News Lecture 23: Drag 8 More Siding Spring pics Partial solar eclipse yesterday Cassini is flying by Titan on Friday for the 107 th 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)

Siding Spring’s hydrogen coma Lecture 23: Drag 9

ASEN 5050 SPACEFLIGHT DYNAMICS Perturbations Prof. Jeffrey S. Parker University of Colorado – Boulder Lecture 23: Drag 10

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 23: Drag 11 ✔ ✔ ✔ ✔

Atmospheric Drag Atmospheric drag is 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 23: Drag 12

Lecture 23: Drag Atmospheric Drag Drag tends to change a and e the most. The drag acceleration can be written as: 13

Atmospheric Drag How does this relationship impact a satellite in orbit? Lecture 23: Drag 14

Lecture 23: Drag 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  0 = ref density, h 0 = ref. altitude, h ellp = altitude, H = scale height 15

Lecture 23: Drag Atmospheric Drag 16

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 23: Drag 17

Lecture 23: Drag Atmospheric Drag 18

Lecture 23: Drag Atmospheric Drag 19

Lecture 23: Drag Atmospheric Models 20

Measuring Atmospheric Density Using Satellite Data Lecture 23: Drag 21

Lecture 23: Drag 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). Initial mass: 522 kg Attitude control: (2 ± 0.1)° STAR sampling rate: 1 Hz STAR resolution: 3·10 -9 m/s 2 /Hz 0.5 Tracking: GPS and SLR 87° orbit inclination LST precession 5.44 min/day 24-hr local time sampling in 133 days Altitude range: km The CHAMP Mission 22

Lecture 23: Drag Accelerometers - ONERA 23

Lecture 23: Drag The STAR Reference Frame 24

Lecture 23: Drag Champ Along-Track Accelerations 25

Lecture 23: Drag STAR Accelerations vs Models 26

Lecture 23: Drag April 15-24,

Lecture 23: Drag CHAMP Total Density at 410 km 28

Lecture 23: Drag CHAMP Density at 410 km 29

Lecture 23: Drag Density versus Latitude/Time 30

Lecture 23: Drag Day/Night Animation 31

Lecture 23: Drag North Pole Animation 32

Lecture 23: Drag South Pole Animation 33

Lecture 23: Drag CHAMP Coverage, Sept 1-15,

Lecture 23: Drag Total Density: September 1-14,

Lecture 23: Drag Total Density: September 1-14,

Lecture 23: Drag Total Density: September 1-14,

Lecture 23: Drag Wave Structures Observed 38

Lecture 23: Drag CHAMP Density at 400 km, Ascending

Lecture 23: Drag CHAMP Density at 400 km, Ascending

Lecture 23: Drag Zonal Winds Observed 41

Lecture 23: Drag Density Ratios: May 14 - Aug 15, 2001 DTM2000 DTM94 MSIS86 Jacchia 70 42

Lecture 23: Drag Density Ratio: May 14, May 1, 2002 DTM2000 DTM94MSIS86 Jacchia 70 43

GOCE Lecture 18: Perturbations 44

GOCE Uses electric propulsion to remain at an altitude of ~167 km Not long ago, it ran out of fuel. Not long ago, it re-entered Earth’s atmosphere Lecture 18: Perturbations 45

ISS Altitude Lecture 18: Perturbations 46

ISS Altitude Lecture 18: Perturbations 47

lecture16.ppt ©R.S. Nerem Oblateness Perturbations

lecture16.ppt ©R.S. Nerem General Perturbation Techniques Which is a “secularly precessing ellipse”. The equatorial bulge introduces a force component toward the equator causing a regression of the node (for prograde orbits) and a rotation of periapse. Note:

lecture16.ppt ©R.S. Nerem General Perturbation Techniques

lecture16.ppt ©R.S. Nerem General Perturbation Techniques

lecture16.ppt ©R.S. Nerem General Perturbation Techniques Periapse also precesses. = 0 at the critical inclination, i  = 63.4  (116.6  )

lecture16.ppt ©R.S. Nerem General Perturbation Techniques

lecture16.ppt ©R.S. Nerem General Perturbation Techniques Gravity perturbations also affect geosynchronous orbits.

lecture16.ppt ©R.S. Nerem General Perturbation Techniques Application: Sun Synchronous orbits

lecture16.ppt ©R.S. Nerem General Perturbation Techniques Sun Synchronous orbits: –Orbit plane remains at a constant angle (  ’ ) with respect to the Earth-Sun line. –Orbit plane precession about the Earth is equal to period of Earth’s orbit about the Sun.

Lecture 18: Perturbations 57 Perturbations Special Perturbation Techniques – Numerical integration. Straightforward – however obtaining a good understanding of the effects on the orbit is difficult General Perturbations – Use approximations to obtain analytical descriptions of the effects of the perturbations on the orbit. Assumes perturbative forces are small Early work used general perturbations because of a lack of computational power. Modern work uses special perturbations (numerical integration) because of the wide availability of computers. GP still useful for increasing your understanding. Still used by AF for maintaining space object catalog (> 7000 objects).

Trend Analyses While it’s useful to be able to numerically integrate high- fidelity equations of motion, it’s also useful to have an expectation for what may appear! Drag –Clear reduction in a and e SRP –Depends, but in some circumstances it can increase e Earth’s oblateness –Dramatic change in Ω, ω, and M Third-body effects –Precession of the nodes, same effect as oblateness. Lecture 18: Perturbations 58

Trend Analyses Secular Trends Long periodic effects Short periodic effects Mean elements Osculating elements Lecture 18: Perturbations 59

lecture15.ppt ©R.S. Nerem General Perturbation Techniques Perturbations can be categorized as secular, short period, long period.

lecture15.ppt ©R.S. Nerem Perturbations secular long-periodic mixed-periodic short-periodic This equation is known as a “Poisson Series”

Perturbation Magnitudes Lecture 18: Perturbations 62 ISS Orbit

Perturbation Magnitudes Lecture 18: Perturbations 63 GPS Orbit

Perturbation Magnitudes Lecture 18: Perturbations 64 Earth – Mars