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Lecture 5: Asteroid Discovery and Characterization Using Stellar Occultation

Lecture 5: Asteroid Discovery and Characterization Using Stellar Occultation. 1. On the Idea Of Shadows.

malcolm-holcomb
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Lecture 5: Asteroid Discovery and Characterization Using Stellar Occultation

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  1. Lecture 5: Asteroid Discovery and Characterization Using Stellar Occultation 1

  2. On the Idea Of Shadows “Shadow is not of darkness, but rather the footprint of darkness in light, or the footprint of light in darkness… Nor does Nature suffer an immediate progression from one extreme to the other, but only through mediating shadows” De Umbris Idearum, Giordano Bruno, 1582

  3. Basic technique: A set of observers note the time and duration that a star disappears from sight. Then plot the ground track of the asteroid during the occultations and get the asteroid shape (silhouette) This seems very straightforward, so what’s left to learn? Answer: The simple technique assumes the asteroid is big enough (10s to 100s of km) to cast a sharp shadow. “Small” asteroids (like Apophis) may create “interference patterns”, not well defined shadows! 3

  4. NEA Detection Summary Only 1% detected, and if you wait for sharp shadows, it’s probably too late! 4

  5. The Realm of Shadows Interference zone a Shadow zone Fraunhofer region Fresnel region F = 10 F = 5 F = 1 F = 0.2

  6. Stellar Occultation System Distant star Array of light collecting apertures, each equipped with a photo detector Shadow pattern Resolved silhouette Phase Retrieval algorithm Huygens Fresnel Inversion

  7. Phase Retrieval • Intensity measurements give only the magnitude (not the phase) of the complex field amplitude U(x). • x is the position vector of a telescope projected onto the plane normal to the line of sight (u-v plane) • Given the magnitude data and the silhouette constraints (black silhuette, illuminated background) we can reconstruct the phase of U(x). Thus we determine U(x) completely

  8. Huygens-Fresnel Inversion • From the H-F principle: • U(x) is the Fourier transform of . Thus we can invert the relation:

  9. Example: A twelve-aperture, 5 km diameter circular array We assume that the speed and direction of the shadow motion are known y Cross-track direction x Along-track direction • Each aperture records the intensity time history, then we plot it as a function of the x-coordinate, using x = V(t-t0). t0 is the time we start recording.

  10. Example: A twelve-aperture, 5 km diameter circular array y x • Along the track of each aperture we have a plot of the magnitude of the intensity as a function of distance , x, in the along-track direction

  11. Example: A twelve-aperture, circular array ~Producing the shadow pattern~ Raw time history data Data strips aligned along x-axis Interpolation along the cross-track axis gives the shadow pattern. The light distribution as seen on a plane that moves with the shadow.

  12. Silhouette Computation 1st scan 2nd scan 3rd and final scan Raster scan the silhouette. At each pixel, change the color and compute the shadow pattern that would result. If agreement with the shadow pattern data is improved, keep the new color. If not, rescind the color change

  13. y Derived Requirements on the Array Size and Spacing Knowing the approximate size of the asteroid, decide how many pixels across, Npix,the image of its silhouette should be The end-to-end size of the array must be as big as the shadow, W 40m Same number of pixels on a side. Thus y, the average separation of the telescopes in the cross-track direction, must = W/Npix

  14. Example: A twelve-aperture, circular array Intensity measurement for each pixel, SNR y

  15. 428 Spring 2013 Design Challenge 15 • Design a spacecraft system to identify and characterize Near Earth Asteroids (NEAs) using stellar occultation • Focus on asteroid size range 40m to 140m • Maximize number of asteroids accurately characterized • Use an array of small telescopes in space • Obtain silhouette of each asteroid with at least 10 pixels across and SNR>10

  16. NEA Candidates Survey : Purpose • To determine • The number of detectable asteroids that fall within a size range for a specified SNR and aperture size (aperture diameter) • The average lateral velocity, width of the shadow region, and asteroid diameter (formation size) • The frequency of an asteroid occultation (system utility) • To collaborate with Optics to determine the optimal telescope aperture

  17. Candidate Survey Code Loop 278,000 times Define Parameters Not Detectable Determine SNR of Asteroid Randomly Generate Orbital Elements and Diameter Calculate Cross-Track Velocity at SEL-2 Detectable Log Asteroid Data Transform Coordinates Location to SEL-2 Calculate the Heliocentric Rectangular Coordinates of Asteroid

  18. Detection Frequency

  19. Characterization Frequency

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