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Celestial Mechanics I

Today's Lecture. First orbit determination according to the method of Gauss (calculate orbital elements from few observed positions)Orbit improvement (reduction of uncertainties in orbital elements by using many observed positions). Why is this important?. Planned observations requires known orbit

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Celestial Mechanics I

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    1. Celestial Mechanics I

    2. Today’s Lecture First orbit determination according to the method of Gauss (calculate orbital elements from few observed positions) Orbit improvement (reduction of uncertainties in orbital elements by using many observed positions)

    3. Why is this important? Planned observations requires known orbits Scientific value of orbit statistics Potentially Hazardous Asteroids (PHA)

    4. Search Programmes Discovery statistic, numbered asteroids LINEAR (81641) NEAT (11464) Spacewatch (11007) LONEOS (9365) UDAS (105). Number 68 worldwide Minor Planet Center (MPC) International Astronomical Union (IAU)

    5. Gauss’ Method Position- and velocity vectors at one point in orbit ? {a,e,i,?,?,T} Gauss’ method assumes three sets of observations available How do we find the geocentric distances?

    6. Derivation of Gauss’ Method

    7. Derivation of Gauss’ Method

    8. Derivation of Gauss’ Method

    9. Derivation of Gauss’ Method

    10. Algorithm Use {aj,d j} to calculate ?j unit direction vectors Use ?j to calculate {?2, ?2, ?2, ?3, ?3} and Req?C Transform ?j and R¤,j vectors to C system. We need to know c1 and c3! Assume y2/ y1= y2/ y3=1. Calculate the geocentric distances! Calculate the approximate heliocentric position vectors of the object! But now we can estimate overswept areas, i.e., more realistic values of c1 and c3 can be calculated. Iterate!

    11. Steffensen’s Method

    12. Numerical example

    13. Orbit Improvement ?: Orbital elements ?: Method (e.g., two-body) ?: Ephemerides

    14. Orbit Improvement

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