| 1. | The osculating elements would remain constant in the absence of perturbations.
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| 2. | The formula follows by verifying it for the osculating circle.
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| 3. | This is the osculating circle to the curve.
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| 4. | The word " osculate " derives from a Latin word meaning " to kiss ".
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| 5. | The plane containing the two vectors and is called the osculating plane to the curve at.
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| 6. | In a mystical scheme this grouped separately created genera in " osculating " ( kissing ) circles.
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| 7. | The "'center of curvature "'is the center of the osculating circle.
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| 8. | The curvature of a smooth curve is defined as the curvature of its osculating circle at each point.
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| 9. | However, real astronomical orbits experience perturbations that cause the osculating elements to evolve, sometimes very quickly.
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| 10. | Such element sets are known as osculating elements because they coincide with the actual orbit only at that moment.
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