HW5 - powers of e multiplying sines and multiples of the...

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MAE146: Astronautics – Homework #5 Assigned: Friday, February 13 th , 2008 Due date: Friday , February 20 th , 2008, (at the beginning of the lecture) Note: “Textbook” refers to Wiesel’s book, “Space±ight dynamics”. Please justify all of your answers. Problem 1 (20 pts): Halley’s comet Textbook, page 70, # 3: “Halley’s comet last passed perihelion on February 9, 1986. It has a semi-major axis a = 17 . 9564 AU and eccentricity e = 0 . 967298. [One astronomical unit (AU) is the distance between the Earth and the Sun.] Calculate the period of Halley’s comet and predict the date of the next return. Solve Kepler’s equation and calculate E, ν and the scalalr radius vector r for the due date of this homework.” Problem 2 (30 pts): Eccentric anomaly Textbook, page 71, #5: “Continue the series solution to Kepler’s equation begun in equation (2.65) to the second order in the eccentricity e . Expand any sines and cosines of small angles, and obtain a ²nal answer involving only
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Unformatted text preview: powers of e multiplying sines and multiples of the mean anomaly M .” Problem 3 (50 pts): Debris and collisions Debris and other unidenti²ed objects can be a threat to spacecraft due to the non-zero risk of collision, as recently observed in the news. In this problem we consider two measurements of space objects relative to an Earth Centered Inertial (ECI) frame: Unidenti²ed object Spacecraft x = +7007 . 7 km ; ˙ x =-2 . 7460 km/s x = +4274 . 1 km ; ˙ x =-4 . 7951 km/s y = +1511 . 8 km ; ˙ y =-6 . 8505 km/s y = +5648 . 3 km ; ˙ y = +4 . 7412 km/s z = +4045 . 9 km ; ˙ z = +1 . 5854 km/s z =-2467 . 6 km ; ˙ z = +2 . 7685 km/s Assuming the gravitational parameter of the Earth to be μ = 398600 . km 3 /s 2 , determine if the objects are likely to collide each other (justify!). 1...
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This note was uploaded on 03/10/2009 for the course MAE 146 taught by Professor Villac during the Spring '08 term at UC Irvine.

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