I40 1 Three position fixes of an asteroid in interplanetary

I40) 1. Three position fixes of an asteroid in interplanetary space times t 0.1 year, t 0.2 year, and 0.3 year are found to be at r1 1.11 1.06 0.99 1.06 (au) r2 1.08 (au) 1.11 (au) 0.85 0.95 1.0 a) Explain why equation (.51) in the notes cannot be used to find the velocity vz. b) Use equation (7.53) in the notes to calculate V2. c) Calculate the angular momentum (per unit mass) and the total energy (per unit mass) of the asteroid. d) is the trajectory of the asteroid rectilinear, parabolic, el ptic or hyperbolic? Explain why. l35) 2. Determine the minimum av needed to change the inclination of a circular orbit having a 7000 km radius by a) 30 b) 45\" 125) 3. Vanguard ID was launched on March 17, 1958 into a 356 x 2074 nautical mile orbit. Although communication was lost in 1964, it remains the oldest man-made satellite still in orbit. The satellite is a 64 inch diameter sphere weighing 3.2 lbs. Estimate the orbital lifetime of the satellite. Physical constants The Earth Mean Radius 6368 km 4m2 au\'lyra 1.327 x 10\'\' km\'sec\' HeartA\" 3.986 x 105 km /sec? Mean distance from the sun lau x 10\' km 496 Conversion factors l nautical mile 6076 ft 1 km 3281 ft 1 ft 2 in

Solution

c) We know that angular momentum per unit mass is given as

L = r X V

YOu have the value of V from a and b. YOu can find r using the three points. Similary energy can be found.