# HW3 - MAE146 Astronautics Homework#3 Assigned Friday...

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MAE146: Astronautics – Homework #3 Assigned: Friday, January 25 th , 2008 Due date: Friday , February 8 st , 2008, (at the beginning of the lecture) Note: “Textbook” refers to Wiesel’s book, “Spaceflight dynamics”. Please justify all of your answers. Problem 1 (20 pts): Apparent acceleration of gravity In everyday life, we consider the local frames attached to the surface of the Earth to be inertial and consider the acceleration of gravity to be the result of the Earth gravitational attraction alone. This is not the case... But by how much? In the following, you should assume the local frame is centered at Irvine, at a latitude of 33 o 39 and longitude of 117 o 47 . The Earth is assumed to be a uniform sphere of density 5 , 515 . 3 kg/m and radius Re = 6367 km. 1. Estimate the gravitational force in the local reference frame on a sample mass of 1 kg (at rest with respect to the local frame). 2. Assuming that the rotation of the Earth is uniform about the North pole (+90 o latitude) with a period of 24 h, what are the non-inertial accelerations for a mass at rest in the local frame of reference? Determine the “acceleration of gravity” in the local frame (that is, the initial acceleration that one would measure of a mass falling in vacuum near the surface of the Earth). What happens when the mass is moving with respect to the Earth surface? Problem 2 (30 pts): Perturbed motion 1. (10pts) Textbook, page 72, #9 2. (10pts) Assuming the Earth is moving around the Sun in a circular motion of radius R = 149 . 6 × 10 6 km and

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