AEE 4263 HW 8

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Florida Institute of Technology *

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4263

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Mechanical Engineering

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Apr 3, 2024

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docx

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AEE 4263-02 Space Flight Mechanics Homework HW8 Fall 2023 Use the following constants: Earth gravitational parameter: μ = 398600.4418 km 3 / s 2 Earth radius: R E = 6378.137 km For other celestial bodies, use the gravitational parameter ( μ ) found in table A.2 of the text 1. (8 Points) Using the data in table A.1 in text (also found in lecture 16, slide 8), compute the synodic period between the Earth and Saturn in years to two decimal places. Solution: Synodic Period between the Earth and Saturn = 1.04 years MATLAB: %% Homework 8 Problem 1 close all clear all clc mu= 398600.4418; %km^3/s^2 RE= 6378.137; %km T_earth= 365.256; %days T_saturn= 29.46*T_earth; %days T_syn_days= (T_earth * T_saturn) / (abs(T_earth - T_saturn)); %days T_syn_years= T_syn_days/T_earth %years 1
2. (15 Points) Compute the transfer time (i.e., Half the period of a Hohmann ellipse) between Earth and Saturn to the nearest day. Solution: Transfer Time = 2222 days MATLAB: %% Homework 8 Problem 2 close all clear all clc RE= 149.6*10^6; %km RS= 1.433*10^9; %km a= (RE+RS)/2; %km mu_sun= 132712440018; %km^3/s^2 t_s= sqrt(a^3/mu_sun)*pi; %sec t_d= t_s/86400 %days 2
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