# Celestial Mechanics and Orbital Period Assignment

Words: 330

AE-641 Problems Set No. 1 1. The orbital period of an Earth satellite is 106 min. Find the apogee altitude if the perigee altitude is 200 km. 2. Find the orbital period of a satellite if the perigee and apogee altitudes are 250 km and 300 km, respectively. 3. Find the maximum and minimum orbital speed of the Earth if the eccentricity of the Earth’s orbit around Sun is 1/60. What is the mean speed if the mean radius is 1 AU? (Sun’s Gm1=1. 327×10 11 km3/s 2. ) 4.

Given the orbital period of Mars around Sun as 687 Earth mean solar days, find the semi-major axis of Mars orbit in AU. 5. Estimate solar gravitational constant using Kepler’s third law. 6. A spacecraft in a 200 km high circular Earth orbit fires its retro-rocket, reducing speed instantly by 600 m/s. What is the speed of the spacecraft when it reaches an altitude of 100 km? (Assume zero atmospheric drag. ) 7. What is the parabolic escape velocity from a geosynchronous orbit?