Orbital mechanics is a modern offshoot of celestial mechanics which is the study of the motions of natural celestial bodies such as the moon and planets. To help you along your journey, there are examples included with many of the formulas (and more forthcoming). Orbital Mechanics Course Notes David J. Westpfahl Professor of Astrophysics, New Mexico Institute of Mining and Technology March 31, 2011 The velocity of a satellite in a circular orbit, is a function of the gravitation parameter of the body being orbited, μ, and the radius of the orbit, r. The specific energy of an elliptical orbit, ε, is negative and is a function of the gravitational parameter, μ, and the semi-major axis. Chapter 1 Two-Body Problem 1.1 Introduction The starting point for astrodynamics is the study of the classical two-body problem. An earth satellite has a perigee altitude of 1270 km and a perigee speed of 9 km/s. Kudos! star planet A 1 A 2 Figure 1.2: Sketch of Kepler’s first and second laws. Climb at airspeed for max RC. Climb at airspeed for max . Orbital mechanics, also called flight mechanics, is the study of the motions of artificial satellites and space vehicles moving under the influence of forces such as gravity, atmospheric drag, thrust, etc. Chapter 1 Two-Body Problem 1.1 Introduction The starting point for astrodynamics is the study of the classical two-body problem. The equations for flight path angle and anomaly versus time given in Orbital flight are also usable for hyperbolic trajectories. Launch windows.

2 G. Colasurdo, G. Avanzini - Astrodynamics – 1. Chapters 5 through 8 carry on with the subject of orbital mechanics. of a planet from the Sun varies and the area being swept remains constant, a planet has variable Coverage of Chapters 5, 7 and 8 is optional. Chapter 6 on orbital maneuvers should be included in any case. At 15,000 m accelerate to Mach 2 B. However, if all of Chapter 8 on interplanetary missions is to form a part of the course, then the solution of Lambert’s problem (Section 5.3) must be studied beforehand. The variation of the entry flight path angle with π−θ, the polar angle of entry measured from the point of application of ΔV is shown in Figure 5.13 for initial circular orbital values of r 1 =300, 400, and 500 km.

It is required to change its orbital eccentricity to 0.4, without rotating the apse line, by a delta-v maneuver at θ = 100°. Two–Body Orbital Mechanics Figure 1.1: Kepler’s second law. AE2104 Flight and Orbital Mechanics 3 | Introduction Question What is the most efficient way (minimum time) to go from take-off at sea-level to Mach 1.5 at 15,000 m? Orbital Mechanics Course Notes David J. Westpfahl Professor of Astrophysics, New Mexico Institute of Mining and Technology March 31, 2011

(Assuming no drag or perturbations, two body orbital mechanics) My answers I am getting are V = 25,370.7 ft/s at a flight-path angle of -60.029 degrees. A. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent? Obviously, for the small entry flight path angles desired for … Calculate the magnitude of the required Δv and the change in flight path angle Δγ.

Flight and Orbital Mechanics Lecture 7 –Equations of motion Mark Voskuijl.