Orbital Mechanics Course Notes David J. Westpfahl Professor of Astrophysics, New Mexico Institute of Mining and Technology March 31, 2011 The two-body problem consists of a spacecraft in motion relative to a planet.

To help you along your journey, there are examples included with many of the formulas (and more forthcoming). 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. Flight and Orbital Mechanics Lecture 7 –Equations of motion Mark Voskuijl. 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. Launch windows. Chapter 1 Two-Body Problem 1.1 Introduction The starting point for astrodynamics is the study of the classical two-body problem. Two–Body Orbital Mechanics Figure 1.1: Kepler’s second law. Chapter 1 Two-Body Problem 1.1 Introduction The starting point for astrodynamics is the study of the classical two-body problem. At 15,000 m accelerate to Mach 2 B. 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. Kudos! 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. It is required to change its orbital eccentricity to 0.4, without rotating the apse line, by a delta-v maneuver at θ = 100°. The equations for flight path angle and anomaly versus time given in Orbital flight are also usable for hyperbolic trajectories.

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? Climb at airspeed for max . If you've found your way here, you are obviously one of the brave souls who dare to tackle orbital mechanics the old fashioned way — with grit and determination.

There is a great deal of variation with time of the velocity change required for a mission, because of the constantly varying relative positions of the planets. star planet A 1 A 2 Figure 1.2: Sketch of Kepler’s first and second laws. Chapters 5 through 8 carry on with the subject of orbital mechanics. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent? (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. Obviously, for the small entry flight path angles desired for … A. Referring again Figure 5.2, we see that the flight path angle of the transfer orbit is positive at the first Mars orbit crossing and negative at the second Mars orbit crossing. Orbital Mechanics Course Notes David J. Westpfahl Professor of Astrophysics, New Mexico Institute of Mining and Technology March 31, 2011 2 G. Colasurdo, G. Avanzini - Astrodynamics – 1. 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. {Ans. of a planet from the Sun varies and the area being swept remains constant, a planet has variable An earth satellite has a perigee altitude of 1270 km and a perigee speed of 9 km/s. Orbital Mechanics Principles of Space Systems Design Orbital Mechanics • Energy and velocity in orbit • Elliptical orbit parameters • Orbital elements • Coplanar orbital transfers • Noncoplanar transfers • Time and flight path angle as a function of orbital position • Relative orbital motion (“proximity operations”) Chapter 6 on orbital maneuvers should be included in any case. Climb at airspeed for max RC.

Calculate the magnitude of the required Δv and the change in flight path angle Δγ. The two-body problem consists of a spacecraft in motion relative to a planet. Coverage of Chapters 5, 7 and 8 is optional.