2. When an entry module is far from the Earth, it is easy to take a large scale view and use an origin at the center of

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2 When An Entry Module Is Far From The Earth It Is Easy To Take A Large Scale View And Use An Origin At The Center Of 1 (650.43 KiB) Viewed 30 times

2. When an entry module is far from the Earth, it is easy to take a large scale view and use an origin at the center of the Earth (or the Sun) as our inertial frame. But, during the launch and entry, it is often tempting to use coordinates like altitude and horizontal distance flown: the type of coordinates used to describe the flight of aircraft. Examine Figure, where s is downrange distance flown from some starting point, and H is the entry module's altitude from the surface of the Earth. Figure 2: The local horizon frame and entry capsule. The entry module will travel large enough distance that we will have to admit that the Earth is round. Also, it will travel fast enough that some care is needed in calculating the inertial acceleration. The nearest acceptable inertial origin is the center of the Earth. The h frame has its origin at the center of the Earth, with h in the downrange direction, and h2 in the local vertical direction. The third vector he is out of the page, and completes the right hand set. This is not an inertial frame. Question: Assume that the module is instantaneously and always) along the vertical axis, h. Derive the inertial acceleration vector when it is expressed in terms of the unit vectors of the h frame. hint: We need to know the angular velocity vector of the h frame relative to the inertial frame, wh/i. Its magnitude can be related to the velocity and radius of the entry module as S Whil = RE +H (3) where Re denotes the mean radius of the Earth and S is the time derivative of the arc length. Here we have assumed that velocity of the entry module is purely tangential.