Write a program that uses physics to model the flight of the Freedom 7. Since the capsule moves over a significant portion of the Earth, you must use the universal law of gravitation, as you did with modeling the orbit of Jupiter, rather than the near Earth approximation in the previous problem. The capsule must travel approximately 487 km to the target area, and reach an “apogee” (maximum height above the Earth) of 187.5 km.As before, this program makes some simplifying assumptions. Only the capsule is launched, not the lower stage. Also, you can assume the rocket reaches its maximum speed right away—very unhealthy for the astronaut! In addition, it ignores the rotation of the Earth itself. (Katherine Johnson definitely could notafford to ignore the Earth’s motion in her calculations. It would have led to a significant error in the result, and Alan Shepard would likely have been lost at sea.)21. (Challenging) Write a new GlowScript program, called “Glennflight,” that models astronaut John Glenn’s orbital flight. As mentioned in Hidden Figures, this involves transitioning the spacecraft from roughly parabolic motion, as in Shepard’s flight, to circular motion. Then to return to Earth, the opposite procedure must be carried out. In order to do this effectively, you must model the force of the rocket engines on Glenn’s capsule, Friendship 7, during the launch. You will have to choose an appropriate size of the force exerted by the engines. You must also apply it in an appropriate direction (which may change during the flight) and for a sufficient period of time.L e s s o n 6 (PHYSICS, PROGRAMMING)
J o u r n e y s i n F i l m: H i d d e n F i g u r e sH a n d o u t 1 •p . 10Using GlowScript to Solve Problems22. In general, Katherine Johnson used “iterative methods” for solving equations with derivatives in them (called “differential equations”) numerically. This was an important step forward in predicting the trajectories of spacecraft. Research the difference between the two methods. The programs above that simulate trajectories use iterative methods. Identify in the code the iterative part. Why are iterative methods especially suited to solutions carried out on a machine computer?23. Up until this point, you have been learning how to simulate physical reality by writing code yourself and running it immediately. However, when machine computers (as opposed to “human computers”) were first invented, programmers had to write their code beforehand, carefully and diligently check and recheck it for errors, and then finally feed it into the machine. Results could take minutes, hours, or even longer. Recall that Dorothy Vaughan learned the programming language FORTRAN from a textbook, which she went to great lengths to obtain. How did she teach her coworkers the language? These women did not have much of a choice, but these days there are many ways to learn to program a computer. What are some possible advantages to learning programming from reading a textbook or attending a lecture? Are there any advantages to “learning by doing,” as you have just done? Are there situations where one is preferable to the other?