Canonical Projectile Problem: Finding the Escape Velocity of the Earth

David J. Wollkind () and Bonni J. Dichone
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David J. Wollkind: Washington State University, Department of Mathematics
Bonni J. Dichone: Gonzaga University, Department of Mathematics

Chapter Chapter 2 in Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, 2017, pp 9-29 from Springer

Abstract: Abstract The escape velocity of the Earth is calculated using an idealized projectile model that allows for the determination of projectile velocity as a function of its altitude. In order to obtain an approximate solution for projectile altitude as a function of time which cannot be determined by an exact solution the concept of regular perturbation theory in ordinary differential equations is introduced as a pastoral interlude. Then a regular perturbation expansion is performed on the model to obtain the desired asymptotic solution of altitude as a function of time when the initial projectile velocity is much less than that of the escape velocity. An energy argument making use of the fact that gravity acts as a conservative force for this canonical model is also introduced to examine this phenomenon in more detail. The problems extend these analyses to the rest of the solar system planets and to two other canonical projectile problems that are nonconservative.

Date: 2017
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DOI: 10.1007/978-3-319-73518-4_2

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