IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-73518-4_2.html
   My bibliography  Save this book chapter

Canonical Projectile Problem: Finding the Escape Velocity of the Earth

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

Listed:
  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

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.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Canonical Projectile Problem: Finding the Escape Velocity of the Earth," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 9-29, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_2
    DOI: 10.1007/978-3-319-73518-4_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-319-73518-4_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.