IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4362-d1263889.html
   My bibliography  Save this article

A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics

Author

Listed:
  • Gerassimos Manoussakis

    (Department of Mathematics, School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Iroon Polytechneiou 9, 157 80 Zografos, Greece)

Abstract

In this work, it is shown that the geometry of a gravity field generated by a spheroid with low eccentricity can be described with the help of a newly modified Helmholtz equation. To distinguish this equation from the modified Helmholtz equation, we refer to it as the G-modified Helmholtz equation. The use of this new equation to study the spheroid’s gravity field is advantageous in expressing the gravity vector as a vector series of spherical harmonics. The solution of the G-modified Helmholtz equation involves both the gravity intensity g (or simply gravity g ) and the intensity E of an electrostatic field as shown in sequel. An electrostatic field generated by an oblate spheroid charged with l electrons (uniform ellipsoidal charge distribution) is demonstrated to be a special case. Both gravity intensity g and intensity E are governed by the same law and can be expressed as a series of spherical harmonics, and thus the G-modified Helmholtz equation is useful for describing the gravity and electrostatic fields.

Suggested Citation

  • Gerassimos Manoussakis, 2023. "A New Modified Helmholtz Equation for the Expression of the Gravity Gradient and the Intensity of an Electrostatic Field in Spherical Harmonics," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4362-:d:1263889
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4362/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4362/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gerassimos Manoussakis, 2023. "The Gravity Force Generated by a Non-Rotating Level Ellipsoid of Revolution with Low Eccentricity as a Series of Spherical Harmonics," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:gam:jmathe:v:11:y:2023:i:20:p:4362-:d:1263889. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.