**ERIC Number:**EJ844002

**Record Type:**Journal

**Publication Date:**2009-Jul

**Pages:**8

**Abstractor:**As Provided

**Reference Count:**15

**ISBN:**N/A

**ISSN:**ISSN-0143-0807

Where Else Is Null the Gravitational Field between Two Massive Spheres?

Lima, F. M. S.

European Journal of Physics, v30 n4 p785-792 Jul 2009

To find the point between two massive spherical bodies at which their gravitational fields cancel is an apparently simple problem usually found in introductory physics textbooks. However, by noting that such a point does not exist when the distance between the spheres is small and one of the masses is much smaller than the other--e.g., between the Earth and a billiard ball near the ground--I develop here a simple analysis for establishing existence conditions for this point. Unexpectedly, I have found that the net gravitational field can be null also in certain points inside each sphere. The position of these "inner" points can be determined by solving a cubic equation via the standard method, known as "Cardan's solution". However, when the discriminant of this equation is negative one has the "irreducible" case, for which Cardan's solution "fails", but a trigonometric method proposed recently yields exact closed-form expressions. Interestingly, it is shown that these "inner points" do occur in the Earth-Moon system, in which they are determined just by solving irreducible cubic equations. (Contains 13 footnotes and 2 figures.)

Descriptors: Textbooks, Physics, Science Instruction, Equations (Mathematics), Trigonometry, Problem Solving, Scientific Concepts, Undergraduate Study, College Science, Teaching Methods

Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP

**Publication Type:**Journal Articles; Reports - Evaluative

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A