Gravitational Field Strength

2 Key excerpts on "Gravitational Field Strength"

• 

  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  r.

  The Gravitational Field Strength functions for the special cases discussed so far are:

  uniform field:
  radial field due to a point mass M:

  For problems based on the material presented in this section visit up.ucc.ie/5/ and follow the link to the problems.

  5.3 The concept of flux

  The gravitational force is just one example of a number of ‘inverse square law’ forces which arise in nature (we will meet further examples in Chapters 16 and 18 ). Whenever an inverse square law force is encountered, it turns out to be useful to introduce the concept of a flux. In such contexts, the concept is purely abstract but is adopted deliberately by analogy with examples of real fluxes that arise frequently in nature; for example, the flow of water from a garden hosepipe, the flow of light from an electric bulb, the flow of particles from a radioactive source, etc. It is conventional to define the total flux emanating from such a source as being equal to the strength of the source; for example, in the case of a light bulb the light flux can be measured in terms of the rate at which the bulb dissipates electrical energy, measured in watts. Other examples are given in Table 5.1

  Table 5.1

  Some examples of flux and flux density

  Source	Total flux from source	Flux density at a point
  water hose	litre per second	litre s−1 m−2
  light bulb	watt	watt m−2
  radioactive source	particles per second	particles s−1 m−2
  mass	kilogram (*)	kg m−2 (* )

  (* ) Note: In this case the flux is entirely abstract.

  Gravitational flux density

  The effect of a flux at a point some distance from its source can be described in terms of the flux per unit area in the neighbourhood of that point. As an example, consider a lawn being watered by a garden hose: the strength of the source, and hence the corresponding flux, may be considered as the volume of water per unit time emitted from the hosepipe. The effect at any point of the lawn (the amount of wetting) is determined by the volume per unit time per unit area landing at that point of the lawn. This latter measure is an example of a flux density (see the right hand column of Table 5.1

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Space, Time, Matter

  • Hermann Weyl(Author)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  The fact that a given gravitational field imparts the same acceleration to every mass that is brought into the field constitutes the real essence of the problem of gravitation. In the electrostatic field a slightly charged particle is acted on by the force e. E, the electric charge e depending only on the particle, and E, the electric intensity of field, depending only on the field. If no other forces are acting, this force imparts to the particle whose inertial mass is m an acceleration which is given by the fundamental equation of mechanics m b = e E. There is something fully analogous to this in the gravitational field. The force that acts on the particle is equal to g G, in which g, the “g ravitational char g e,” depends only on the particle, whereas G depends only on the field : the acceleration is determined here again by the equation m b = g G. The curious fact now manifests itself that the “g ravitational charge” or the “gravitational mass” g is equal to the “inertial mass” m. Eötvös has comparatively recently tested the accuracy of this law by actual experiments of the greatest refinement (vide note 3). The centrifugal force imparted to a body at the earth’s surface by the earth’s rotation is proportional to its inertial mass but its weight is proportional to its gravitational mass. The resultant of these two, the apparent weight, would have different directions for different bodies if gravitational and inertial mass were not proportional throughout. The absence of this difference of direction was demonstrated by Eotvos by means of the exceedingly sensitive instrument known as the torsion-balance : it enables the inertial mass of a body to be measured to the samedegree of accuracy as that to which its weight may be determined by the most sensitive balance

  Sign up to read

  Learn more about book