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5.4.1: Field of a Point Mass

  • Page ID
    8131
  • [ "article:topic", "authorname:tatumj" ]

    Equation 5.3.1, together with the definition of field strength as the force experienced by unit mass, means that the field at a distance \(r\) from a point mass \(M\) is

    \[g = \frac{GM}{r^2} \quad \text{N kg}^{-1} \text{  or  m s}^{-2} \label{5.4.1} \tag{5.4.1}\]

    In vector form, this can be written as

    \[\textbf{g} = -\frac{GM}{r^2} \hat{\textbf{r}} \quad \text{N kg}^{-1} \text{  or  m s}^{-2} \label{5.4.2} \tag{5.4.2}\]

    Here \(\hat{\textbf{r}}\) is a dimensionless unit vector in the radial direction.

    It can also be written as

    \[\textbf{g} = -\frac{GM}{r^3} \textbf{r} \quad \text{N kg}^{-1} \text{  or  m s}^{-2} \label{5.4.3} \tag{5.4.3}\]

    Here \(\textbf{r}\) is a vector of magnitude \(r\) − hence the \(r^3\) in the denominator.