Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 14 / a / i

Table of contents
- Solution i

Solution

For the force magnitude in Newton's law of universal gravitation, the total differential is

d F = \frac{G m _{2}}{r ^{2}} d m_{1} + \frac{G m _{1}}{r ^{2}} d m_{2} - \frac{2 G m _{1} m _{2}}{r ^{3}} d r .

Dividing by the positive value

F

gives the particularly useful relative form

\frac{d F}{F} = \frac{d m _{1}}{m _{1}} + \frac{d m _{2}}{m _{2}} - 2 \frac{d r}{r} .

For finite small changes this gives the first-order approximation to the fractional change; higher-order products of increments are omitted.

 Ancestors (13)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version