CK-12-Physics - Intermediate

http://www.ck12.org Chapter 9. Newton’s Universal Law of Gravity

FIGURE 9.1

Johannes Kepler.

FIGURE 9.2

Tycho Brahe.

all points that are equal distance from a single point. An ellipse is the set of all points where the sum of the

distance to two foci is always equal. SeeFigure9.3.

2. If an imaginary line is drawn from the sun to a planet as the planet orbits the sun, this line will sweep out equal
   areas in equal times. (A planet moves faster when it is closer to the sun and slower when it is farther away
   from the sun.) SeeFigure9.4.


3. The square of the timeT^2 for one orbitalperiodof a planet about the sun is proportional to the cube of the
   average distancer^3 between the sun and the planet. That is,T^2 ∝r^3 (where∝is read as “proportional to”). As
   an equation we writeT^2 =kr^3 where the value ofkis the constant of proportionality, and its corresponding
   form in the SI system of units.

For the time being, we can treatkas unity if we choose time in units of years and distance in units of astronomical
units (AU) –where 1.0 AU is the average distance between the sun and the earth). For example, since Mars is, on
average, about one and one half times farther from the sun than the Earth, Mars is 1.5 AU from the sun, or, more
precisely 1.52 AU.