IB Physics Glossary



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K

Kepler's 3rd law

of planetary motion states the orbital period squared is proportional to the mean orbital radius cubed:
$$T^2 \propto r^3$$.


Derivation

$$F = G \frac{Mm}{r^2}=\frac{mv^2}{r}$$.
or
$$ G \frac{M}{r}=v^2$$.

Since the speed, $$v$$, is the distance travelled in one orbit, $$2 \pi r$$, divided by the orbital period $$T$$ we can write

$$ G \frac{M}{r}=(\frac{2 \pi r}{T})^2$$
or
$$ G \frac{M}{r}=\frac{4 \pi^2 r^2}{T^2}$$

then

$$T^2 = \frac{4 \pi^2}{GM} \times r^3$$

or

$$T^2 = constant \times r^3 => T^2 \propto r^3$$.

Kinetic energy

is the energy of a moving object.

Kinetic theory of gases


is a theory which treats molecules in a gas as mechanical objects. We assume that

1. A gas contains a large number of molecules;

2. Molecules have a range of kinetic energies, and therefore a range of speeds;

3. A gas molecule occupies a volume much less than that of the volume of the gas;

4. Collisions of molecules with other molecules and with the walls of the container are elastic;

5. Molecules exert forces on other molecules or on container walls only when contact occurs;

6. Collisions times are small compared to time between collisions;

7. Molecules obey the laws of Newtonian mechanics;