Page:The Solar System - Six Lectures - Lowell.djvu/141

Cosmogony

123

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sents the body's momentum, and therefore cannot change the area swept out.

When two bodies collide, therefore, they each bring an eternal definite amount of motion to the collision; this amount is unaffected by the shock.

Nor can the mutual attraction of the two bodies themselves alter it; for, since a force is measured by the amount of velocity it can generate in a given time, the velocities generated must be as the opposite masses, and therefore the momentum produced in each be the same.

Let $\scriptstyle m$ and $\scriptstyle m_{1}$ be the masses.

Then

$\scriptstyle f_{m}t={m_{1}}{v_{m_{1}}}$

and

$\scriptstyle f_{m_{1}}t=mv_{m_{1}}$

and

$\scriptstyle {\frac {v_{m}}{v_{m_{1}}}}={\frac {m}{m_{1}}}$

whence

$\scriptstyle m_{1}v_{m}=mv_{m_{1}}$

or

$\scriptstyle Aa=-Bb$

where

$\scriptstyle Aa={\frac {v_{m}}{m}}$ and $\scriptstyle Bb={\frac {v_{m_{1}}}{m_{1}}}$

FIG. XVII