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authorPrefetch2023-01-01 16:40:56 +0100
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@@ -19,7 +19,8 @@ Let 2 be initially at rest, and 1 approach it with velocity $$\vb{v}_1$$.
Coulomb repulsion causes 1 to deflect by an angle $$\theta$$,
and pushes 2 away in the process:
-{% include image.html file="two-body-full.png" width="50%" alt="Two-body repulsive 'collision'" %}
+{% include image.html file="two-body-full.png" width="50%"
+ alt="Two-body repulsive 'collision'" %}
Here, $$b$$ is called the **impact parameter**.
Intuitively, we expect $$\theta$$ to be larger for smaller $$b$$.
@@ -67,7 +68,8 @@ then by comparing $$t > 0$$ and $$t < 0$$
we can see that $$v_x$$ is unchanged for any given $$\pm t$$,
while $$v_y$$ simply changes sign:
-{% include image.html file="one-body-full.png" width="60%" alt="Equivalent one-body deflection" %}
+{% include image.html file="one-body-full.png" width="60%"
+ alt="Equivalent one-body deflection" %}
From our expression for $$\vb{r}$$,
we can find $$\vb{v}$$ by differentiating with respect to time: