Step 1:

Let the foci be at $F(ae,0),F'(-ae,0)$ and the vertices at $A(a,0),A'(-a,0)$.

Let the earth be at $F(ae,0)$.

Step 2:

The shortest distance of the satellite is at $A$

$FA=a-ae=400$

Now $e=\large\frac{1}{2}$

Therefore $a(1-e)=400$

$\large\frac{a}{2}$$=400\Rightarrow a=800$

Step 3:

The maximum distance of the satellite is at $A'$

(i.e) $FA'=a+ae$

$\Rightarrow a(1+e)$.

$\Rightarrow 806\times \large\frac{3}{2}$

$\Rightarrow 1200m$

Therefore the longest distance that the satellite from the earth is 1200 m.