3. The orbit of a certain spacecraft is an ellipse with the Earth's center $F$ as the left focus. It is measured that the distance from the perigee $A$ to the ground is $m \mathrm{~km}$, and the distance from the apogee $B$ to the ground is $n \mathrm{~km}$. The radius of the Earth is $r \mathrm{~km}$. There are four statements about this ellipse:
(1) The focal distance is $n-m$;
(2) The length of the minor axis is $\sqrt{(m+r)(n+r)}$;
(3) The eccentricity $e=\frac{n-m}{m+n+2 r}$;
(4) Taking the direction of $A B$ as the positive direction of the $x$-axis, and $F$ as the origin, the equation of the left directrix is
$$
x=-\frac{2(m+r)(n+r)}{n-m} .
$$

The correct statements among the above are
3. (1),(3),(4).

Taking $F$ as the origin and $AB$ as the $x$-axis to establish a rectangular coordinate system, and let the major axis of the ellipse be $2a$, the minor axis be $2b$. The focal distance is $2c$. Using the definition, it is easy to prove that (1), (3), and (4) are correct.