Project Blue Book Mariana UFO Incident PDF

$$
\mathrm {r} \triangleq \mathrm {R} / \mathrm {R} _ {0}
$$

$$
a _ {0} \triangleq A _ {0} / R _ {0}
$$

$$
t \triangleq V _ {0} T / R _ {0}
$$

$$
f _ {0} \triangleq L _ {0} / R _ {0}
$$

Consideration of figure 7 and application of the law of cosines together with trigonometric manipulation yields:

$$
\mathrm {t a n h} = \frac {\tan h _ {0}}{\sqrt {1 + 2 t \sin \delta_ {0} + t ^ {2}}}
$$

$$
\cos \phi = \frac {1 + t \sin \delta}{\sqrt {1 + 2 t \sin \delta_ {0} + t ^ {2}}}
$$

$$
\frac {\theta_ {0}}{\theta} \approx \frac {1 + 2 t \sin \delta_ {0} + t ^ {2}}{1 + t \sin \varepsilon_ {0}}
$$

In the example at hand the total elapsed time of observation is on the order of 16 seconds and the angular sweep of the objects across the sky $ \phi $ is about $ 2 0^{\circ} $ . Thus

$$
0 \leq t < 0. 3
$$

Using equations (1), (2) and (3) the dashed lines depicting theoretical azimuth headings (figures 5a and 5b) are computed.

There does exist a random error (attributed to errors in measurement or to slight variations of the UFO's motion) about the theoretical $ 1 7 1^{\circ} $ azimuth heading line of $ +5^{\prime} $ in the case of the altitude and azimuth plot and $ +0.01 $ in the time vs. separation plot. This random scattering of experimental points could at most mask a variation in distance, altitude or separation of $ +1\% $ . In particular, there is a slight variation in both plots (frames 120 to 175) towards the $ 1 6 9^{\circ} $ azimuth heading. However, the general tendency of the points to maintain the same angular direction on the plot without an offset indicates that this slight variation doesn't represent a true change in direction, but rather a slight reorientation, slipping or curving motion of the objects. If a curving motion was responsible, the tangents to the curve would lie somewhere between $ 1 6 9^{\circ} $ and $ 1 7 3^{\circ} $ azimuth heading.