The Physics and Metaphysics of Unidentified Flying Objects

Read from the scan by GLM-OCR; expect the odd misread word.

# Approved For Release 2001/04/02 : CIA-RDP81R00560R000100010007-4

has been accepted by one agency of the U.S. Government-namely, the U.S. Patent Office-which states (/):

Table 1. Approximate specs, relative kinetic energies, and flight times for various hypothetical flight missions.

The views of the Office are in accord with those of the scientists who have investigated the subject, and are to the effect that mechanical perpetual motion is a physical impossibility. These views can be reburied only by the exhibition of a working model . . . [In] no instance has the requirement of the Patent Office for a working model ever been complied with . Alleged inventions of perpetual motion machines are refused patents.

No.	Speed	Ekg(joules/kg)	Mission
1	8km/sec	$3\times10^{7}$	Orbit, near earth; period,90.31 years
2	13km/sec	$8\times10^{7}$	To moon and return;t,1 week
3	20km/sec	$2\times10^{8}$	To nearby planet and return;t,2 years
4	100km/sec	$5\times10^{9}$	To $\alpha$ Centauri and return;t,25000 years
5	0.5c	$1\times10^{10}$	To $\alpha$ Centauri and return;t,11 years;$\tau$,15 years
6	$(1-10^{-11})c$	$2\times10^{22}$	To Andromeda Galaxy and return distance,$2\times10^{6}$ light years;t,4$\times10^{0}$ years;$\tau$,18 years

The dynamics of rocket flight have been studied intensively during the past 40 years. The equations for space flight by chemical rockets, ions, nuclear engines, and photons (pressure of light), and the effects of relativity, had been derived by 1952 (8). Many of the equations are now contained in textbooks. Here I give equations without derivation.

Table 1 gives the speeds, relative energies, and times of flight for a number of hypothetical missions. The term $ E_{\mathrm{kg}} $ is the kinetic energy per kilogram of rest mass. The round-trip time for people on the earth is t, and for people in the spacecraft, $ \tau $

where m is the mass expelled per second and $ \nu_{o} $ is the exhaust speed relative to the rocket. The initial acceleration is 15 SEPTEMBER 1966 Approved For Release

## Flight Principles:

The principles of celestial mechanics which govern the flight of bodies under the action of gravitation were enunciated by Newton in 1687. They are still valid today for speeds that are small in comparison to the speed of light. For high speeds we must use the modifications of Einstein—that is, the equations of relativity.

$$
a = (\mathrm {t h r u s t} - \mathrm {w e i g h t}) / \mathrm {m a s s}.
$$

To achieve the required speed, which can be done in steps, acceleration, a, is required. For a gravity field,

## Speed, Energy, Thrust

The weight term is negligible when the craft is in space, but it is important at lauñch. All power generated is wasted until thrust exceeds weight.

$$
F = \dot {m} v _ {0}
$$

Apart from propeller and balloon action, a spacecraft can generate thrust only by expelling mass. This mass may consist of material particles, whose speed is less than that of light, or equivalent photons, which move with the speed of light. The thrust is

small for a chemical rocket or a nuclear-powered spacecraft which expells a propellant. The acceleration increases as fuel or propellant is expelled and mass is reduced.

Let $ \nu $ be the speed of the rocket relative to the rest frame (the earth, effectively), $ S=\nu /\nu_{c} $ , and let R be the ratio of the initial to the final mass. In the absence of gravity and for $ \nu_{c} $ < c the following equation holds:

$$
R = e ^ {8}.
$$

The speed $ \nu $ can exceed $ \nu_{o} $ but R becomes excessively large, for practical purposes, if S approaches 2. Multistaging is used to obtain values as large as 5.

To get an idea of what is required for space exploration, let us consider the Apollo spacecraft (9), shown in Fig. 1. This is designed to take three men to the moon, land two, and return all three to the earth in about 1 week. Its characteristics are as follows: height, 110 meters (364 feet), mass on launching pad, $ 3 \times 1 0^{6} $ kilograms $ (6.5 \times 1 0^{6} $ pound-mass); initial thrust, $ 3.3 \times 1 0^{7} $ newtons $ (7.5 \times 1 0^{6} $ pounds); initial acceleration, 0.15g; acceleration at first-stage burnout, 4g; first-stage fuel consumption, -14,000 kilograms per second for 150 seconds; exhaust speed, 2.5 kilometers per second; mass of recentry package on return to earth, 5400 kilograms.

Thus, we require about 550 kilograms on the launching pad for every kilogram which is to travel to the moon and return. This mass ratio would be enormously greater for any similar mission to a planet, even to a nearby planet such as Mars or Venus. A single Saturn V vehicle, large as it is, cannot accomplish such a mission.

Manned exploration of the planets will be very difficult with chemical rockets alone. Studies under way envisage the use of ion propulsion and nuclear engines after the spacecraft

has been removed from the earth by chemical rockets.

The value of $ \nu_{c} $ obtained with chemical rockets is small, about $ 8 \times 1 0^{-8} c $ In theory, nuclear reactions might be used to obtain high speeds. The products of fission of $ \mathrm{U}^{235} $ have speed about 0.03c. If we sound from helium from the fusion of hydrogen, the speed of the helium would be 0.001 tical problem would remalte the ucts formed would fly directions.

In practice, nuclear engi by heating a propellant—an example—and expeltin propellant is gone, There is a gain over chemical and the gain makes this type of potentially useful for planetation.

If matter and antimatter are stored in a rocket and are together, gamma-ray photons traveling with speed c, would be produced all directions. If the radiation can be aligned and the process were 100 percent efficient, then the following equation would hold:

$$
R = (1 + v / c) ^ {2} / (1 - v / c) ^ {2}.
$$

A round trip to another star would require two accelerations and two decelerations. The overall mass ratio would be $ Q=R^{4}. $ For $ \nu=0. 5 c, $ $ Q=9; $ for $ \nu=0. 9 c, $ $ Q=3 6 1. $ If a voyage of exploration were made to three stars and back, the mass ratio would be $ R^{8}. $

The thrust that would be obtained if the radiation from the annihilation of matter could be aligned is $ F = \dot{m} c $ where $ \dot{m} $ is the annihilation rate. The power is $ P = \dot{m} c^{2} $ . The power to thrust is $ P / F = c $ , and $ 3 \times 1 0^{8} $ watts must be generated for each newton of thrust $ (1.33 \times 10^{0} $ watts per pound).

To lift a spacecraft of mass 5000 kilograms (weight, 49.000 with an acceleration of 1g from the earth would require a power of about