## Space Flight

Newton's law of gravitation defines the attraction of gravitational force Fg between two bodies in space as follows:

Here G is the universal gravity constant (G = 6.670 x 10~n m3/ kg-sec2), and m2 are the masses of the two attracting bodies (such as the earth and the moon, the earth and a spacecraft, or the sun and a planet) and R is the distance between their centers of mass. The earth's gravitational constant /z is the product of Newton's universal constant G and the mass of the earth mi (5.974 x 1024 kg). It is n = 3.98600 x 1014 m3/sec2.

The rocket offers a means for escaping the earth for lunar and interplanetary travel, for escaping our solar system, and for creating a stationary or moving station in space. The flight velocity required to escape from the earth can be found by equating the kinetic energy of a moving body to the work necessary to overcome gravity, neglecting the rotation of the earth and the attraction of other celestial bodies.

By substituting for g from Eq. 4-12 and by neglecting air friction the following relation for the escape velocity is obtained:

### D I 2g0

Here R0 is the effective earth radius (6374.2 km), h is the orbit altitude above sea level, and g is the acceleration of gravity at the earth surface (9.806 m/sec). The spacecraft radius R measured from the earth's center is R = R0 + h. The velocity of escape at the earth's surface is 11,179 m/sec or 36,676 ft/sec and does not vary appreciably within the earth's atmosphere, as shown by Fig. 4-6. Escape velocities for surface launch are given in Table 4—1 for the sun, the

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