Hohmann's Landing Maneuver

The German engineer Dr. Hohmann deserves the credit for indicating a way out of this dilemma. According to his suggestion, the vehicle will be equipped with wings for landing, similar to an airplane. Furthermore, a tangential (horizontal) velocity component is imparted to the vehicle at the start of the return by means of reaction so that the vehicle does not even impact on the Earth during its descent, but travels around the Earth in such a manner that it approaches within 75 km of the Earth's surface (Figure 39).

Figure 39. During Hohmann's landing process, the return trajectory is artificially influenced to such an extent that the space ship does not even impact the Earth, but travels around it at an altitude of 75 km.

Key: 1. Tangential (horizontal) velocity of approx. 100 m/sec; 2. Return trajectory (descent to Earth); 3. At an altitude 75 km above the Earth's surface; 4. Descent velocity of approximately 11,000 m/sec; 5. Earth

This process can be explained in a simple fashion as follows: if a stone is thrown horizontally instead of allowing it to simply drop, then it hits the ground a certain distance away, and, more specifically, at a greater distance, the greater the horizontal velocity at which it was thrown. If this horizontal velocity could now be arbitrarily increased such that the stone falls not a distance of 10 or 100 meters, not even at distances of 100 or 1,000 km, but only reaches the Earth at a distance of 40,000 km away, then in reality the stone would no longer descend at all because the entire circumference of the Earth measures only 40,000 km. It would then circle the Earth in a free obit like a tiny moon. However, in order to achieve this from a point on the Earth's surface, the very high horizontal velocity of approximately 8,000 meters per second would have to be imparted to the stone. This velocity, however, becomes that much smaller the further the position from which the object starts is distant from the Earth. At a distance of several hundred thousand km, the velocity is only around 100 meters per second (Figure 39). This can be understood if we visualize that the vehicle gains velocity more and more solely due to its descent to Earth. According to what was stated previously, if the descent velocity finally attains the value of 11,000 meters per second, it is then greater by more than 3,000 meters per second than the velocity of exactly 7,850 meters per second that the vehicle would have to have so that it would travel around the Earth (similar to the stone) in a free circular orbit at an altitude of 75 km.

Figure 40. If the centrifugal force becomes extremely large due to excessively rapid travel, it hurls the automobile off the road.

Key: 1. Friction of the wheels on the ground; 2. Direction of motion of the automobile being hurled out (tangential); 3. Centrifugal force; 4. Road.

Due to the excessive velocity, the space ship is now more forcefully pushed outward by the centrifugal force than the force of gravity is capable of pulling it inward towards the Earth. This is a process similar, for instance, to that of an automobile driving (too "sharply") through a curve at too high a speed (Figure 40). Exactly as this automobile is hurled outward because the centrifugal force trying to force it off the road is greater than the friction of the wheels trying to keep it on the road, our space ship will in an analogous way also strive to exit the free circular orbit in an outward direction and, as a result, to move again away from the Earth (Figure 41).

Figure 41. Due to the travel velocity (11,000 instead of 7,850 m/sec!) which is excessive by around 3,000 m/sec, the centrifugal force is greater than the force of gravity, consequently forcing the space ship outward out of the free circular orbit.

Key: 1. Descent trajectory; 2. Free circular orbit; 3. Velocity in the free circular orbit of 7,850 m/sec; 4. Earth; 5. Force of gravity; 6. Descent velocity of around 11,000 m/sec; 7. Centrifugal force.

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