Interplanetary space probes often take advantage of the gravity pull of planets and large moons to alter course and gain speed. For these so-called gravity assist maneuvers, a spacecraft flies by a planet and uses its gravitational field and the planet's orbital velocity around the Sun to pick up speed and change direction. It can be somewhat compared to a Ping-Pong ball hitting a revolving fan; the ball will bounce back at a much higher speed and in a different direction from which it was hit into the fan. The maneuver can also work the other way around: if a spacecraft flies by against the direction in which the planet moves around the Sun, the spacecraft will slow down.
There are many more asteroids than planets and moons, but they are all fairly small, and hence their gravity fields are too weak for gravity-assist maneuvers. However, instead of gravity a long tether may be used in an asteroid slingshot flyby. Imagine an interplanetary spacecraft on its way to Jupiter approaching an asteroid, somewhere beyond the orbit of Mars. When it gets relatively close, it fires a tethered harpoon into the space rock—kind of like how the comic-book figure Spiderman slings around the corners of New York skyscrapers. The spacecraft will whirl in an arc around the asteroid. At the right moment the tether is severed and the probe flies off in a different direction and with a different speed due to the asteroid's orbital velocity (the asteroid has dragged the spacecraft on for a little while) (Fig. 1.11).
The force on the spacecraft is determined by the square of its flyby velocity divided by the length of the tether (this is mathematically equivalent to the earlier described artificial gravity being a function of the length of the tether times the square of the rotational speed, because the rotational speed is equivalent to the tip velocity divided by the tether length). If the probe has
an initial speed of a modest 2 km/s (1.2 miles/s) and the force on the tether and spacecraft needs to be limited to ten times the gravity on the Earth's surface (called 10g), the tether has to have a length of at least 40 km (25 miles). Shooting a harpoon from a fast-flying space probe into an asteroid over a distance of tens of kilometers is extremely difficult, and the risk that the harpoon would slip out of the ground during the slingshot maneuver would be very high. The idea is therefore interesting, but probably not very practical.
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