Gravitational Maneuver

 This model illustrates the concept of gravitational maneuvers. As a spacecraft passes a planet, the planetary gravitational field gives the shuttle additional acceleration. The spacecraft enters the planet's gravisphere along an asymptote with velocity vinf in respect to the planet. It will turn at an angle φ=2arctg(GM/cνinf) (c is the sighting range - the distance between a straight line that is parallel to the spacecraft velocity vector in infinity, and the planet's center). The spacecraft will then continue to move with the same speed vinf in respect to the planet, in accordance with the pulse preservation law. Maximal angle of the turn occurs when the sighting range is equal to planet radius: φmax=arctg(νI/νinf) Where vI - first space velocity that is inherent to this planet. A celestial body emanating the gravity field is displayed at the center of the model against the background of starry sky. You may select different celestial bodies from the list that includes the Sun, the Moon, and 9 large planets of the solar system. Press "Run" button and observe the spacecraft move with initial velocity ν0. As the spacecraft passes the planet, it changes its direction by the angle φ (the angular value is displayed in the message window), or collides with the planetary surface (it the distance from the spacecraft to the planet is too small). Modify the parameters of spacecraft motion by using Initial Speed and Deflection Distance controls, and observe the ensuing changes. Press "Stop" button to bring the animation to a halt. Press "Reset" to return the animation to its initial state. As we have already mentioned, the objective of a gravitational maneuver is to increase the speed of the spacecraft. Consider a ball that is moving with speed v and hits an elastic wall that is moving counter-currently to the ball with speed u. After the collision, the ball acquires a speed of 2u - ν (which becomes clear if we look at the collision from the wall's frame of reference.) A similar situation occurs in the case when a satellite is performing a gravitational maneuver, as the massive planet plays the role of the elastic wall.