MECHANICS SLINGSHOT EFFECT Ian Cooper School of Physics, University of Sydney ian.cooper@sydney.edu.au mec_slingshot.m The mscript is used to create an animated gif of the slingshot effect where a spacecraft approaches a planet. The planet can be stationary or moving towards the spacecraft. The motion of the spacecraft is animated and changes in the kinetic energy and gravitational potential energy are displayed as well as plots of the speed of the spacecraft and its separation distance from the planet. A finite difference method is used to solve Newton’s Second Law for the gravitational attraction between the spacecraft and planet. From the solution you can calculate the trajectory of the spacecraft, its velocity, kinetic energy, potential and total energies of the system as functions of time. SLINGSHOT EFFECT The slingshot effect is also known as a planetary swing-by or a gravity-assist manoeuvre. It is performed to achieve an increase in speed and/or a change of direction of a spacecraft as it passes close to a planet. As it approaches, the spacecraft is caught by the gravitational field of the planet, and swings around it. The speed acquired is then sufficient to throw the spacecraft back out again, away from the planet. By controlling the approach, the outcome of the manoeuvre can be manipulated and the spacecraft can acquire some of the planet’s velocity, relative to the Sun. The manoeuvre can be analysed as an elastic mechanical interaction, in which both momentum and kinetic energy are conserved. As a result of the interaction, the spacecraft will have sped up relative to the Sun, acquiring kinetic energy. The planet will have slowed very marginally, losing an equivalent amount of kinetic energy. Remember that EK = ½ m v2 and the mass of a planet is
MECHANICS SLINGSHOT EFFECT Ian Cooper School of Physics, University of Sydney ian.cooper@sydney.edu.au mec_slingshot.m The mscript is used to create an animated gif of the slingshot effect where a spacecraft approaches a planet. The planet can be stationary or moving towards the spacecraft. The motion of the spacecraft is animated and changes in the kinetic energy and gravitational potential energy are displayed as well as plots of the speed of the spacecraft and its separation distance from the planet. A finite difference method is used to solve Newton’s Second Law for the gravitational attraction between the spacecraft and planet. From the solution you can calculate the trajectory of the spacecraft, its velocity, kinetic energy, potential and total energies of the system as functions of time. SLINGSHOT EFFECT The slingshot effect is also known as a planetary swing-by or a gravity-assist manoeuvre. It is performed to achieve an increase in speed and/or a change of direction of a spacecraft as it passes close to a planet. As it approaches, the spacecraft is caught by the gravitational field of the planet, and swings around it. The speed acquired is then sufficient to throw the spacecraft back out again, away from the planet. By controlling the approach, the outcome of the manoeuvre can be manipulated and the spacecraft can acquire some of the planet’s velocity, relative to the Sun. The manoeuvre can be analysed as an elastic mechanical interaction, in which both momentum and kinetic energy are conserved. As a result of the interaction, the spacecraft will have sped up relative to the Sun, acquiring kinetic energy. The planet will have slowed very marginally, losing an equivalent amount of kinetic energy. Remember that EK = ½ m v2 and the mass of a planet is