9755

Gravitational Slingshot Effect

In astronautical mechanics, the gravitational slingshot maneuver, which NASA calls a "gravity assist", exploits the gravitational attraction of a planet to alter the speed and trajectory of an interplanetary spacecraft. A spacecraft can thereby be accelerated by a near planetary flyby to enable considerable savings of fuel in missions to the outer planets, such as Jupiter and Saturn. At first sight, this might seem like a cosmic something-for-nothing scam. But the physics depends straightforwardly on conservation of momentum and energy and the huge planet-to-spacecraft mass ratio, which leaves the planetary orbit essentially undisturbed.
This Demonstration considers a hypothetical slingshot maneuver around the planet Jupiter (orange sphere with radius ≈ 143,000 km), which moves at an average speed of 13.1 km/sec in its orbit around the Sun. A spacecraft, with initial speed , which has a negligible mass and size compared to the planet, follows a hyperbolic path in Jupiter's frame of reference. In the Sun's frame of reference, however, the hyperbolic path is tilted and moves with velocity , which provides a terrific boost to the spacecraft after it crosses the orbit of the planet. The graphic shown is highly schematic, with both space and time scales significantly distorted. Refer to the references for more accurate formulas when you plan your next space mission.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The encounter of the spacecraft with the planet can be simulated by an elastic collision. In the simplest case of a head-on collision, the initial state can be represented by the diagram: ¤ and the final state by: ¤. The planet is so massive compared to the spacecraft that its motion is essentially unperturbed. In the actual situation, the final speed of the spacecraft is given by , where is the initial angle between and .
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+