Blog Post 12, Free Form Post, Gravitational Slingshots

NASA's New Horizons mission to Pluto still has everyone in awe since its close flyby of Pluto on July 14, 2015. Though New Horizons is now about 0.61 AU (as of 9/28/15) away from Pluto* (more than half the distance from the Earth to the Sun!), the probe continues to send back more and more stunning images like the following: 

(Source: http://pluto.jhuapl.edu/Multimedia/Science-Photos/pics/P_LORRI_FULLFRAME_COLOR.png)

But how did New Horizons manage to make it to Pluto in just nine years? Though it seems like a long time, had the New Horizons team not employed a gravitational slingshot around Jupiter, the trip would have taken an extra five years.

A gravitational slingshot (or gravity assist) is a method of using the orbital momentum of a planet (or other object) to either positively or negatively accelerate the velocity of a spacecraft. How does a gravitational slingshot work? Let's look at the system below, with a spacecraft of initial velocity v approaching a planet of initial velocity U.  As the spacecraft flies closer to the planet, the gravitational attraction between the much larger planet and the much smaller spacecraft draws the spacecraft in very close to the planet. 

(Source: https://en.wikipedia.org/wiki/File:Gravitational_slingshot.svg)

We know that the total energy of the system must be the same before and after the gravity assist. If we consider the system from the planet's point of view, the velocity of the planet is zero (the planet is at rest), and the velocity of the approaching spacecraft is U + v, or the original velocity (v) added to the velocity of the reference frame (U). As the spacecraft leaves the planet, the spacecraft must have the same velocity as when it entered, or U + v, but in the opposite direction as before. Then, to switch back to the reference frame of the observer, we must add the velocity of the reference frame (U), to get a final velocity of 2U + v. 

Obviously, the path of a spacecraft approaching an object will not always enter and exit in parallel paths. As it turns out, the path of the spacecraft will be hyperbolic, and the amount by which the velocity increases is dependent upon the angle at which the spacecraft enters and exits. In general, if the spacecraft's velocity is more in the direction of the planet's orbit after its encounter, the velocity of the spacecraft will increase. In turn, the velocity of the planet will actually slow down the smallest bit, because of Newton's Third Law - every action has an equal and opposite reaction. The momentum gained by the spacecraft is lost by the planet. Check out some examples of spacecrafts entering at different angles: 

Source: http://www.planetary.org/blogs/guest-blogs/2013/20130926-gravity-assist.html

So thank you, gravitational assists, for our newest images of Pluto! For more information, check out the following links: 

http://www.planetary.org/blogs/guest-blogs/2013/20130926-gravity-assist.html

http://physics.stackexchange.com/questions/53050/why-does-gravity-assist-transfer-twice-the-planets-velocity

https://en.wikipedia.org/wiki/Gravity_assist

http://www.askamathematician.com/2010/05/q-how-does-a-gravitational-sling-shot-actually-speed-things-up/