Traversing the Cosmos — With a Little Help from My Friends (Pt II)

By Kevin Grazier | June 22, 2010 10:24 pm

“In Pt. I, all you did was snark about TV and films that, you feel, didn’t depict gravity assist, something that you admit is a difficult concept, correctly.”

Well, every science educator has their “pet” topics–things they really like to convey to receptive minds. This is one of mine (tides are another and we’ll be visiting that topic soon).

“So how IS it done, Mr. Smarty Pants?”

The notion that a spacecraft could gain (or lose) energy by passing close to a planet was first developed in the early 1960s by Michael Minovitch, a very clever UCLA graduate student who was working as a summer student at JPL. Previous research had suggested that a spacecraft would be accelerated by passing close to a planet (or moon)—the spacecraft gains a bit of momentum while the planet loses the exact same amount. Minovitch showed that this technique could be used to reach places in the Solar System using far less fuel. Using chemical propulsion alone, it icassini-trajectorys nearly impossible to reach many places within the Solar System: both near to (Mercury) and far from (the Jovian planets beyond Jupiter) the Sun. Gravity assist opened up new venues of exploration.

The Voyager II spacecraft used the gravity of Jupiter and Saturn to reach Uranus and Neptune.  Galileo swung past Venus, Earth, and Earth again, to reach Jupiter. Cassini (at right) used Venus, Venus again, Earth, then Jupiter in order to reach Saturn (notice also in the graphic that the spacecraft followed the same kind of spiral path outwards that Icarus would have followed inwards to the Sun, as mentioned in Part I). Other spacecraft have employed the technique; even the Dawn Mission used a gravity assist from Mars en route to the asteroids Ceres and Vesta. (You can see the current position of Dawn here.)

It begins with the concept of a gravitational sphere of influence.  There are different definitions of this gravitational sphere of influence: the activity sphere or Hill Sphere (here’s a cool Hill Sphere calculator). They are all supposed to define a (nearly) spherical region around a planet.  Outside of the gravitational sphere of influence the trajectory of a spacecraft is dictated chiefly by the gravitational attraction of the sun, with a nearby planet giving a slight gravitational tug, or perturbation, to that trajectory. Within the sphere of influence the roles are reversed – it is the planet’s gravity that primarily dictates the spacecraft’s trajectory, with the sun’s gravity being a perturbation.

Geometry of a Gravity Assist

Geometry of a Gravity Assist

To perform a gravity assist a spacecraft enters the sphere of influence of a planet–let’s use Neptune as an example–its trajectory is bent by the planet’s gravity, and it leaves along a different path. If the diagram above is accurate, the magnitude of the velocity/energy is the same going in as going out–by the law of conservation of energyGravity_assist_vectors1The magnitude of the inward velocity vector, Vin, is the same as the magnitude of Vout (red vectors). That is entirely true, and this is why the notion of gravity assist gets very confusing!  Remember, though that these velocities are relative to Neptune. The gravity assist is relative to the Sun, however, and Neptune is moving with velocity Vn. If we determine the velocity of the spacecraft relative to the Sun, which we do by adding Vin and Vout to Vn (blue vector), nose-to-tail fashion, a different picture emerges. The white vectors below are the heliocentric (sun-centered) velocities. We see that not only does the heliocentric inbound velocity vector (Vhi) change direction when outbound (Vho), it increases in magnitude. The spacecraft has picked up speed and there’s your assist!

Gravity_assist_vectors3

For a gravity assist in the real world, a spacecraft passes behind a planet (as above) to gain speed/kinetic energy, and behind ahead to lose it.

A good scientist understands his/her biases, so I will admit up front that I’m highly biased here , but a moreB-plane realistic cinematic depiction of gravity assist, one that incorporated all the above, was in the pilot episode for the Fox series (not picked up) Virtuality. As with the development of gravity assist at JPL in the early 1960’s, Virtuality had an advisor who was a very clever former UCLA graduate student who currently works at JPL.

In Virtuality, as the crew of the starship Phaeton approached Neptune, they also approached the “Go/No-Go” point in their mission to the star Epsilon Eridani. If the Commanding Officer, Captain Pike, decided to “go”, they would “slingshot” around Neptune, out of the Solar System, and engage their Orion Drive to take them to Eridani. Approach Neptune another way, and they would be rerouted back home to Earth.

During their “slingshot”, one of the crewmembers, Dr. Jules Braun, reports that their trajectory is off  by “Five milliarcseconds in the B Plane.” Simply, Dr. Braun was referring to an imaginary plane, the B-plane, that dissects a planet perpendicular to the incoming trajectory. To get the desired gravity assist, a spacecraft aims at a pre-determined point (not coincidentally called the “aim point”) in the B-plane.

So consistent with our previous statement “pass behind to gain speed/pass ahead to lose”, if  Phaeton approached Neptune as in the diagram, they would be catapulted out of the Solar System and onto Eridani. Approach Neptune on the opposite side of the planet, and they would be rerouted back home to Earth.

There! Gravity assist explained simply, if not in a nutshell, with a cinematic example to boot!

CATEGORIZED UNDER: Physics, Space, Space Flight

Comments (4)

  1. Nekura

    What would you recommend as a good introductory book to read more about orbital mechanics? I’ve always been curious about it, like how getting to Phobos would be much easier then getting to Mars itself, but only find equation dense papers when I try to look stuff up online. And I have some mistaken ideas, like, I though that slingshot maneuvers stole rotational energy from a planet, rather than orbital energy, or that thrust/break maneuvers at aphelion/perihelion would change the height of the other, making dropping into the sun really easy. Reading bits and pieces doesn’t give a whole, connected picture.

    Thank you
    Nekura

  2. It seems there is a bit of confusion with your wording.

    “For a gravity assist in the real world, a spacecraft passes behind a planet (as above) to gain speed/kinetic energy, and behind to lose it.”

    and

    “So consistent with our previous statement “pass behind to gain speed/pass behind to lose”, if Phaeton approached Neptune as in the diagram, they would be catapulted out of the Solar System and onto Eridani.”

    You said ‘pass behind’ all instances… Wouldn’t you need to pass ahead of the planet to lose speed?

  3. Kevin Grazier

    You are correct, and I have edited that to read: ““So consistent with our previous statement “pass behind to gain speed/pass ahead to lose”, if Phaeton approached Neptune as in the diagram, they would be catapulted out of the Solar System and onto Eridani.” – KRG

  4. Ryan Upton

    What if your spaceship travels back in time close to the big bang era. Moves a small distance without effecting anything. Then travels back to the present day. In this way you could move large distance across the universe and you wouldn’t even have to break Einsteins rule of ‘no faster then light travel’.

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