In the Sun frame, where the sun (not the planet) is stationary, what are the variables?

David Shortt explains some of the variables that change in considering the Sun frame calculation of the gravity assist, in the paragraphs below.

Velocity

Now let’s consider what the encounter looks like in the Sun frame, where the Sun is stationary and the planet is moving. The difference between the planet frame and the Sun frame is just the velocity of the planet with respect to the Sun.

To convert from the planet frame to the Sun frame, we simply add the velocity of the planet to both the planet and the spacecraft.

Direction

This velocity is a vector, which means direction is important, and it can be in any arbitrary direction depending on the planet’s position in its orbit at the time of the encounter (It also changes with time because the planet is following a curved orbit around the sun, but during the relatively short encounter with the spacecraft it’s a reasonable approximation to consider the planet as moving in a straight line).

Because the direction of the spacecraft changes when it encounters the planet and because the original direction of the spacecraft is also arbitrary, it’s not immediately obvious how the encounter will look in the Sun frame. The arbitrariness of the directions gives rise to a rich set of possible behavior in the Sun frame, all in accordance with Newton’s laws of motion, even though in the planet frame the encounters are simple hyperbolic trajectories.

With velocity as a vector, change direction, and you alter speed (a quantity).

Crucially, because the direction changes, the speed of the spacecraft is different before and after the encounter when viewed in the Sun frame. The outgoing speed is not the same as the incoming speed, and the spacecraft can either speed up or slow down. Let’s see by example how this works.

If you carefully read the last paragraph, you will want to see the illustrations provided by David Shortt on his blog. You can read the full article and see his illustrations here.

When you return to this article, please visit the next page to see one more image of a gravity assist at work.