In this model, the velocity of the spacecraft at position 2 is a.) equal to b.) greater than c.) less than the velocity of the craft at position 4. at position 1, the direction of the spacecraft changes because of a.) the gravitational force between earth and the spacecraft b.) the momentum of the spacecraft c.) secondary fuel tanks. position 3 represents the a.) final destination of the spacecraft b.) gravitational force of the spacecraft on earth c.) orbital path or velocity of earth

This is due the gravity field of the planet (The Earth in this case) is used to accelerate the craft. This is true when in a specific point the direction of the movement of the craft is the same direction of the movement of the planet.

In this case the craft will be “catched” by the Earth’s gravitational field, making the craft  to enter a circular orbit.

As explained in the prior answer, this is the exact and correct point where the trajectory of the spacecraft enters into a circular orbit because of the attraction due gravity of the Earth and therefore changes its direction.

Being this the orbital path of the Earth and considering the trajectory of the craft, the condition of accelerating the craft is accomplished.

If the orbital path of the Earth were the opposite from the shown in the figure, the effect on the craft would be braking.

Note all of these is related to the gravitational assistance.

Gravitational assistance is the maneuver in which the energy of the gravitational field of a planet or satellite is used to obtain an acceleration or braking of the probe changing its trajectory.

This maneuver is also called slingshot effect, swing-by or gravity assist. It is a common technique in space for the outer Solar System missions , in order to save costs in the launch rocket and thrusters.

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