### Rendezvous

**
Payton M -
**

Hello, welcome back to my blog!

We are now at the first stop on our journey to Eris– Jupiter, the final destination of the Hohmann Transfer (HT). The third stage of this first section is called the Jovian Rendezvous with stage one being the Orbit Raising Maneuvers (ORMs) and stage two being the HT. The rendezvous can be thought of as the departure from the last orbit in the ORM but in reverse. The first step is to change the focus of the spacecraft’s orbit from the Sun (the focus of the interplanetary HT trajectory) to Jupiter (the arrival planet and focus of the capture orbit). The last leg of the heliocentric HT is the beginning of the Jupiter-focused rendezvous, and the speed of the spacecraft at this point is known as the approach velocity V_{A}. The speed of Jupiter needs to be subtracted to find the speed of the spacecraft with respect to Jupiter to find the hyperbolic approach velocity (V_{∞}), since with respect to Jupiter, it is now in a hyperbolic trajectory. This value is used in multiple equations to solve for the ideal capture orbit perijove radius at point P (r_{p}).

In MATLAB, I created a for loop to determine the ideal capture orbit eccentricity and r_{p} value, essential for finding the total change in velocity and fuel needed to attain the capture orbit. Using calculus, an equation for the optimal r_{p} value can be derived, and is dependent on a capture orbit eccentricity value. However, we don’t know this eccentricity value, or which value would be best, so the for loop runs different eccentricity values from 0.1 -> 1 in 0.1 increments through each equation to ultimately output the delta-v needed to transfer from the hyperbolic path to the capture orbit for each eccentricity option. Then, it takes the minimum value and calculates the amount of fuel needed.

This week I finished the next section– the plane change– and am working on finding the correct orientation needed to depart for Eris!

Thanks for reading and following along on this journey to Eris!

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