### Orbit Raising Maneuvers

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Payton M -
**

Hello! Welcome back to my blog!

In addition to moving forward with the code, this week I’ve been working on reviewing the code I wrote back in T1 and T2– the orbit raising maneuvers and Hohmann transfers. Today, I’ll share some information on the orbit raising maneuvers and how I’ve used them in my code.

For some background, the orbit raising maneuver is drawn from the Indian Space Research Organization’s (ISRO) mission to Mars and more recently the Chandrayaan-3 mission to the moon and is a modification of the popular Hohmann Transfer (HT) maneuver. Costing less than the making of the movie Interstellar, the Chandrayaan-3 spacecraft landed on the moon in August of 2023! ISRO was able to do this partially by using very fuel efficient orbital maneuvers. They used these orbit raising maneuvers (ORM) to incrementally increase the speed of the spacecraft to reach the moon with less fuel than one large thrust burn. In the image below where the words “Injection Orbit” are is the **perigee** location of the spacecraft– the orbit’s closest point to earth. As you can see, this altitude is constant, meaning the perigee radius is constant for each orbit, while the orbit’s farthest point, called the **apogee, **is increasing. At perigee, a small thrust burn is completed, giving the spacecraft a small force, and increasing its speed. This causes the next orbit to become more eccentric (elliptical), and therefore have a greater apogee value. When the spacecraft comes back to the perigee point it is moving faster than it was at that location in the previous orbit. The spacecraft’s kinetic energy increases in each ORM because it is getting energy from the thrust firing as well as the Earth’s rotation. In total, using ORM uses less fuel than one large thrust burn to attain the same increase in velocity.

I began the trajectory with the spacecraft in a circular parking orbit around Earth, 170 km above the surface since the Chandrayaan-3 mission’s initial orbit was 170 km x 35,000 km (perigee x apogee) after it launched from Earth. In MATLAB, I created a for loop to determine how many orbit raising maneuvers were needed to reach the speed required to depart for the transfer trajectory of the HT. The code runs through a sequence of equations, adding a ‘change in mass of fuel’ over ‘total mass’ ratio of 2% each time. One problem I encountered was that the speed needed for the HT was greater than Earth’s escape velocity, so after 13 ORMs, the eccentricity values exceeded 1 (hyperbolic) and the apogee values were unreasonable, as the spacecraft had enough velocity to exit Earth’s gravity well and did not come back to perigee for the next thrust burn. So, after 12 ORM, the spacecraft is traveling just under Earth’s escape velocity, and one more larger thrust burn is needed to attain the speed needed for departure to Jupiter.

This week, I’m focused on minimizing the total amount of fuel used in this stage even more by fine tuning the specific impulse value (isp), or efficiency of the fuel. When I changed the isp from 310 which corresponds to Nitric acid/monomethyl hydrazine fuel to liquid oxygen/liquid hydrogen with an isp of 455, only 8 ORMs were needed. I’m doing more research to determine the ideal isp value for this specific mission.

Thank you for reading, and I’ll be sharing more about the actual Hohmann transfer next week!

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