Issue 127

Doing the Math: Estimated Fuel Requirement for SJ-21/25 Maneuvers

15 Aug: I asked Integrity ISR's astro-wizard Jason Dean to take a look at the recent SJ-21 and SJ-25 maneuvers and give an estimate of the fuel requirements. Looking at the series of maneuvers holistically Jason calculated the energy requirements to maneuver the satellites (currently docked) from their 8 August orbit…

15 Aug: I asked Integrity ISR’s astro-wizard Jason Dean to take a look at the recent SJ-21 and SJ-25 maneuvers and give an estimate of the fuel requirements. Looking at the series of maneuvers holistically Jason calculated the energy requirements to maneuver the satellites (currently docked) from their 8 August orbit to what they were on 15 August. While we lack certain specific information for an exact calculation, here are the numbers Jason was able to deduce. Bottom line is SJ-21 and SJ-25 combined required about 332.2 m/sec of energy (fuel) to change their semi-major axis and plane (inclination and RAAN). Note the energy (fuel) requirements for the plane change maneuvers dwarfed that of the SMA change…331.8m/sec vs 0.4m/sec respectively. Thank you Jason!

Step 1: determine the semimajor axis of the transfer orbit.

Step 2: solve for the specific mechanical energy of the transfer orbit.

Step 3: solve for the energy and velocity of the docking orbit.

Step 4: solve for the transfer-orbit velocity at the docking orbit.

Step 5: calculate the change in velocity required for the transfer burn.

Step 6: solve for the energy and velocity at the current orbit.

Step 7: solve for the transfer-orbit velocity at the current orbit.

Step 8: calculate the change in velocity required for the final recircularization burn.

Step 9: determine the total delta-V for the altitude change, approximately 0.9 m/s.

Step 10: calculate the combined plane-change maneuver and total delta-V, approximately 332.2 m/s.