This is the Lunar Module Systems Activation Checklist Book of Apollo 13. The handwritten numbers are part of the calculations made by Commander James Lovell, just two hours after a service module's oxygen tank explosion left them marooned in space.
The values were written by Lovell on the manual—which was sold in an auction yesterday night for £28,000—and were crucial to putting the ship on the course that would return it to Earth. Lovell explains it briefly in that blue post-it note:
"This pub[lication] was utilized to transfer CSM guidance data to LM guidance system so the spacecraft data of our attitude with respect to the celestial sphere would not be lost. Note the time these calculations were made GET 58 08 06 about two hours after the explosion. James Lovell."
Establishing the right course to use the Moon's gravity to return to Earth was the first step of the complex process ultimately saved their lives. They had to transfer these calculations to the Lunar Module because, as they were losing oxygen and power, they were planning to use its descent engine to accelerate their trip:
"This is Apollo Control at 57 hours 58 minutes ground elapsed time. To recap briefly the situation here in Mission Control Center, we have an apparently serious problem with a leak in the cryogenic oxygen in the Service Module, which provides the electrical power system coming out of the fuel cells, and also, breathing oxygen for the crew."
"Now in the process of manning the Lunar Module. Standby... The current thinking is to use the Lunar Module descent propulsion system, a big engine of the LM to propel the entire spacecraft stack to higher velocity as they go around behind the Moon to come back to Earth a day earlier than a normal free return trajectory would return the spacecraft."
The situation was critical at this point, and Lovell was nervous that his math could be erroneous. He contacted mission control to double check the numbers:
"Houston. Okay. I want you to double check my arithmetic to make sure we got a good course align."
This is the whole transcript of the conversation, as recorded by NASA:
058:00:51 LMP (HAISE)
Okay. What next, James? Course align?
058:00:57 CDR (LOVELL)
Do it right. Take your time.
058:01:32 CC (CAPCOM)
And, Aquarius, Houston. We'd like you to, on your alignment, can you continue right on through the fine align Activation 31? Go right on through step 7. Over.
058:01:45 LMP (HAISE)
Okay. You want to go on 31 through step number 7, Jack.
058:02:26 LMP (HAISE)
Okay. VERB 41, NOUN 20. Okay. You want plus? Plus or minus? Plus 302.43? Is that right?
058:03:12 LMP (HAISE)
Okay. Let me enter it. Okay. What's the next one? Plus 347.78. 347.78. Okay. 081.3. [???] that right? ENTER. Okay.
058:03:53 CC (CAPCOM)
Odyssey, Houston - - 02 10 03 54 CDR
058:04:01 CC (CAPCOM)
Go ahead, Aquarius.
058:04:03 CDR (LOVELL)
Houston. Okay. I want you to double check my arithmetic to make sure we got a good course align- The roll CAL angle was minus 2 degrees. The command module angles were 355.57, 167.78, 351.87.
058:04:36 CC (CAPCOM)
Okay, Jim. We copy the roll CAL at minus 2.0. The command module is 355.57, 167.78, 351.87.
058:05:19 LMP (HAISE)
Okay. VERB 41, we've done that. Okay.
058:07:11 CC (CAPCOM)
Okay, Jack. Thank you. And, Aquarius, your arithmetic looks good on the course align, there.
058:07:20 CMP (SWIGERT)
Okay. Okay stand by for an ENTER.
058:07:26 CMP (SWIGERT)
058:07:39 CMP (SWIGERT)
Get the GET; we need the GET. What is it? What's that? 58? 58:07?
058:08:15 CMP (SWIGERT)
058:09:16 CDR (LOVELL)
058:09:18 CC (CAPCOM)
Go ahead, Aquarius.
058:09:23 CDR (LOVELL)
Here are the gimbal angles. Command module, 356.69, 163.42, 346.67. Aquarius is 302.26, 345.92, 011.79. Over.
058:09:47 CC (CAPCOM)
Okay, Jim. I got command module 356.65 [sic], 163.42, 346.67. Aquarius, 302.26, 345.92, 011.78.
058:10:07 CDR (LOVELL)
058:10:11 CC (CAPCOM)
Say again, please.
058:10:17 CDR (LOVELL)
The LM middle gimbal is 011.79.
058:10:22 CC (CAPCOM)
011.79. Got it.
Houston confirmed the numbers and so began their journey back home. A lot more things went wrong, but the courage and training of the astronauts combined with the genius and dedicated team work down on Earth finally saved the day, making Apollo 13 the most successful failure in the history of the space program. [Heritage Auctions]