Post by ajv on Aug 23, 2008 1:44:40 GMT -4
I've done some more investigation into the Lunar Sphere of Influence issue.
The links section of the yaAGC website contains a collection of (large) PDF documents describing many of the onboard computer programs. In the document R-577: Guidance System Operations Plan for Manned CM Earth Orbital and Lunar Missions Using Program Colossus 1 (Rev. 237) and Program Colossus 1A (Rev. 249). we find the following paragraph:
On page 5.9-1 we find the definition of rSPH
In the actual Colossus Build 249 source code (PDF page 1334) we can see the value defined:
The definition in the Luminary 1C, Build 131 source code (PDF page 1245) is identical.
Incidentally, yes, the Apollo Computers internals used metric values which were converted to feet and nautical miles etc. for presentation to the crew.
So, what is the value 64,373,760m? Is it a complicated-to-describe, hard-to-determine value calculated by solving a complex equation based on the Earth's mass and the Moon's mass and the Earth/Moon distance at that particular instant during the mission?
No.
64,373,760 m is equal to 40,000 (statute) miles exactly. 40,000 miles EXACTLY! i.e. someone said "Let's use the value 40,000 statue miles - what's that in meters?"
Incidentally, the Reference 14 above is to Astronautical Guidance, Richard H. Battin, McGraw Hill Book Co, 1964 and note 3 says:
So rSPH is just an arbitrary value, inside of which they switch from the Earth-based coordinate system to the Moon-based system. And after plotting the surfaces it's not a very good approximation to the equigravisphere. But that doesn't mean it's a bad surface to use for switching coordinate systems.
Ok, so why does the PAO in Apollo 11 report that the sphere of influence was crossed when the spacecraft was 33,822 nautical miles from the moon? 33,822 nautical miles is 38,921 statute miles not 40,000. Is the FIDO on the ground using a different definition? A definition based on some complicated, hard-to-determine value calculated by solving ...?
To answer that, let's look at the PAO reports of the sphere of influence event from some of the other missions:
Apollo 8: 33820 nautical miles
Apollo 11: 33822 nautical miles
Apollo 16: 33821 nautical miles
What is the first thing that strikes you about these numbers? It's that they're all the same. In each of these three missions the location of the lunar sphere of influence change is exactly the same value.
Have you ever had one of those "it's staring you in the face" moments?
Take the value
Convert to statue miles
And then add the radius of the moon: 1080 statute miles
So the only significance of time and location when the PAO mentions that "we'll be crossing into the sphere of influence of the moon" is that the spacecraft is currently crossing the arbitrary 40,000 mile line.
The 40,000 value remains the same over all the Apollo lunar expeditions. It's hard coded into the AGC programs. It's not based on a deep analysis of the particular trajectory and it's not the point where the magnitude of the gravitational forces are equal. It's just the point to switch coordinate systems.
Oh, and it means that whenever the PAO says they're such-and-such nautical miles from the Moon they're actually reading from a figure that is the distance to the theoretical surface of the Moon not to the center.
Oh2, this means that my "single mistake" calculation in the John Lear thread actually needs two mistakes. It's a mistake to subtract rather than add the Moon's diameter.
The links section of the yaAGC website contains a collection of (large) PDF documents describing many of the onboard computer programs. In the document R-577: Guidance System Operations Plan for Manned CM Earth Orbital and Lunar Missions Using Program Colossus 1 (Rev. 237) and Program Colossus 1A (Rev. 249). we find the following paragraph:
This [Basic Reference] coordinate system is shifted from earth-centered to moon-centered when the estimated vehicle position from the moon first falls below a specified value rSPH, and is likewise shifted from moon-centered to earth-centered when the estimated vehicle position from the moon exceeds rSPH. This procedure is described in Section 5.2.2.6 and Fig 2.2-3.
Section 5.1.4.1 (page 5.1-31)
On page 5.9-1 we find the definition of rSPH
rSPH m[eters] 64,373,760 [Reference 14] [Comment 3]
In the actual Colossus Build 249 source code (PDF page 1334) we can see the value defined:
RSPHERE 2DEC 64373.76 E3 B-29
The definition in the Luminary 1C, Build 131 source code (PDF page 1245) is identical.
Incidentally, yes, the Apollo Computers internals used metric values which were converted to feet and nautical miles etc. for presentation to the crew.
So, what is the value 64,373,760m? Is it a complicated-to-describe, hard-to-determine value calculated by solving a complex equation based on the Earth's mass and the Moon's mass and the Earth/Moon distance at that particular instant during the mission?
No.
64,373,760 m is equal to 40,000 (statute) miles exactly. 40,000 miles EXACTLY! i.e. someone said "Let's use the value 40,000 statue miles - what's that in meters?"
Incidentally, the Reference 14 above is to Astronautical Guidance, Richard H. Battin, McGraw Hill Book Co, 1964 and note 3 says:
The quantity rSPH is the radius of a sphere that approximates the surface of influence of the Moon as given in Fig 1.3 of Reference 14.
So rSPH is just an arbitrary value, inside of which they switch from the Earth-based coordinate system to the Moon-based system. And after plotting the surfaces it's not a very good approximation to the equigravisphere. But that doesn't mean it's a bad surface to use for switching coordinate systems.
Ok, so why does the PAO in Apollo 11 report that the sphere of influence was crossed when the spacecraft was 33,822 nautical miles from the moon? 33,822 nautical miles is 38,921 statute miles not 40,000. Is the FIDO on the ground using a different definition? A definition based on some complicated, hard-to-determine value calculated by solving ...?
To answer that, let's look at the PAO reports of the sphere of influence event from some of the other missions:
Apollo 8: 33820 nautical miles
Apollo 11: 33822 nautical miles
Apollo 16: 33821 nautical miles
What is the first thing that strikes you about these numbers? It's that they're all the same. In each of these three missions the location of the lunar sphere of influence change is exactly the same value.
Have you ever had one of those "it's staring you in the face" moments?
Take the value
33821 nautical miles from the moon
Convert to statue miles
38920 statute miles from the moon
And then add the radius of the moon: 1080 statute miles
40000 statute miles from the center of the moon
So the only significance of time and location when the PAO mentions that "we'll be crossing into the sphere of influence of the moon" is that the spacecraft is currently crossing the arbitrary 40,000 mile line.
The 40,000 value remains the same over all the Apollo lunar expeditions. It's hard coded into the AGC programs. It's not based on a deep analysis of the particular trajectory and it's not the point where the magnitude of the gravitational forces are equal. It's just the point to switch coordinate systems.
Oh, and it means that whenever the PAO says they're such-and-such nautical miles from the Moon they're actually reading from a figure that is the distance to the theoretical surface of the Moon not to the center.
Oh2, this means that my "single mistake" calculation in the John Lear thread actually needs two mistakes. It's a mistake to subtract rather than add the Moon's diameter.
