The Study of Spacetime and Gravity: Part Two

As Dr. Tyson does in discussing, “Don’t Believe the Hype about Dark Matter”,  we record the data without assumption.  Sort of a  “Just the facts,” approach of any detective.

I relish in the facts that the Magnetospheric Multiscale (MMS) probes have been able to “fix” their positions 12 times at ~100,000 miles into the interlunar space from the GPS constellation encircling Earth.  I find it extremely plausible.  There is no other massive object near the MMS probes, so why not?  Free-fall into a natural world-line with the MMS probes is the same as free-fall into a natural world-line with the ISS.


“April 4, 2019

“The four Magnetospheric Multiscale (MMS) spacecraft recently broke the world record for navigating with GPS signals farther from Earth than ever before. MMS’ success indicates that NASA spacecraft may soon be able to navigate via GPS as far away as the Moon, which will prove important to the Gateway, a planned space station in lunar orbit.

“After navigation maneuvers conducted this February, MMS now reaches over 116,300 miles from Earth at the highest point of its orbit, or about halfway to the Moon. At this altitude, MMS continued to receive strong enough GPS signals to determine its position, shattering previous records it set first in October 2016 and again in February 2017. This demonstrates that GPS signals extend farther than expected and that future missions can reliably use GPS at extreme altitudes.”  – NASA Report

Editor: I added the emphasis and italics


 

NASA predicts and asserts a reliability of GPS at “extreme altitudes” all the way to The Moon.  Yet, of course, they have not tried GPS on the Moon, nor anywhere close to the Moon.  We had hoped this bravado and administrative ignorance had left NASA. Feynman warned about administrative and “bureaucratic justification,” like the now-infamous “60 Space Shuttle Missions a year,” claim when, in fact, NASA has never had a year in which 60 launches were performed of the Space Shuttle.

However they report, only 4 GPS satellites were necessary to fix the probes’ positions in spacetime…“At the first apogee after the maneuvers, MMS1 had 12 GPS fixes, each requiring signals from four GPS satellites,” said Trevor Williams, the MMS flight dynamics lead at NASA’s Goddard Space Flight Center in Greenbelt, Maryland. “When we began the mission, we had no idea high-altitude GPS would be such a robust capability…”

The question is not the strength or weakness of the GPS satellites’ signals, but treating this as if MMS probes are just on top of a tall mountain on Earth…”high-altitude.”  They are decidedly NOT.*

First, they should need 5 GPS satellites to determine their position precisely.  Why?  Remember, each GPS satellite is designed to give a time-stamped distance to a geographic position.  A hypotenuse or radius of a topological circle.  Two give two intersecting circle.  Two intersections.  Three gives three intersecting circles with one intersection.  Four gives the time of the one intersection, with the concomitant precision.  For interlunar space, Five GPS satellites at a minimum would be necessary to eliminate one of the two intersections in time.  One when the MMS probes are moving away from Earth in apogee, and the other when it is moving towards Earth in perigee. They just eliminated the perigee from their considerations.  They “knew” by dead reckoning that the MMS probes were at apogee.  Just as we only “need” three GPS satellites if we know we are on land, and not at an intersection point over water, or vice-versa, for example.

Still its an assumption, not stated.

 

Second, it works because there is not another massive object near the MMS probes.  Once we introduced the lunar gravitational strong-fields, all bets are off.  As, obviously any lunar-orbiting Gateway, a planned space station in orbit around the Moon utilizes.   The reason for the GPS not working is the timing on the Gateway will be different from the GPS satellites and the MMS probes, and Earth, and even on the Lunar Surface.  All have their own frames of reference.   We know this, because General Relativity tells as much.  That’s how GPS works.  Two videos below explain this.  The last one at T = 6.00 minutes with Dr Tyson starts his discussion of GPS timing.




*The GPS system currently has 31 active satellites in orbits inclined 55 degrees to the equator. The satellites orbit about 20,000 km (12,200 miles) from the earth’s surface and make two orbits per day. The orbits are designed so that there are always 6 satellites in view, from most places on the earth.

The GPS receiver gets a signal from each GPS satellite:

The satellites transmit the exact time the signals are sent.  By subtracting the time the signal was transmitted from the time it was received, the GPS can tell how far it is from each satellite. The GPS receiver also knows the exact position in the sky of the satellites, at the moment they sent their signals. So given the travel time of the GPS signals from three satellites and their exact position in the sky, the GPS receiver can determine your position in three dimensions – east, north and altitude.

There is a complication. To calculate the time the GPS signals took to arrive, the GPS receiver needs to know the time very accurately. The GPS satellites have atomic clocks that keep very precise time in their free-fall frame of reference, but it’s not feasible to equip a GPS receiver with an atomic clock on Earth.   Even if it was, corrections for a change of frame of reference would be necessary.   However, if the GPS receiver uses the signal from a fourth satellite it can solve an equation that lets it determine the exact time, without needing an atomic clock.

If the GPS receiver is only able to get signals from 3 satellites, you can still get your position, but it will be less accurate. As we noted above, the GPS receiver needs 4 satellites to work out your position in 3-dimensions. If only 3 satellites are available, the GPS receiver can get an approximate position by making the assumption that you are at mean sea level. If you really are at mean sea level, the position will be reasonably accurate. However if you are in the mountains, the 2-D fix could be hundreds of  feet off.

A modern GPS receiver will typically track all of the available satellites simultaneously, but only a selection of them will be used to calculate your position.


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