The Combined Study of Relativity

We need a new approach, a new beginning- not more education – on Spacetime, Gravity and Relativity.

As a Combined Study of  Relativity and Gravity. 

And here’s why…

So many assumptions stand in our way when we head from a co-ordinate system, whether a Cartesian- or Riemann-space co-ordinate system, to gravitation without co-ordinates.  So many routines about education.  So many topics of curricula that every instructor at whatever level of physics education must meet in a specific, formal, disciplined order.   We have grown accustomed to a certain route; a certain viewpoint; an easy viewpoint; a comfortable viewpoint.

Like gravitational “waves”,  although we do not go out and measure a “wave” height with a yardstick [this was discussed in a much early series of posts, here].  What is measured is a unique gravity signature or spacetime fluctuation of a laser beam.

It is real, but it is as much a leap to judge this fluctuation a “wave”  as to judge “dark matter” as “matter,” simply because its signature is the presence of more gravity where no visible matter exists.

Let’s begin with Dr. Neil Degrasse Tyson on Dark “Matter”…  

Data Without Assumptions’

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

“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

I relish the fact that NASA’s recent Magnetospheric Multiscale (MMS) probes have been able to “fix” their positions 12 times at ~100,000 miles into the interlunar space between Earth and The Moon from the GPS constellation encircling Earth.

This specific feat is extremely plausible.  There is no other massive object near NASA’s MMS probes, so why not?  Free-fall into a natural world-line with the MMS probes is nearly the same as free-fall into a natural world-line with the International Space Station (ISS).

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 hoped this bravado and administrative ignorance had left NASA. Apparently it hasn’t.  Prof. Dr. Richard Feynman warned about administrative and “bureaucratic justification,” like the now-infamous “60 Space Shuttle Missions a year,” claim when NASA has never had a year in which 60 launches were performed of the Space Shuttles…


“At the first apogee after the maneuvers, MMS 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…”


NASA reports only 4 GPS satellites were necessary to fix the probes’ positions precisely in free-fall spacetime, just like on the surface of the Earth (which is anything, but free-fall spacetime for the object.)

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

First, FIVE (5) GPS satellites are needed to determine their position precisely, not four.  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.

It is an assumption, not stated.  Fatal if not understood.

Second, it works as there are no other 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 us 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.

Screen Shot 2019-04-09 at 11.52.30 AM

I believe if you don’t have a better idea than that proposed by authorities (e.g., NASA “engineers” in this case) , you should be honest with it anyway.  And just say,  “This is not a better idea, but your idea will possibly destroy billions of tax-payer dollars or maybe even hurt someone.”

In this particular case, I think I have a far better idea than relying on the GPS for position of space probes and The Gateway Space Station orbiting The Moon.

Let’s do a simple, back-of-the-envelop calculation in one-dimension (1D) to show the enormity of the problem…

Ge is Earth’s general relativity time correction of 45,900 nanosecond and Se is the GPS satellite’s special relativity time correction of -7,200 nanoseconds slower for speeding around Earth.

Ge – Se = corrected time of +38,700 nanoseconds

As a result, the atomic cesium clocks on each GPS satellite are set to run at +38,700 nanoseconds faster than similar ones on Earth. This time correction compensates for “the effect” of Combined Relativity.

Now, to receive a an accurate and precise time and position near the lunar surface, we need to do these calculations…

The earth’s mass is = E =  597.2 × 1022 kg

The Moon’s mass is = M = 7.34767309 × 1022 kg

It is from the proximity of this massive object, Earth, that general relativity can be thought to function for us and our frame of reference, as opposed to the GPS satellites.

Earth is 81.28 times more massive than The Moon  (E/M = 81.28)

In this one-dimensional, straight-line approach we can see there will be different time-delays involved with Moon orbit.

As we have just shown above, For Earth and near-Earth orbit…

Se = 7,200 ns slower

Ge= 45,900 ns faster

Delay T = +38,700 ns faster on GPS, so the GPS atomic cesium clocks are set faster by this amount. On Earth we see no difference.

In Lunar orbit or near the Lunar surface, both Delay times are different

Gm =  Moon’s general relativity time correction  = 45,900 ns/81.28 = +565 ns

Sm = GPS satellite’s special relativity time correction as seen from The Moon = TBA

Delay T = +[(38,700 ns + Gm) – Sm] =  from at least  +6,635 ns  to  -6,635 ns

Their is a sometimes a sign change in time delay.  Again, this is only a simple one-dimensional straight-line representation of the tensor, guv –  the Metric Tensor – or simply “The Metric”, which holds all info on spacetime and mass variation, curvature, and separates for us, future from past.

In ALL four-dimensional calculations of the tensor, it may have both positive and negative reversals.

My better idea is to solve the 4-D Metric numerically, taking into account all topology on the lunar surface, and any known assymmtries under the surface, BEFORE making any pronouncement on how we can use GPS all the way into Lunar orbit.  Or just have a separate LPS (Lunar Positioning System) in orbit around the Moon.  Peace Out.


*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.

Leave a Reply

Please log in using one of these methods to post your comment: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s