Lunar Plane
Coordinate System
Kenji MISHIMA ,Ph.D.

Typical Coordinate Systems
In the case of the earth, a typical Coordinate System
is following three coordinate systems.
(1) 3-Dimensional Coordinate System
The Cartesian Coordinate System with the directionof the north pole of rotation axis as the Z axis.

(2) Latitude and Longitude
Latitude and Longitude on the ellipsoid.
(3) Plane Coordinate System
The coordinate system of projection
for the spherical surface into plane.

Lunar 3-D Coodinate System

The 3 Dimensional Coordinate System,
Including the moon,
have already been determinedbythe International Astronomical Union ( IAU ).

Lunar 3-D Coordinate System

Lunar 3-D Coordinate System

The 3 Dimensional Coordinate System,
for the Moon and Earth polar axis (ME)system is recommended.

Lunar 3-D Coordinate System

Parameter for
dwarf planets,
minor planets,
their satellites,
andComet
have already been determined.

Lunar Latitude and Longitude

The latitude and longitude of the lunar
coordinate system has been
determined by NASA

Lunar Latitude and Longitude
The prime meridian (longitude 0) is the center visible from Earth.

The latitude and longitude of the lunar
coordinate system has been
determined by NASA

Plane Coordinate System
The 3 Dimensional and Latitude and Longitude
coordinate system has already been determined,
but there is no Planar Coordinate System.
The 3 D coordinate system is difficult to use on the lunar
surface, and the latitude and longitude coordinate
system is difficult to use because its units are angles
It is more efficient to carry out building layout
and infrastructure maintenanceon the moon in metricNecessity of the plane coordinate system
When developing infrastructure on the moon,
it is planned and designed on a flat surface using CAD
In cases such as complex plant construction,high layout accuracy is required.

Construction is difficult in latitude and longitude,
therefore, construction is required in metric

Planar coordinate system needs to be preparedProblems when projecting
a spherical surface onto a plane
Meridian passing through the Greenwich Observatory
Prime meridian (longitude 0°)

Problems when projecting
a spherical surface onto a plane
Meridian passing through the Greenwich Observatory
Prime meridian (longitude 0°)

equatorProblems when projecting
a spherical surface onto a plane
Meridian passing through the Greenwich Observatory
Prime meridian (longitude 0°)

longitude 90°

equatorsum of interior angles of this triangle = 270°（ ≠180°）

Problems when projecting
a spherical surface onto a plane
Moon is an ellipsoid
The shapes on the lunar surface are on a curved surface

When a figure on a spherical surface is projected onto the plane,
Angle
DistanceAreacannot be projected correctly.
Euclidean geometry does not hold.

Mercator’s Projection &Transversal Mercator’s Projection
The UTM coordinate system is commonly used
as a globally used coordinate system.

( UTM : Universal Transversal Mercator )The Mercator’s projection
distorts the polar regions.

Antarctica

Next sheet

Transversal Mercator Projection
In the case of Earth :Reconsidering the width of each Zone

Reconsidering the Origin Coordinate Values
The origin coordinates are not zeroand are biased to avoid negative coordinates.

Transversal Mercator Projection
In the case of Earth :Reconsidering the width of each Zone

Universal Transversal Mercatoron the Earth
In the case of Earth :Earth’s major axis :, flattening facor :Latitude and Longitude, central meridian :is calculatedby the following formula.

Reconsidering
the parameters of the formula for converting
latitude and longitude to plane coordinates.

[ km ] ,[ km ]

Universal Transversal Mercatoron the Earth
In the case of Earth :Scale factor :Reconsidering
the parameters of the formula for computing
the Scale factor and the Meridian convergence.
Meridian convergence :UPS Coordinate System
Universal Polar Stereographic ( UPS )projection is a map projection method
for the area around the North Pole andthe South Pole,and is a plane coordinate system.
Combined with theUniversal Transverse Mercator ( UTM )projection,
it covers the entire earth surface.

UPS Coordinate SystemTargets areas north of 84°N
and south of 80°S.

In order to connect
with the target areaof ​the UTM projection,
it is assumed
that it will extend
outward by 0.5°.

UPS Coordinate System
Scale factor :On Earth, the polar regions are rarely used,
so the accuracy of the scale factor is not important.
However, the moon is planned to be usedin the south polar region.
Research optimal coefficients and parameters.

Issue of Planar coordinate systemon the moonIssue of Planar coordinate systemon the moonIssue of Planar coordinate systemon the moon
Width of Zone

Origin Factor

New Coordinate System
If the parameters of both UTM & UPS
coordinate systems are found to beinappropriate,
considering a new optimalplane coordinate system.

More detailed proposals
will be made up
at the next meeting

Thank you for your attention