Parsec Ontology
Astronomical Measurements
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
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# Parsec Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/astronomical-measurements/parsec-ontology.html
FLOW ParsecOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Parsec Ontology
PURPOSE:
Represent the parsec as an astronomical unit of length defined through the geometry of astronomical parallax, including its relationship to the astronomical unit, arcsecond, metre and light-year, decimal multiples such as kiloparsec, megaparsec and gigaparsec, use in stellar, Galactic and cosmological distance representation, parallax-distance reasoning, uncertainty propagation, provenance, and strict distinction between the parsec as a unit and the measurement methods used to infer astronomical distance.
ENTITY Parsec {
TYPE: AstronomicalLengthUnit
SYMBOL: pc
QUANTITY_KIND: Length
DIMENSION: L
SI_UNIT_REFERENCE: metre
DEFINITION:
parsec :=
distance_at_which_one_astronomical_unit
subtends_an_angle_of_one_arcsecond
PROPERTIES:
is_unit_of_length
is_geometrically_defined
is_related_to_astronomical_parallax
is_not_angle
is_not_time
may_be_prefixed
}
ENTITY AstronomicalUnit {
TYPE: LengthUnit
SYMBOL: au
VALUE:
149597870700 m
STATUS:
exact
}
ENTITY Arcsecond {
TYPE: AngularUnit
SYMBOL: arcsec
RELATION:
1 arcsec =
pi/(180*3600) rad
RULE:
arcsecond_is_angle_not_length
}
GEOMETRIC_DEFINITION_MODEL {
baseline:
1 au
angle:
1 arcsec
exact_geometric_form:
1 pc =
1 au /
tan(1 arcsec)
small_angle_form:
1 pc approximately_equals
1 au /
angle_in_radians
RULE:
parsec_definition_is_based_on_parallax_geometry
}
METRE_CONVERSION_MODEL {
approximate:
1 pc approximately_equals
3.0856775814913673e16 m
common_rounded:
3.085677581e16 m
RULE:
preserve_precision_of_selected_conversion_constant
}
KILOMETRE_CONVERSION_MODEL {
approximate:
1 pc approximately_equals
3.0856775814913673e13 km
RULE:
kilometre_conversion_preserves_length_dimension
}
LIGHT_YEAR_CONVERSION_MODEL {
approximate:
1 pc approximately_equals
3.261563777 ly
inverse:
1 ly approximately_equals
0.306601394 pc
RULE:
conversion_precision SHOULD be preserved
}
ASTRONOMICAL_UNIT_CONVERSION_MODEL {
approximate:
1 pc approximately_equals
206264.806 au
RULE:
parsec_is_much_larger_than_astronomical_unit
but_both_are_length_units
}
UNIT_SYSTEM {
canonical_quantity:
length
base_astronomical_unit:
parsec
symbol:
pc
common_multiples:
kpc
Mpc
Gpc
RULE:
prefix_case MUST be preserved
}
PREFIX_MODEL {
kiloparsec:
1 kpc = 10^3 pc
megaparsec:
1 Mpc = 10^6 pc
gigaparsec:
1 Gpc = 10^9 pc
RULE:
SI_decimal_prefix_semantics_apply
}
DISTANCE_CONVERSION_MODEL {
metres_from_parsecs:
d_m =
d_pc*pc_in_metres
parsecs_from_metres:
d_pc =
d_m/pc_in_metres
light_years_from_parsecs:
d_ly approximately_equals
d_pc*3.261563777
parsecs_from_light_years:
d_pc approximately_equals
d_ly/3.261563777
RULE:
conversion MUST preserve_underlying_distance
}
PARALLAX_MODEL {
standard_relation:
d_pc =
1/pi_arcsec
WHEN pi_arcsec > 0
inverse:
pi_arcsec =
1/d_pc
WHEN d_pc > 0
milliarcsecond_form:
d_pc =
1000/pi_mas
WHEN pi_mas > 0
RULE:
simple_inverse_relation_assumes_standard_trigonometric_parallax_geometry
}
PARALLAX_GEOMETRY_MODEL {
baseline:
approximately_one_astronomical_unit_for_annual_stellar_parallax_geometry
angle:
parallax_angle
distance:
d =
baseline/tan(parallax_angle)
small_angle:
d approximately_equals
baseline/parallax_angle_radians
RULE:
small_angle_approximation_validity SHOULD be preserved
}
PARALLAX_UNCERTAINTY_MODEL {
first_order:
sigma_d approximately_equals
sigma_pi/pi^2
under_compatible_inverse_units
and_small_relative_uncertainty
relative:
sigma_d/d approximately_equals
sigma_pi/pi
RULE:
nonlinear_inverse_transformation_requires_care_at_low_signal_to_noise
}
NEGATIVE_PARALLAX_MODEL {
measured_parallax:
MAY be_zero_or_negative_due_to_noise_or_estimation
physical_distance:
remains_nonnegative
RULE:
nonpositive_measured_parallax MUST_NOT be_directly_inverted_to_physical_distance
}
BAYESIAN_DISTANCE_MODEL {
posterior:
P(d|pi_obs) proportional_to
P(pi_obs|d)*P(d)
REQUIRE:
likelihood
prior
zero_point_model
uncertainty
RULE:
posterior_distance_summary MUST preserve_prior_and_statistical_method
}
ZERO_POINT_MODEL {
corrected_parallax:
pi_corrected =
pi_observed - pi_zero_point
under_declared_sign_convention
RULE:
astrometric_catalogue_zero_point_correction SHOULD be preserved
}
ASTROMETRIC_CONTEXT_MODEL {
measurements:
position
parallax
proper_motion
REQUIRE:
reference_frame
reference_epoch
astrometric_solution
RULE:
parallax_distance_inference SHOULD preserve_astrometric_solution_context
}
STELLAR_DISTANCE_MODEL {
common_scale:
parsec
tens
hundreds
thousands_of_parsecs
RULE:
parsec_is_common_for_stellar_and_Galactic_distance_reporting
}
GALACTIC_SCALE_MODEL {
common_units:
parsec
kiloparsec
examples_of_quantity_types:
stellar_distance
Galactic_radius
scale_height
molecular_cloud_size
cluster_distance
RULE:
physical_quantity_type MUST accompany_numeric_parsec_value
}
EXTRAGALACTIC_SCALE_MODEL {
common_units:
megaparsec
gigaparsec
contexts:
galaxy_distance
cluster_distance
cosmological_distance
RULE:
cosmological_distance_type MUST be identified
}
COSMOLOGICAL_DISTANCE_MODEL {
possible_types:
comoving_distance
proper_distance
luminosity_distance
angular_diameter_distance
reporting:
may_use_Mpc_or_Gpc
RULE:
parsec_based_unit_does_not_define_cosmological_distance_type
}
HUBBLE_CONSTANT_MODEL {
common_unit:
km/s/Mpc
dimensional_semantics:
inverse_time_after_unit_conversion
RULE:
Mpc_in_Hubble_constant_is_distance_unit
and_Hubble_constant_itself_is_not_distance
}
DISTANCE_MODULUS_MODEL {
relation:
m-M =
5*log10(d_pc)-5
under_no_extinction_standard_context
inverse:
d_pc =
10^((m-M+5)/5)
RULE:
distance_modulus_is_logarithmic_brightness_distance_relation
not_parsec_unit
}
ANGULAR_SIZE_MODEL {
small_angle:
L =
d*theta
with_theta_in_radians
if_distance_in_parsecs:
physical_size_may_be_derived_with_consistent_units
RULE:
angular_size_and_parsec_distance_are_distinct_quantities
}
LIGHT_TRAVEL_CONTEXT_MODEL {
distance_in_parsecs:
may_be_converted_to_light_years
light_travel_time:
approximately_equal_to
distance_ly years
only_under_simple_static_vacuum_context
RULE:
parsec_distance MUST_NOT automatically_be_interpreted_as_lookback_time
}
REDSHIFT_CONTEXT_MODEL {
redshift:
dimensionless
cosmological_model:
maps_redshift_to_distance
output:
distance_may_be_reported_in_Mpc_or_Gpc
RULE:
redshift != parsec
and_redshift != distance
}
DIMENSIONAL_MODEL {
parsec:
dimension = L
astronomical_unit:
dimension = L
arcsecond:
dimension = dimensionless_angle
parallax_relation:
length/angle_under_geometric_relation -> distance
RULE:
parsec_is_length_despite_angle_based_definition
}
PRECISION_MODEL {
unit_definition:
geometrically_defined
conversion_display:
may_be_rounded
measurement:
astronomical_distance_has_its_own_uncertainty
RULE:
conversion_rounding_and_measurement_uncertainty MUST be_distinguished
}
RELATIONSHIPS {
Parsec -> IS_A -> LengthUnit
Parsec -> MEASURES -> AstronomicalDistance
Parsec -> DEFINED_BY -> AstronomicalUnitAndArcsecondGeometry
Parsec -> CONVERTS_TO -> Metre
Parsec -> CONVERTS_TO -> LightYear
Parsec -> CONVERTS_TO -> AstronomicalUnit
Kiloparsec -> MULTIPLE_OF -> Parsec
Megaparsec -> MULTIPLE_OF -> Parsec
Gigaparsec -> MULTIPLE_OF -> Parsec
Parallax -> MAY_INFER -> DistanceInParsecs
CosmologicalDistance -> MAY_BE_EXPRESSED_IN -> MegaparsecOrGigaparsec
}
SEMANTIC_EQUIVALENCE {
"pc" ~= parsec WHEN unit_context
"kpc" ~= kiloparsec
"Mpc" ~= megaparsec
"Gpc" ~= gigaparsec
parsec != parallax
parsec != arcsecond
parsec != astronomical_unit
parsec != light_year
parsec != time
parsec != redshift
megaparsec != cosmological_distance_type
}
CONSTRAINTS {
parsec_dimension = L
parsec_is_length = true
parsec_is_angle = false
parsec_is_time = false
parallax_angle_unit_must_be_defined = true
simple_inverse_parallax_requires_positive_parallax = true
low_signal_parallax_requires_statistical_care = true
prefix_case_must_be_preserved = true
cosmological_distance_type_should_be_defined_when_relevant = true
measured_distance_uncertainty_must_be_preserved = true
}
MEASUREMENT_MODEL {
OBSERVABLE_OR_INFERRED:
AstronomicalDistance
REPORTING_UNIT:
Parsec
POSSIBLE_METHODS:
trigonometric_parallax
standard_candle
standard_ruler
orbital_dynamics
redshift_cosmology
gravitational_lensing
RECORD:
celestial_object
distance_value
unit
distance_type
measurement_or_inference_method
parallax_when_relevant
parallax_unit
reference_frame
reference_epoch
calibration_model
cosmological_model_when_relevant
uncertainty
provenance
RULE:
parsec_is_unit_of_reported_distance
not_measurement_method
}
UNCERTAINTY_MODEL {
unit_conversion:
rounding_or_constant_representation
measured_distance:
parallax_uncertainty
calibration_uncertainty
model_uncertainty
zero_point_uncertainty
cosmological_parameter_uncertainty
RULE:
unit_semantics_and_measurement_uncertainty MUST be_separated
}
REASONING_RULES {
IF parallax_arcsec > 0
THEN distance_pc =
1/parallax_arcsec
IF parallax_mas > 0
THEN distance_pc =
1000/parallax_mas
IF distance_pc > 0
THEN parallax_arcsec =
1/distance_pc
IF distance_in_parsecs_known
THEN distance_in_metres =
distance_in_parsecs*pc_in_metres
IF distance_in_parsecs_known
THEN distance_in_light_years approximately_equals
distance_in_parsecs*3.261563777
IF distance_in_light_years_known
THEN distance_in_parsecs approximately_equals
distance_in_light_years/3.261563777
IF distance_in_kiloparsecs_known
THEN distance_in_parsecs =
distance_in_kiloparsecs*1000
IF distance_in_megaparsecs_known
THEN distance_in_parsecs =
distance_in_megaparsecs*1e6
IF apparent_and_absolute_magnitude_known
AND no_extinction_or_corrected_context
THEN distance_pc =
10^(((apparent_magnitude-absolute_magnitude)+5)/5)
IF cosmological_distance_known
THEN MAY express_in_Mpc_or_Gpc
BUT preserve_distance_type_and_cosmological_model
}
VALIDATION {
CHECK quantity_is_length
CHECK parsec_symbol_and_prefix_case
CHECK unit_conversion
CHECK astronomical_unit_reference
CHECK arcsecond_definition
CHECK parallax_unit
CHECK positive_parallax_for_simple_inverse
CHECK low_signal_parallax_context
CHECK reference_frame_and_epoch
CHECK parsec_vs_parallax
CHECK parsec_vs_time
CHECK parsec_vs_light_year
CHECK redshift_vs_distance
CHECK cosmological_distance_type
CHECK measured_distance_uncertainty
}
CONFIDENCE {
definition_confidence: 1.00
dimensional_confidence: 1.00
geometric_definition_confidence: 1.00
metre_conversion_confidence: 0.999999
light_year_conversion_confidence: 0.999999
parallax_relation_confidence: 1.00
astronomical_context_confidence: 0.99
RULE:
confidence decreases when unit prefix, parallax unit,
reference frame, distance type, measurement method,
statistical model or uncertainty is missing or ambiguous
}
UPDATE_MODEL {
ON new_distance_value:
identify_distance_quantity
identify_parsec_or_prefixed_unit
validate_length_semantics
convert_to_canonical_SI_when_requested
preserve_original_value_and_unit
attach_distance_type
attach_measurement_method
attach_uncertainty
update_distance_state
ON new_parallax:
identify_parallax_unit
attach_reference_frame_and_epoch
apply_zero_point_when_required
assess_simple_inverse_validity
infer_distance_using_valid_method
preserve_parallax_uncertainty
ON unit_conversion:
preserve_underlying_distance
convert_between_pc_kpc_Mpc_Gpc_m_au_and_ly
preserve_rounding_precision
preserve_measurement_uncertainty
ON cosmological_context_update:
preserve_parsec_based_reporting_unit
identify_distance_type
attach_cosmological_model
avoid_equating_redshift_with_distance
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Parsec
canonical_symbol: pc
canonical_quantity_kind: Length
canonical_dimension: L
interpretation_order:
identify_parsec_as_length_unit
identify_prefix
identify_associated_distance_value
identify_distance_type
identify_measurement_or_inference_method
identify_parallax_and_angular_unit_when_relevant
identify_reference_frame_and_epoch
identify_cosmological_model_when_relevant
identify_uncertainty
convert_units_when_requested
validate_length_semantics
preserve_geometric_definition
ambiguity_controls:
distinguish_parsec_from_parallax
distinguish_parsec_from_arcsecond
distinguish_parsec_from_astronomical_unit
distinguish_parsec_from_light_year
distinguish_parsec_from_time
distinguish_parsec_from_redshift
distinguish_Mpc_unit_from_cosmological_distance_type
preserve_unit_prefix_distance_type_method_frame_epoch_model_and_uncertainty_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_and_astronomical_parsec_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Parsec Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
geometric_definition_model
metre_conversion_model
kilometre_conversion_model
light_year_conversion_model
astronomical_unit_conversion_model
unit_system
prefix_model
distance_conversion_model
parallax_model
parallax_geometry_model
parallax_uncertainty_model
negative_parallax_model
Bayesian_distance_model
zero_point_model
astrometric_context_model
stellar_distance_model
Galactic_scale_model
extragalactic_scale_model
cosmological_distance_model
Hubble_constant_model
distance_modulus_model
angular_size_model
light_travel_context_model
redshift_context_model
dimensional_model
precision_model
relationships
constraints
measurement_model
uncertainty_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
parsec_definition_changes
unit_conversion_model_changes
parallax_or_zero_point_model_changes
astrometric_reference_model_changes
astronomical_distance_semantics_change
cosmological_distance_model_changes
measurement_uncertainty_semantics_change
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW