Astronomical Distance Ontology
Astronomical Measurements
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
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# Astronomical Distance Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/astronomical-measurements/astronomical-distance-ontology.html
FLOW AstronomicalDistanceOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Astronomical Distance Ontology
PURPOSE:
Represent astronomical distance as a family of length and model-dependent distance quantities between an observer, reference origin and celestial object, including astronomical units, light-years and parsecs, trigonometric parallax, standard candles, standard rulers, distance modulus, radar ranging, light-travel distance, orbital and dynamical inference, luminosity distance, angular-diameter distance, comoving distance, proper distance, cosmological redshift-distance relations, calibration, uncertainty, provenance, and strict distinction between directly measured geometric distances and model-dependent inferred distances.
ENTITY AstronomicalDistance {
TYPE: AstronomicalLengthQuantity
SYMBOL: d
DIMENSION: L
SI_UNIT: metre
SI_SYMBOL: m
DEFINITION:
astronomical_distance :=
separation_between_declared_reference_origin_and_celestial_object
under_declared_geometric_or_cosmological_distance_definition
PROPERTIES:
is_nonnegative
has_reference_origin
has_distance_type
may_be_geometric
may_be_inferred
may_be_model_dependent
may_depend_on_epoch
may_have_uncertainty
}
ENTITY AstronomicalUnit {
TYPE: LengthUnit
SYMBOL: au
DEFINITION:
exact_SI_length_defined_for_astronomical_use
VALUE:
149597870700 metre
}
ENTITY LightYear {
TYPE: LengthUnit
SYMBOL: ly
DEFINITION:
distance_light_travels_in_vacuum_during_one_Julian_year
APPROXIMATE_VALUE:
9.4607304725808e15 metre
}
ENTITY Parsec {
TYPE: LengthUnit
SYMBOL: pc
DEFINITION:
distance_corresponding_to_parallax_of_one_arcsecond
under_standard_geometric_definition
APPROXIMATE_VALUE:
3.085677581e16 metre
}
UNIT_SYSTEM {
SI:
metre
common_astronomical:
astronomical_unit
light_year
parsec
kiloparsec
megaparsec
gigaparsec
conversions:
1 au = 149597870700 m
1 kpc = 1000 pc
1 Mpc = 1e6 pc
1 Gpc = 1e9 pc
RULE:
preserve_original_unit_and_normalized_length_when_valid
}
REFERENCE_ORIGIN_MODEL {
possible_origins:
observer
geocentre
Earth_surface_observatory
barycentre
heliocentre
Solar_System_barycentre
galaxy_centre
cosmological_observer
RULE:
distance_without_reference_origin MAY be semantically_incomplete
}
DISTANCE_TYPE_MODEL {
possible_types:
geometric_distance
range
light_travel_distance
parallax_distance
photometric_distance
spectroscopic_distance
luminosity_distance
angular_diameter_distance
comoving_distance
proper_distance
orbital_distance
RULE:
distance_type MUST be identified_before_cross_method_comparison
}
EUCLIDEAN_DISTANCE_MODEL {
Cartesian:
d =
sqrt(
(x_2-x_1)^2
+ (y_2-y_1)^2
+ (z_2-z_1)^2
)
REQUIRE:
common_coordinate_frame
compatible_epoch
Euclidean_geometry_context
RULE:
cosmological_distances MAY require_non_Euclidean_spacetime_model
}
PARALLAX_MODEL {
parallax_angle:
pi
standard_relation:
d_pc =
1/pi_arcsec
WHEN pi_arcsec > 0
equivalent:
d =
baseline/tan(pi)
under_declared_geometry
RULE:
parallax_distance_is_geometric_but_inverse_transformation_of_noisy_parallax_can_be_statistically_nontrivial
}
PARALLAX_UNCERTAINTY_MODEL {
first_order:
sigma_d approximately_equals
sigma_pi/pi^2
in_consistent_inverse_units
for_small_relative_parallax_uncertainty
RULE:
simple_inverse_parallax_uncertainty_is_inadequate_for_low_signal_to_noise_or_nonpositive_measured_parallax
}
BAYESIAN_DISTANCE_MODEL {
posterior:
P(d|pi_obs) proportional_to
P(pi_obs|d)*P(d)
REQUIRE:
parallax_likelihood
prior
zero_point_model_when_relevant
RULE:
Bayesian_distance_estimate MUST preserve_prior_and_summary_statistic
}
PARALLAX_ZERO_POINT_MODEL {
corrected_parallax:
pi_corrected =
pi_observed - pi_zero_point
under_declared_sign_convention
RULE:
zero_point_model_version_and_dependencies MUST be preserved
}
RADAR_RANGING_MODEL {
two_way_light_time:
delta_t
geometric_range:
d =
c*delta_t/2
REQUIRE:
timing_reference
propagation_corrections
target_motion
observer_motion
RULE:
radar_range_requires_light_time_and_ephemeris_correction_for_precision
}
LASER_RANGING_MODEL {
two_way_time:
delta_t
range:
d =
c*delta_t/2
after_declared_atmospheric_and_relativistic_corrections
RULE:
raw_round_trip_time != corrected_range
}
LIGHT_TRAVEL_DISTANCE_MODEL {
simple_static:
d_light =
c*delta_t
RULE:
light_travel_distance != present_proper_distance_in_expanding_cosmology
}
DISTANCE_MODULUS_MODEL {
no_extinction:
mu =
m-M =
5*log10(d_pc)-5
inverse:
d_pc =
10^((mu+5)/5)
extinction_adjusted:
m-M =
5*log10(d_pc)-5+A_band
RULE:
apparent_and_absolute_magnitude_systems_and_extinction MUST be compatible
}
STANDARD_CANDLE_MODEL {
principle:
infer_distance_from_known_or_calibrated_intrinsic_luminosity
flux_relation:
F =
L/(4*pi*d^2)
under_applicable_geometry
inferred_distance:
d =
sqrt(L/(4*pi*F))
possible_objects:
Cepheid_variable
RR_Lyrae
Type_Ia_supernova
other_calibrated_luminosity_indicator
RULE:
luminosity_calibration_extinction_and_population_effects MUST be preserved
}
CEPHEID_MODEL {
period_luminosity_relation:
absolute_magnitude =
f(log_period, band, metallicity, calibration)
distance:
inferred_through_distance_modulus
RULE:
period_luminosity_calibration_and_bandpass MUST be preserved
}
SUPERNOVA_DISTANCE_MODEL {
Type_Ia:
standardisable_candle
standardisation:
corrected_luminosity =
f(light_curve_shape, colour, calibration)
RULE:
standardisation_model_and_cosmological_corrections MUST be preserved
}
STANDARD_RULER_MODEL {
known_or_modelled_physical_size:
L
observed_angular_size:
theta
small_angle:
d_A approximately_equals
L/theta_radians
RULE:
standard_ruler_in_cosmology_infers_angular_diameter_distance
}
SPECTROSCOPIC_DISTANCE_MODEL {
method:
infer_intrinsic_luminosity_or_absolute_magnitude_from_spectral_properties
then_compare_with_observed_brightness
RULE:
spectroscopic_distance_is_model_dependent
}
MAIN_SEQUENCE_FITTING_MODEL {
method:
compare_cluster_colour_magnitude_sequence
with_calibrated_reference_sequence
dependencies:
metallicity
extinction
photometric calibration
RULE:
fitted_distance_requires_population_and_extinction_model
}
ORBITAL_DISTANCE_MODEL {
possible_methods:
orbital_dynamics
Keplerian_geometry
ephemeris fitting
RULE:
orbital_distance_is_time_dependent_and_requires_epoch
}
DYNAMICAL_DISTANCE_MODEL {
possible_relations:
proper_motion_plus_radial_velocity
orbital_motion
expansion_parallax
RULE:
dynamical_distance_requires_motion_model_and_geometry
}
EXPANSION_PARALLAX_MODEL {
physical_expansion_speed:
v_exp
angular_expansion_rate:
mu_exp
distance:
d =
v_exp/mu_exp
with_compatible_angular_units
RULE:
geometric_projection_and_pattern_vs_material_speed MUST be considered
}
REDSHIFT_MODEL {
z =
(lambda_obs-lambda_rest)/lambda_rest
RULE:
redshift_is_observable_related_to_distance_through_cosmological_model
not_distance_itself
}
HUBBLE_LOW_Z_MODEL {
approximation:
v approximately_equals
H_0*d
redshift:
v approximately_equals c*z
only_at_low_z
combined:
d approximately_equals
c*z/H_0
RULE:
low_redshift_Hubble_relation MUST NOT be extrapolated_without_cosmological_model
}
COSMOLOGICAL_MODEL {
parameters:
H_0
Omega_m
Omega_r
Omega_k
Omega_Lambda
dark_energy_model_when_relevant
expansion:
H(z)
RULE:
cosmological_distance_values depend_on_adopted_cosmological_parameters
}
COMOVING_DISTANCE_MODEL {
line_of_sight:
D_C =
c*integral_0^z(dz_prime/H(z_prime))
RULE:
comoving_distance_preserves_expansion_factored_coordinate_separation
under_declared_cosmology
}
TRANSVERSE_COMOVING_DISTANCE_MODEL {
D_M:
curvature_dependent_function_of_D_C
flat_universe:
D_M = D_C
RULE:
curvature_model MUST be preserved
}
ANGULAR_DIAMETER_DISTANCE_MODEL {
D_A =
physical_transverse_size/angular_size_radians
cosmological_relation:
D_A =
D_M/(1+z)
RULE:
angular_diameter_distance != luminosity_distance
}
LUMINOSITY_DISTANCE_MODEL {
definition:
F =
L/(4*pi*D_L^2)
cosmological_relation:
D_L =
(1+z)*D_M
reciprocity:
D_L =
(1+z)^2*D_A
under_standard_distance_duality_conditions
RULE:
luminosity_distance_is_defined_through_flux_luminosity_relation
}
PROPER_DISTANCE_MODEL {
definition:
spatial_separation_at_declared_cosmic_time
under_declared_cosmological slicing
RULE:
proper_distance_is_epoch_dependent
}
LOOKBACK_TIME_MODEL {
lookback_time:
t_L =
integral_0^z(
dz_prime/
((1+z_prime)*H(z_prime))
)
RULE:
lookback_time_is_time_quantity_not_distance
}
DISTANCE_LADDER_MODEL {
stages:
geometric_calibration
parallax
variable_stars
standard_candles
supernovae
cosmological_distance_scale
RULE:
each_rung_inherits_calibration_and_uncertainty_from_previous_rungs
}
EXTINCTION_MODEL {
observed_magnitude:
m_obs =
m_intrinsic_effective + A_band
corrected:
m_corrected =
m_obs-A_band
RULE:
extinction_and_reddening_model MUST be preserved_for_photometric_distance
}
K_CORRECTION_MODEL {
purpose:
account_for_redshifted_spectrum_relative_to_observer_and_rest_frame_bandpasses
RULE:
high_redshift_photometric_distance_inference MAY require_K_correction
}
LENSING_MODEL {
gravitational_lensing:
alters_observed_flux_and_apparent_geometry
possible_distance_combinations:
observer_lens
observer_source
lens_source
RULE:
lensing_distance_inference_requires_lens_model_and_cosmology
}
ANGULAR_SCALE_MODEL {
physical_scale_per_angle:
S =
D_A*theta
common:
kpc_per_arcsec
RULE:
angular_scale_depends_on_angular_diameter_distance
}
REFERENCE_FRAME_MODEL {
possible_origins:
topocentric
geocentric
heliocentric
barycentric
RULE:
nearby_object_range_and_position MAY require_reference_origin_and_light_time_correction
}
TEMPORAL_MODEL {
distance_may_change_due_to:
orbital_motion
proper_motion
radial_motion
cosmic_expansion
RULE:
distance_epoch SHOULD be preserved_when_change_is_material
}
RELATIONSHIPS {
AstronomicalDistance -> HAS_DIMENSION -> Length
AstronomicalDistance -> REFERENCED_TO -> OriginOrObserver
Parallax -> MAY_INFER -> GeometricDistance
RadarLightTime -> MAY_INFER -> Range
StandardCandle -> MAY_INFER -> LuminosityDistance
StandardRuler -> MAY_INFER -> AngularDiameterDistance
DistanceModulus -> RELATES -> ApparentAbsoluteMagnitudeAndDistance
Redshift -> MAPS_TO -> CosmologicalDistanceThroughModel
CosmologicalModel -> DETERMINES -> DistanceRedshiftRelation
LuminosityDistance -> RELATES -> FluxAndLuminosity
AngularDiameterDistance -> RELATES -> AngularAndPhysicalSize
DistanceLadder -> PROPAGATES -> CalibrationAndUncertainty
}
SEMANTIC_EQUIVALENCE {
"astronomical distance" ~= celestial_distance WHEN distance_type_defined
"parallax distance" ~= inverse_parallax_geometric_distance_under_valid_context
parallax != distance
redshift != distance
light_travel_time != distance_without_model
luminosity_distance != angular_diameter_distance
comoving_distance != proper_distance
lookback_time != distance
apparent_magnitude != distance_modulus
physical_size != angular_size
}
CONSTRAINTS {
astronomical_distance_dimension = L
reference_origin_should_be_defined = true
distance_type_must_be_defined = true
parallax_inverse_requires_positive_parallax_for_simple_direct_use = true
low_signal_parallax_requires_statistical_model = true
photometric_distance_requires_calibration_and_extinction_context = true
cosmological_distance_requires_cosmological_model = true
luminosity_and_angular_diameter_distance_are_not_semantically_equivalent = true
distance_epoch_should_be_preserved_when_time_dependence_is_material = true
uncertainty_should_include_measurement_calibration_and_model_components = true
}
MEASUREMENT_MODEL {
OBSERVABLE_OR_INFERRED:
AstronomicalDistance
GeometricDistance
ParallaxDistance
LuminosityDistance
AngularDiameterDistance
ComovingDistance
ProperDistance
COMMON_METHODS:
radar_ranging
laser_ranging
trigonometric_parallax
orbital_dynamics
standard_candle
standard_ruler
main_sequence_fitting
spectroscopic_distance
redshift_cosmology
gravitational_lensing
RECORD:
celestial_object
object_identifier
distance_value
unit
distance_type
reference_origin
coordinate_frame
observation_epoch
parallax_and_uncertainty
apparent_magnitude
absolute_magnitude_or_luminosity
photometric_band
extinction
redshift
cosmological_parameters
standard_candle_or_ruler_model
calibration_source
inference_method
processing_version
quality_flag
uncertainty
provenance
UNCERTAINTY:
measured_or_inferred_astronomical_distance =
best_estimate +/- uncertainty
}
UNCERTAINTY_MODEL {
sources:
parallax
parallax_zero_point
timing
baseline
flux
photometric_zero_point
extinction
intrinsic_luminosity_calibration
population_model
redshift
peculiar_velocity
cosmological_parameters
lensing
model_selection
calibration_ladder
PROPAGATION:
astronomical_distance_uncertainty
<- observational_calibration_statistical_and_model_uncertainties
}
REASONING_RULES {
IF parallax_arcsec > 0
AND simple_inverse_parallax_valid
THEN distance_pc =
1/parallax_arcsec
IF radar_round_trip_time_known
THEN geometric_range =
c*round_trip_time/2
after_required_propagation_and_motion_corrections
IF apparent_and_absolute_magnitude_known
AND extinction_known_or_zero_by_assumption
THEN distance_modulus =
apparent_magnitude-absolute_magnitude-extinction
IF distance_modulus_known
THEN distance_pc =
10^((distance_modulus+5)/5)
IF luminosity_and_flux_known
AND flux > 0
THEN luminosity_distance =
sqrt(luminosity/(4*pi*flux))
IF physical_transverse_size_and_angular_size_radians_known
AND angular_size != 0
THEN angular_diameter_distance =
physical_transverse_size/angular_size
IF redshift_and_cosmological_model_known
THEN compute_comoving_luminosity_and_angular_diameter_distances
using_declared_cosmology
IF D_A_and_redshift_known
THEN D_L =
(1+redshift)^2*D_A
under_standard_distance_duality_conditions
IF proper_motion_and_tangential_speed_model_known
THEN MAY infer_dynamical_distance
under_declared_geometry
}
VALIDATION {
CHECK celestial_object_identity
CHECK length_unit
CHECK distance_type
CHECK reference_origin
CHECK coordinate_frame
CHECK observation_epoch
CHECK parallax_value_and_uncertainty
CHECK simple_inverse_parallax_validity
CHECK distance_modulus_definition
CHECK photometric_band_and_extinction
CHECK standard_candle_or_ruler_calibration
CHECK redshift_vs_distance
CHECK cosmological_model_and_parameters
CHECK luminosity_vs_angular_diameter_distance
CHECK comoving_vs_proper_distance
CHECK lookback_time_vs_distance
CHECK calibration_source
CHECK quality_flag
CHECK uncertainty_representation
}
CONFIDENCE {
definition_confidence: 1.00
dimensional_confidence: 1.00
geometric_ranging_confidence: 1.00
parallax_relationship_confidence: 1.00
distance_modulus_confidence: 0.99
standard_candle_confidence: 0.97
cosmological_distance_confidence: 0.96
measurement_context_confidence: 0.98
RULE:
confidence decreases when distance type, origin, parallax quality,
extinction, calibration, cosmological parameters,
model assumptions or uncertainty is missing or ambiguous
}
UPDATE_MODEL {
ON new_distance_measurement:
identify_celestial_object
identify_distance_type
validate_unit
attach_reference_origin_and_frame
attach_observation_epoch
identify_measurement_or_inference_method
preserve_raw_observables
attach_calibration_and_model
compute_distance_when_valid
attach_quality_flag
attach_uncertainty
update_distance_state
ON parallax_revision:
preserve_raw_astrometric_solution
update_parallax_and_zero_point_model
select_valid_distance_inference_method
recompute_distance_posterior_or_estimate
update_uncertainty
ON photometric_calibration_revision:
preserve_observed_photometry
update_zero_point_extinction_or_standard_candle_calibration
recompute_distance_modulus_and_distance
update_uncertainty
ON cosmology_revision:
preserve_redshift
preserve_previous_cosmological_parameters
recompute_comoving_luminosity_angular_diameter_and_proper_distances
update_provenance_and_uncertainty
ON epoch_revision:
preserve_previous_distance
update_orbital_motion_or_kinematic_model
recompute_time_dependent_range_when_required
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: AstronomicalDistance
canonical_symbol: d
canonical_dimension: L
canonical_SI_unit: metre
interpretation_order:
identify_celestial_object
identify_distance_value_and_unit
identify_distance_type
identify_reference_origin
identify_coordinate_frame_and_epoch
identify_geometric_parallax_photometric_dynamical_or_cosmological_method
identify_raw_observables
identify_calibration
identify_extinction_when_photometric
identify_redshift_and_cosmological_parameters_when_cosmological
identify_quality_flag
identify_uncertainty
normalize_units
validate_method_and_reference_context
infer_distance_relationships
ambiguity_controls:
distinguish_parallax_from_distance
distinguish_redshift_from_distance
distinguish_light_travel_time_from_distance
distinguish_luminosity_from_angular_diameter_distance
distinguish_comoving_from_proper_distance
distinguish_lookback_time_from_distance
distinguish_apparent_magnitude_from_distance_modulus
distinguish_angular_size_from_physical_size
preserve_object_origin_frame_epoch_method_calibration_cosmology_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_and_astronomical_distance_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Astronomical Measurements
-> Astronomical Distance Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
reference_origin_model
distance_type_model
Euclidean_distance_model
parallax_model
parallax_uncertainty_model
Bayesian_distance_model
parallax_zero_point_model
radar_ranging_model
laser_ranging_model
light_travel_distance_model
distance_modulus_model
standard_candle_model
Cepheid_model
supernova_distance_model
standard_ruler_model
spectroscopic_distance_model
main_sequence_fitting_model
orbital_distance_model
dynamical_distance_model
expansion_parallax_model
redshift_model
Hubble_low_z_model
cosmological_model
comoving_distance_model
transverse_comoving_distance_model
angular_diameter_distance_model
luminosity_distance_model
proper_distance_model
lookback_time_model
distance_ladder_model
extinction_model
K_correction_model
lensing_model
angular_scale_model
reference_frame_model
temporal_model
relationships
constraints
measurement_model
uncertainty_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
astronomical_distance_type_changes
reference_origin_or_frame_changes
parallax_or_zero_point_model_changes
standard_candle_or_ruler_calibration_changes
photometric_or_extinction_model_changes
cosmological_parameter_or_distance_model_changes
ranging_or_dynamical_model_changes
measurement_model_changes
constraint_model_changes
reasoning_rule_changes
unit_model_changes
}
}
END FLOW