Description
Interpolate supplied DUT1 observations through UT1−TAI, then recover UT1−UTC and TT−UT1.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Interpolate supplied DUT1 observations through UT1−TAI, then recover UT1−UTC and TT−UT1.
The checked IERS table lists TAI−UTC steps from the ten-second 1972 baseline and states an expiry of 28 June 2027. This tool uses an embedded snapshot rather than downloading a current table.1
When to use this tool
Use this tool when you need to interpolate supplied DUT1 observations through UT1−TAI, then recover UT1−UTC and TT−UT1.
How to use the tool and how it works
- Enter utcJulianDays, dut1Seconds, queryUtcJulianDay using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.ut1MinusUtcSeconds, result.ttMinusUt1Seconds, result.taiMinusUtcSeconds, result.leftIndex, result.rightIndex, using the stated boundary, ordering, sign and absence conventions.
For each UTC-Julian-day knot, subtract the table’s TAI−UTC step from supplied DUT1=UT1−UTC to obtain continuous UT1−TAI. Interpolate that quantity linearly at the query, then restore TAI−UTC for DUT1 and use 32.184−(UT1−TAI) for TT−UT1.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| utcJulianDays | At least two strictly increasing UTC-Julian-day knots within the pinned leap-table range. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| dut1Seconds | Supplied UT1−UTC in seconds, each magnitude≤0.9, aligned to utcJulianDays. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| queryUtcJulianDay | Query UTC-Julian-day coordinate inside the supplied knot interval and pinned leap-table range. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.ut1MinusUtcSeconds | Interpolated DUT1 in seconds after restoring the query’s leap-table offset. |
| result.ttMinusUt1Seconds | TT−UT1 in seconds from TT−TAI=32.184 s and interpolated UT1−TAI. |
| result.taiMinusUtcSeconds | Pinned table TAI−UTC step in seconds at the requested date. |
| result.leftIndex | Zero-based left interpolation knot index; equals rightIndex at an exact knot. |
| result.rightIndex | Zero-based right interpolation knot index; equals leftIndex at an exact knot. |
{
"input": {
"utcJulianDays": [
2451544.5,
2451545.5
],
"dut1Seconds": [
0.2,
0.4
],
"queryUtcJulianDay": 2451545
},
"output": {
"result": {
"ut1MinusUtcSeconds": 0.3,
"ttMinusUt1Seconds": 63.884,
"taiMinusUtcSeconds": 32,
"leftIndex": 0,
"rightIndex": 1
}
}
}Limitations and assumptions
- Use at least two increasing aligned knots and an in-range query, all within the pinned 1972-01-01 to 2027-06-27 table. DUT1 magnitudes≤0.9 s; no extrapolation or live Earth-orientation retrieval. Exact knots return equal left/right indexes. Linear interpolation follows the numeric UTC-JD coordinate convention.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
-
TAI−UTC step table, updated through Bulletin C 72 — IERS Earth Orientation Centre
-
Tool behavior and example: UT1-UTC Delta T Rough Interpolator Note Generator — tool.io
Similar or alternative tools
- Leap Second Count Since 1972 Counter
Count leap seconds since the 1972 baseline using a pinned, date-bounded IERS table.
- Greenwich Sidereal Time Approximation Hours Calculator
Calculate approximate Greenwich mean sidereal hours from an explicit UT1 Julian date.