Description
Compose two collinear special-relativistic velocity fractions.
Cosmology uses several distance measures and often expresses the expansion rate in mixed astronomical units. Scale-factor relations, inverse-Hubble scales and relativistic velocity composition answer different questions; units and the distinction between local algebra and an integrated expansion history are essential.
Compose two collinear special-relativistic velocity fractions.
When to use this tool
Use Redshift Velocity Composition Gap when checking one explicit cosmological distance, redshift-factor or unit convention.
How to use the tool and how it works
- Enter firstBeta, secondBeta. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read composedBeta, additiveGap. Use the output convention below.
Compose two collinear special-relativistic velocity fractions. Require abs(firstBeta),abs(secondBeta) < 1; composedBeta = (b1+b2)/(1+b1*b2), additiveGap subtracts the simple sum.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstBeta | First signed collinear velocity divided by light speed, strictly between -1 and 1. | Required. Finite number. |
| secondBeta | Second signed collinear velocity divided by light speed, strictly between -1 and 1. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| composedBeta | Composed Beta | Required. Finite number. |
| additiveGap | Additive Gap | Required. Finite number. |
{
"input": {
"firstBeta": 0.5,
"secondBeta": 0.5
},
"output": {
"composedBeta": 0.8,
"additiveGap": -0.19999999999999996
}
}Limitations and assumptions
- Beta is velocity divided by light speed; this is not cosmological recession velocity from redshift.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use a complete cosmological distance/time calculation and the appropriate observation model when an actual source distance, age or velocity is required.
References
Similar or alternative tools
- Cosmological Redshift Peculiar Log Factor Split
Combine supplied cosmological and peculiar redshift factors.
- Galaxy Redshift Bin Rest Frame Width Tool
Normalize a small observed redshift interval by 1+z; this is not a full relativistic velocity-width conversion.