Use a light-travel scale

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Travel years equal distance in light-years divided by one light-year per year. Formula: a/1. Variable key: a = distance (light-years)
• Distinct worked inputs and result: A distinct source at 6 light-years is seen with about 6 years of light-travel delay in the simplified model.
• Assessment case 1: Supplied case 1: distance (light-years)=4, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?
• Assessment case 2: Supplied case 2: distance (light-years)=8, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?
• Assessment case 3: Supplied case 3: distance (light-years)=12, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?
• Assessment case 4: Supplied case 4: distance (light-years)=20, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?
• Assessment case 5: Supplied case 5: distance (light-years)=50, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?
• Assessment case 6: Supplied case 6: distance (light-years)=100, using the explicitly named quantities. Travel years equal distance in light-years divided by one light-year per year. What result follows?

Learn the idea

A light-year is a distance, not a duration. For the supplied constant light-travel model, a distance in light-years divided by speed in light-years per year gives travel time.

Travel years equal distance in light-years divided by one light-year per year. The formula in the supplied model is a/1. Variable key: a = distance (light-years). Separate distance unit light-year from time unit year. Observed light represents past emission.

A distinct source at 6 light-years is seen with about 6 years of light-travel delay in the simplified model. The model omits cosmological expansion. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with distance (light-years)=5. Expected result: 5 years. Explain what changes and keep this assumption: The model omits cosmological expansion.

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