Convert light-year distances and signal delays
Use the syllabus conversion 1 light-year = 9.5 × 10¹⁵ m in both directions.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Use scientific notation.
- Define a light-year as distance.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which operation converts light-years to metres?
What you will learn
- Use the syllabus conversion 1 light-year = 9.5 × 10¹⁵ m in both directions.
- Calculate paths before converting distances or one-way and return delays.
Multiply or divide by the conversion
For this syllabus use 1 light-year = 9.5 × 10¹⁵ m. Multiply a distance in light-years by this factor to obtain metres; divide a distance in metres by it to obtain light-years. Keep the factor and units visible rather than treating the power of ten as an optional decoration.
For example, 2.4 light-years gives 2.4 × 9.5 × 10¹⁵ = 2.28 × 10¹⁶ m. The stated conversion is rounded. Combining it with a rounded vacuum speed and a chosen seconds-per-year convention can produce a small rounding difference, not a new physical contradiction.
Count complete journeys
For stationary endpoints, light takes one year to cross one light-year by definition. At three light-years, an immediate command-and-reply path takes six years. Add any stated remote waiting time once, after including both propagation legs.
Do not apply the light-time equivalence to a spacecraft moving slower than light. Nor can the same simple conversion replace a cosmological distance model when expansion matters. The examples here supply a fixed path or a local stationary-distance approximation.
Sources for this lesson
Pause and explain
How far is 1.9 × 10¹⁶ m in light-years?
Worked example
Convert 3.2 light-years into metres.
Show the worked solution
- Write 3.2 × 9.5 × 10¹⁵ m.
- Calculate the coefficient 30.4.
- Normalise scientific notation.
Answer 3.04 × 10¹⁶ m.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 4.6 light-years into metres.
Give me a hint
Keep 9.5 × 10¹⁵ with its unit throughout the multiplication.
Compare my reasoning
- Write d = 4.6 × 9.5 × 10¹⁵ m.
- Calculate 43.7 × 10¹⁵ m.
- Normalise the coefficient to 4.37.
4.37 × 10¹⁶ m.
Look for these in your work
- Show the conversion direction.
- Keep the correct exponent.
Convert 7.6 × 10¹⁶ m into light-years.
Give me a hint
Divide the metre distance by the metre length of one light-year.
Compare my reasoning
- Form (7.6 × 10¹⁶)/(9.5 × 10¹⁵).
- Separate 7.6/9.5 and 10¹.
- Calculate 0.8 × 10.
8 light-years.
Look for these in your work
- Cancel metre units.
- Return a distance unit.
A fixed beacon is 2.5 light-years away and waits 0.2 year before replying. Give its distance in metres and the complete reply delay.
Give me a hint
Convert the distance once; include two light paths and one wait.
Compare my reasoning
- d = 2.5 × 9.5 × 10¹⁵ = 2.375 × 10¹⁶ m.
- Two propagation legs take 5 years.
- Add the single 0.2-year processing wait.
2.375 × 10¹⁶ m; total delay 5.2 years.
Look for these in your work
- Include both signal legs.
- Add the wait once.
Common mistakes
- Metres to light-years needs division.
- A round trip has two propagation legs.
- Rounded reference constants need consistent precision.
What can you explain now?
How far is 1.9 × 10¹⁶ m in light-years?
Compare with the explanation
2 light-years
Dividing by 9.5 × 10¹⁵ m per light-year gives 2.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Calculate paths before converting distances or one-way and return delays.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.