Convert light-year distances and signal delays
Use the syllabus conversion 1 light-year = 9.5 × 10¹⁵ m in both directions.
Section 6.2.2 · Stars
Exam scope and assessment notes
Extended only (Supplement) · Physics 0972, 2026–2028. Use supplied distances, periods and stated orbital models. Drawings are not to scale. Written practice is self-checked. Human subject-teacher review, supervised practical competence and cumulative assessment remain pending. Cambridge states that IGCSE 0972 has the same subject content as IGCSE 0625, with 9–1 grading. This StudyForA pathway maps the 2026–2028 syllabus only. This 9–1 graded qualification is available only in a limited number of administrative zones. Confirm that your centre can enter you for this code and exam series with Cambridge International. Cambridge has published a separate syllabus for 2029. StudyForA has not reconciled that version yet; this page supports exams in 2026, 2027 and 2028 only.
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.
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.
Your review choice appears on Today. Sign in to sync it across devices.
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.