6.1.2 The Solar System – Light Travel Time
Key Concepts
Light is the fastest thing in the universe. Its speed in a vacuum is constant:
\$c = 3.00 \times 10^{8}\,\text{m/s}\$
To find how long light takes to travel a distance d, use:
\$t = \dfrac{d}{c}\$
Remember: t is in seconds if d is in metres.
Distances in the Solar System (approximate)
| Object Pair | Distance (km) | Light Travel Time (min) |
|---|
| Earth – Sun | 149.6 million km | 8 min 20 s |
| Earth – Mars (closest) | 54.6 million km | 3 min 4 s |
| Earth – Jupiter (closest) | 588 million km | 16 min 15 s |
| Earth – Saturn (closest) | 1.2 billion km | 33 min 30 s |
Analogy: Light as a Super‑Fast Car 🚗💨
Imagine a car that can drive at 300 million km/h (that’s the speed of light!). If the car travels from Earth to the Sun (150 million km), it would cover that distance in just 8 minutes. That’s like a car that can go from your school to the next town in less than the time it takes to finish a math lesson!
Step‑by‑Step Calculation Example
- Choose the distance: Earth–Mars (closest) = 54.6 million km = \$5.46 \times 10^{10}\,\text{m}\$.
- Use the formula: \$t = \dfrac{d}{c}\$.
- Plug in the numbers: \$t = \dfrac{5.46 \times 10^{10}}{3.00 \times 10^{8}}\$.
- Calculate: \$t \approx 182\,\text{s}\$.
- Convert to minutes: \$182\,\text{s} \div 60 \approx 3.0\,\text{min}\$.
- Result: Light takes about 3 minutes 4 seconds to travel from Earth to Mars at its closest approach.
Exam Tips 📚
- Always check units – convert km to metres before using the formula.
- Remember the speed of light: \$3.00 \times 10^{8}\,\text{m/s}\$.
- When converting seconds to minutes, divide by 60.
- Use the “closest” distance for planets unless the question specifies otherwise.
- Show all steps in your answer; partial credit is awarded for correct method even if the final number is slightly off.
Quick Practice Questions
- Calculate the light travel time from Earth to Jupiter when Jupiter is at its farthest point (approx. 628 million km).
- How long does it take light to travel from the Sun to the outer edge of the Solar System (approx. 1.5 billion km)?
- Convert 12 minutes of light travel time into kilometres.
Try solving these before checking the answers in your textbook. Good luck! 🌟