IB MYP 4-5 Physics- Using speed of light to estimate distances- Study Notes - New Syllabus

IB MYP 4-5 Physics-Using speed of light to estimate distances- Study Notes

Using Speed of Light to Estimate Distances

Speed of light in a vacuum is a constant:

\( c = 3.0 \times 10^{8} \, \text{m/s} \)

Definition of a light-year:

A light-year is the distance light travels in one year.

\( 1 \, \text{ly} = c \times \text{time (1 year)} \)

\( 1 \, \text{ly} = 3.0 \times 10^{8} \, \text{m/s} \times (365 \times 24 \times 3600 \, \text{s}) \)

\( 1 \, \text{ly} \approx 9.46 \times 10^{15} \, \text{m} \)

Why use light-years?

- Distances in space are extremely large.
- Using meters or kilometers is impractical, so astronomers use light-years or parsecs.

Estimating distance with light travel time:

If light from a star or galaxy takes \( t \) years to reach Earth, then its distance = \( t \) light-years.

Distance = \( t \, \text{ly} \)

Example:

Light from the Sun takes about 8 minutes to reach Earth. Estimate the distance between the Sun and Earth in meters.

▶️ Answer/Explanation

Time = \( 8 \times 60 = 480 \, \text{s} \)

Distance = \( c \times t = 3.0 \times 10^{8} \times 480 \)

Distance = \( 1.44 \times 10^{11} \, \text{m} \)

So, the Sun–Earth distance ≈ \( \boxed{1.5 \times 10^{11} \, \text{m}} \).

Example:

A nearby star is 4.3 light-years away. How many meters is this distance?

▶️ Answer/Explanation

1 light-year = \( 9.46 \times 10^{15} \, \text{m} \)

Distance = \( 4.3 \times 9.46 \times 10^{15} \)

Distance = \( 4.07 \times 10^{16} \, \text{m} \)

So, the star is about \( \boxed{4.1 \times 10^{16} \, \text{m}} \) away.