Problem — Light travel time Sun-Earth

Problem

How long does light take to travel the Sun–Earth distance? (The mean distance is $d = 1{,}5\cdot 10^{11}\;\text{m}$.)

Solution

Setup. Light in vacuum travels at constant speed $c = 3{,}00\cdot 10^8\;\text{m/s}$. Since this is uniform straight-line motion, the travel time is the ratio between distance and speed:

$t = \frac{d}{c}$

Calculation.

$t = \frac{1{,}5\cdot 10^{11}}{3{,}00\cdot 10^8} = 5{,}0\cdot 10^{2}\;\text{s} = 500\;\text{s}$

Conversion to minutes ($1\;\text{min} = 60\;\text{s}$):

$t = \frac{500}{60} \approx 8{,}3\;\text{min}$

$\ev{t = 500\;\mathrm{s} \approx 8{,}3\;\mathrm{min}}$

This is why we see the Sun “as it was” about 8 minutes ago: if it switched off now, we would only notice more than eight minutes later.

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Topics: Onde elettromagnetiche Skills: Conversione di unità