Question

The average distance from the Sun to Andromeda galaxy is 1.2 × 10¹9 miles and the speed of light is 5.88 x 10¹2 miles per day. How long does it take for light to travel from the Sun to Andromeda galaxy?​

Answer 1

Answer:

2,040,816 days ≈ 2.04 × 10⁶ days

Step-by-step explanation:

To calculate the time it takes for light to travel from the Sun to the Andromeda galaxy, we need to use the formula:

$\boxed{\sf Time = \dfrac{Distance}{Speed}}$

Given:

• Distance from the Sun to Andromeda galaxy = 1.2 × 10¹⁹ miles
• Speed of light = 5.88 × 10¹² miles per day

Substitute these values into the formula:

$\sf Time=\dfrac{1.2 \times 10^{19}\;miles}{5.88 \times 10^{12}\;miles/day}$

Simplify the calculation:

$\sf Time=\dfrac{1.2}{5.88} \times \dfrac{10^{19}}{10^{12}}\;days$

Divide the numbers 1.2 and 5.88:

$\sf Time=0.204081632...\times \dfrac{10^{19}}{10^{12}}\;days$

$\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}$

$\sf Time= 0.204081632...\times 10^{19-12}\;days$

Therefore:

$\begin{aligned}\sf Time&=\sf 0.204081632...\times 10^{7}\;days\\&=\sf 2.04081632...\times 10^{6}\;days\\&=\sf 2,040,816\;days\end{aligned}$

Therefore, it takes approximately 2.04 million days for light to travel from the Sun to the Andromeda galaxy.