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

2,040,816 days ≈ 2.04 × 10⁶ days

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 = (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=(1.2 * 10^(19)\;miles)/(5.88 * 10^(12)\;miles/day)`

Simplify the calculation:

`\sf Time=(1.2)/(5.88) * (10^(19))/(10^(12))\;days`

Divide the numbers 1.2 and 5.88:

`\sf Time=0.204081632...* (10^(19))/(10^(12))\;days`

`\textsf{Apply the exponent rule:} \quad (a^b)/(a^c)=a^(b-c)`

`\sf Time= 0.204081632...* 10^(19-12)\;days`

Therefore:

`\begin{aligned}\sf Time&=\sf 0.204081632...* 10^(7)\;days\\&=\sf 2.04081632...* 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.