Question

The orbital radius of the Earth (the average Earth-Sun distance) is 1.496 × 1011 m. Mercury’s orbital radius is 5.79 × 1010 m and Pluto’s is 5.91 × 1012 m. Calculate the time required for light to travel from the Sun to each of the three celestial bodies

Answer 1

The time required for light to travel from the Sun to Mercury is approximately 3.2 minutes, to Earth is around 8.3 minutes, and to Pluto is approximately 328.33 minutes.

Step-by-step explanation:

The time required for light to travel from the Sun to Mercury can be calculated using the equation Speed = Distance / Time. The average distance between the Sun and Mercury is given as 5.79 × 10^10 m. Since light travels at a speed of approximately 3.00 × 10^8 m/s, we can rearrange the equation to find the time: Time = Distance / Speed.

Therefore, Time = (5.79 × 10^10 m) / (3.00 × 10^8 m/s). With the given values, the time required for light to travel from the Sun to Mercury is approximately 193 seconds or 3.2 minutes.

Similarly, to find the time required for light to travel from the Sun to Earth, we can use the average Earth-Sun distance of 1.496 × 10^11 m. Plugging this value into the equation, we get Time = (1.496 × 10^11 m) / (3.00 × 10^8 m/s). The time turns out to be approximately 498.67 seconds or 8.3 minutes.

Lastly, for the distance between the Sun and Pluto of 5.91 × 10^12 m, the time required for light to travel from the Sun to Pluto can be calculated as Time = (5.91 × 10^12 m) / (3.00 × 10^8 m/s). The result is approximately 19,700 seconds or 328.33 minutes.

Answer 2

Earth:
`t = 498.667\,s`, Mercury:
`t = 193\,s`, Pluto:
`t = 19700\,s`

Step-by-step explanation:

The light travels at a constant speed of approximately
`3* 10^(8)` meters per second. The time (
`t`), in seconds, required for light to travel a given distance is:

`t = (x)/(v_(l))` (1)

Where:

`x` - Travelled distance, in meters.

`v_(l)` - Speed of light, in meters per second.

Now, we calculate the time for light to travel to each planet:

Earth (
`v_(l) = 3* 10^(8)\,(m)/(s)`,
`x = 1.496* 10^(11)\,m`)

`t = (x)/(v_(l))`

`t = 498.667\,s`

Mercury (
`v_(l) = 3* 10^(8)\,(m)/(s)`,
`x = 5.79* 10^(10)\,m`)

`t = (x)/(v_(l))`

`t = 193\,s`

Pluto (
`v_(l) = 3* 10^(8)\,(m)/(s)`,
`x = 5.91* 10^(12)\,m`)

`t = (x)/(v_(l))`

`t = 19700\,s`