Few question about astronomy:

1.how many centimetres is equivalent to a light-nanosecond
2. How long is an astronomical unit (AU) in light-minutes (1min, i.e., the distance that light travels in a vacuum in one minute)?

Please show the calculation if there is any

Thanks

1. speedlight*time= distance

3E8m/s*1E2cm/m*1E-9sec=3E1 or 30 cm

2. speedlight*time=distance
3E8m/s*60sec= ?

2. Sunlight reaches Earth in 8.3 minutes. The Earth-Sun distance is therefore 8.3 light-minutes.

One way to get the answer is to divide the Earth-Sun distance by the distance travelled by light in one minute, using the same units.

1. To calculate how many centimeters are equivalent to a light-nanosecond, we first need to know the speed of light in centimeters per second.

The speed of light in a vacuum is approximately 299,792,458 meters per second. To convert this to centimeters per second, we multiply by 100 because there are 100 centimeters in a meter. Therefore, the speed of light in centimeters per second is 299,792,458 x 100 = 29,979,245,800 cm/s.

A nanosecond is one billionth of a second. So, to find the distance light travels in one nanosecond, we multiply the speed of light in centimeters per second by the number of seconds in a nanosecond (1 x 10^-9 seconds).

Distance = Speed x Time = 29,979,245,800 cm/s x (1 x 10^-9 s) = 29.9792458 cm.

Therefore, a light-nanosecond is approximately 29.9792458 centimeters.

2. An astronomical unit (AU) is the mean distance between the Earth and the Sun, which is about 149,597,870.7 kilometers or 93,000,000 miles.

To calculate how long an AU is in light-minutes, we need to convert the distance from kilometers or miles to light-minutes.

The speed of light is approximately 299,792 kilometers per second or 186,282 miles per second. To convert this to kilometers or miles per minute, we multiply by 60 (since there are 60 seconds in a minute).

Speed of light in kilometers per minute: 299,792 km/s x 60 = 17,987,520 km/min
Speed of light in miles per minute: 186,282 mi/s x 60 = 11,176,920 mi/min

Now, we can calculate the AU in light-minutes.

AU in light-minutes = (AU distance in kilometers or miles) / (Speed of light in kilometers or miles per minute)

AU in light-minutes = 149,597,870.7 km / 17,987,520 km/min ≈ 8.319182 minutes

Or
AU in light-minutes = 93,000,000 mi / 11,176,920 mi/min ≈ 8.318754 minutes

Therefore, an astronomical unit (AU) is approximately 8.319182 or 8.318754 light-minutes.