Question

'The distance of a star from the earth is 8.33 light minutes.' What do you mean by this statement? Express the distance in metres.

Answer 1

Hint: The light-second, like the second, can serve as the foundation for various units of length, ranging from the light-nanosecond (299.8 mm or slightly under one international foot) to the light-minute, light-hour, and light-day, which are occasionally used in popular scientific journals. Because the definition of a year is based on a Julian year of exactly 365.25 days, each of exactly 86400 SI seconds, the more widely used light-year is now defined to be exactly 31,557,600 light-seconds.

Formula used
Speed = $\frac{{{\text{Distance}}}}{{{\text{Time}}}}$

Complete step-by-step solution:
In astronomy, telecommunications, and relativistic physics, the light-second is a unit of length. It is equal to exactly 299,792,458 metres and is defined as the distance that light travels in open space in one second (983,571,056 ft). The light-second is a useful measure for calculating distances in the inner Solar System because it closely matches the radiometric data used to calculate them. (There is a very minor correction for the effects of relativity for an Earth-based observer, so the match isn't perfect.) Earth's average diameter is 0.0425 light-seconds. The lunar distance (the average distance between Earth and the Moon) is approximately 1.282 light-seconds. The Sun's diameter is approximately 4.643 light-seconds. The astronomical unit for the distance between Earth and the Sun is 499.0 light-seconds. The distance between a star and the earth is 8.33 light minutes, which implies that light from the ultimate source of light, the Sun, takes 8.33 minutes to reach the world. Because the distance is so great, a light year is employed.
Speed of light = $3 \times {10^8}m{s^{ - 1}}$
Now using given conditions we write
Time = 8.33 min = 499.8s
Distance = speed × time = \[3 \times {10^8}\; \times 499.8\;\; = 1.5 \times 10{\;^{11\;}}m\]
Hence
$ \Rightarrow {\text{Distance}} = 1.51 \times {10^{11}}m$

 Note:Always try to remember the formulas used. The pace at which an object's location changes in any direction is known as speed. Speed is defined as the ratio of distance travelled to the time it took to travel that distance. Because speed has just one direction and no magnitude, it is a scalar number. When an item travels the same distance in the same amount of time, it is said to be moving at a uniform pace.