Question

A sun-like star is barely visible to naked-eye observers on earth when it is a distance of 7.0 light years, or 6.6 * 1016 m, away. The sun emits a power of 3.8 * 1026 W. Using this information, at what distance would a candle that emits a power of 0.20 W just be visible?

Answer 1

Answer:

At a distance of 1376.49 candle emits 0.2 watt power

Explanation:

Distance between Sun and earth $6.6\times 10^{16}m$

Sun emits a power of $P=3.8\times 10^{26}watt$

Power emitted by candle = 0.20 watt

We know that brightness is given by

$B=\frac{P}{4\pi d^2}$

So $\frac{3.8\times 10^{26}}{4\pi (6\times 10^{16})^2}=\frac{0.20}{4\pi d^2}$

$3.8\times 10^{26}d^2=7.2\times 10^{32}$

$d^2=1.89\times 10^6$

$d=1376.49m$

So at a distance of 1376.49 candle emits 0.2 watt power

Answer 2

A candle that emits a power of 0.20 W just be visible from a distance of 1376. 39 m.

The brightness can be calculated by the formula,

$\bold {B = \dfrac P{4\pi d^2}}$

Where,

P - power of emission = $\bold {3.8 x 10^2^6\ W}$  and  by candle = 0.2 W

d - distance between the sun and the earth  = $\bold{6.6 x 10^1^6 m}$

So,

$\bold {\dfrac {3.8 x 10^2^6\ W}{4\pi (\bold{6.6 x 10^1^6 m})^2} = \dfrac {20}{4\pi d^2}}\\\\\bold {3.8 x 10^2^6\times d^2 = 7.2x10^3^2}\\\\\bold {d = 1376.39 m}$

Therefore, a candle that emits a power of 0.20 W just be visible from a distance of 1376. 39 m.

To know more about Brightness,

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