Can You Deduce The Distance Of The Sun From The Earth?

It takes about eight and a half minutes for light to reach the earth from the sun. How far away is the sun (in meters)?

Details and assumptions:

  • The speed of light in vacuum is 3 × 1 0 8 m/s 3 \times 10^8~\mbox{m/s} .


The answer is 1.53E+11.

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7 solutions

Discussions for this problem are now closed

Prasun Biswas
Dec 27, 2013

Time = 8 1 2 = 17 2 m i n = 17 2 × 60 = 17 × 30 = 510 =8\frac{1}{2} = \frac{17}{2} min = \frac{17}{2}\times 60 = 17\times 30 = 510 sec.

So, we know, Speed of light = 3 × 1 0 8 =3\times 10^{8} m/s.

Now, we know that,

Distance=Speed × \times Time d = 3 × 1 0 8 × 510 = 1530 × 1 0 8 = 1.53 × 1 0 11 = 1.53 E + 11 \implies d=3\times 10^{8} \times 510 = 1530 \times 10^{8} = 1.53\times 10^{11} = \boxed{1.53E+11}

Thanks for the clear calculations

Fresco Johnson - 7 years, 5 months ago

What would have been the case if there would have been a full solar eclipse, then what would be the time taken for light to reach earth from behind the moon.

hitesh sharma - 7 years, 3 months ago

First of all, during a full solar eclipse the view of the Sun from the Earth is fully obscured by the moon. In that case, the part of the Earth where the moon casts its shadow will have no visibility of the Sun till the moon moves about from the path and the other parts of the Earth will view the Sun as usual. So, in case of a full solar eclipse, light from the Sun will not reach that part of the Earth and to the rest of the Earth, the light from the Sun will take the usual 8 1 2 8\frac{1}{2} minutes to reach the surface.

Prasun Biswas - 7 years, 3 months ago

no actually not. Einstein already has explained in his paper on "General relativity" in 1920 that during eclipse light will take a bit more time to reach earth. Reason : the light from sun will slightly bend (near the moon) thereby making an angle to reach the earth. Because of which time taken will be a bit more.

Pragati Patra - 7 years, 3 months ago

@Pragati Patra That is exactly true... Moon's gravity bends the light coming from sun and hence a greater path is traveled by light and thus more time. So in fact though behind the moon, sun will be visible to some population, in other words - sun becomes visible before actual completion of eclipse. though the difference is in mili/micro seconds

hitesh sharma - 7 years, 3 months ago
Ajay Maity
Dec 26, 2013

Let d d be the distance in meters between the sun and earth.

Given, v v = speed of light = 3 × 1 0 8 3 \times 10^{8} m/s

t t = time for the light to travel from sun to earth = 8.5 8.5 minutes = 8.5 × 60 8.5 \times 60 seconds = 510 510 seconds.

Using the equation,

d = v × t d = v \times t

we get

d = 3 × 1 0 8 × 510 d = 3 \times 10^{8} \times 510

d = 1.53 × 1 0 11 d = 1.53 \times 10^{11} meters

That's the answer!

We know : Distance = Speed x Time

T i m e ( i n s e c o n d s ) = T i m e ( i n m i n u t e s ) 60 = 8.5 60 = 510 s Time (in seconds) = Time (in minutes) * 60 = 8.5 * 60 = \boxed{ 510s}

Putting given values we get : * D i s t a n c e = 3 1 0 8 510 s = 1.53 1 0 11 s Distance = 3*10^{8}*510s = 1.53*10^{11}s *

Girija Lenka
Aug 8, 2013

speed of light = 3 x 10^8 time taken by the light to reach the earth from sun = 8 minutes & half minute = 510 seconds so, distance is speed x time Distance = [3 x 10^8]m x [510]seconds = [153 x 10^9]

Michael Tang
Aug 5, 2013

Eight and a half minutes is equal to 510 510 seconds, so the distance between the Earth and the Sun is about 510 ( 3 × 1 0 8 ) = 1.53 × 1 0 11 510 \cdot (3 \times 10^8) = \boxed{1.53 \times 10^{11}} meters.

(You would input this as "1.53E+11".)

Oliver Welsh
Dec 26, 2013

We have v = s t s = t v v=\frac{s}{t} \Rightarrow s = t \cdot v . The speed of the light is 3 1 0 8 m / s 3 \cdot 10^8 m/s and the time it takes for the light to reach the earth is 8.5 m i n = 510 s 8.5 min = 510s . Therefore, the distance is calculated by, s = 510 3 1 0 8 = 1.53 1 0 11 m s = 510 \cdot 3 \cdot 10^8 = 1.53 \cdot 10^{11}m

c = d/t, distance, d = ct = (3E+8)510 = 1.53E+11

Ramesh Bondada - 7 years, 4 months ago
Ayon Pal
Aug 4, 2013

Total time takes = 30 + 8 48 = 510 s e c 30 + 8 * 48 = 510 sec

Speed of light = 3 1 0 8 m / s e c 3 * 10 ^8 m/sec

Total distance = 510 3 1 0 8 = 1.53 E + 11 m 510 * 3 * 10 ^8 = 1.53E+11 m

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