Question

2 planets 'Xargonia' and 'Olfuba' have taken keen interest in our star 'The Sun'. They are observing our sun from the observatories built on their planet.

Xargonia is 1 Light year away and the aperture area of its telescope is $1m^2$, while Olfuba is 2 Light years away and the aperture area of its telescope is $4m^2$.

Find out whose telescope receives more energy? (Assume the Sun radiates E joules of energy per sec.)

• A. Xargonia
• B. Olfuba
• C. Both receive equal
• D. Data insufficient

Answer 1

The correct option is C

Both receive equal

So we have to find the energy received by the telescopes.

Okay, no big deal.

What do I know.

The sun radiates E joules of energy per second. The rate at which energy passes through a sphere at 1 light year distance will be… the SAME.

E J/s, right?

The intensity at this sphere will be (power/ area) $=\frac{E}{4\pi {\left(1lightyear\right)}^2}$------(1)

Similarly, for Olfuba which is 2 light years away the intensity will be $=\frac{E}{4\pi {\left(2lightyear\right)}^2}$------(2)

I hope you remember that a light year is a unit of distance and not time. It’s the distance covered by light in a year.

Now that we know intensity let's find the energy received per unit time at each telescopes.

Intensity $=\frac{Power}{Area}$

$=\frac{Power}{\left(Area\right)}$ (Area 2) will give me back my power.

Let’s find the power received by the telescope at Xargonia.

Intensity on sphere at 1 light year $=\frac{E}{4\pi {\left(1lightyear\right)}^2}$

Area of Aperture of the telescope = $1m^2$

So power (energy/time) $=\frac{E}{4\pi {\left(1lightyear\right)}^2}\times 1$ …(iii)

Similarly

Intensity on sphere at radius 2 light year $=\frac{E}{4\pi {\left(2lightyear\right)}^2}$

Area of Aperture of the telescope = $4m^2$

So power $=\frac{E}{4\pi {\left(2lightyear\right)}^2}\times 4=\frac{4E}{4\pi 4{\left(lightyear\right)}^2}$ …(iv)

Comparing (3) & (4), they both are equal as you can see

$=\frac{E}{4\pi {\left(1lightyear\right)}^2}$

So they both receive equal power.