I feel like I am making this question too difficult... a) Tycho observed superno

Question

I feel like I am making this question too difficult...

a) Tycho observed supernovae SN1572 in 1572 which lies 3kpc away from earth. SN1987A lies 52 kpc away and was first seen in February of 1987. In approximatally what years did these two supernava explode? Which exploded first?  1pc-3.26 ly

b) 2 planets, Abel and Baker, orbit 150 light years from Earth and orbit the star Xantax.Baker circles Xantax every 28 days while Abel takes three times as long. How much further from Xantax is Abel than Baker? How much light does Abel receive from Xantax relative to Baker?

Explanation / Answer

a) supernovae SN1572 exploded in November 1572.

SN1987A exploded in 1987. THus, SN1572 exploded first.

b) Let us assume that both Abel and Baker revolute at the same velocity.

Let r1 be Abel's radius and r2 be Baker's.

Angular velocity of Baker = 2*3.14*r2/28 rad/day

Now, time taken by Abel = 28*3 = 84 days

So, distance travelled by Abel = 84*(2*3.14*r2/28).

Thus, r1/r2 = 3

Thus Abel is 3 times further from Xantax than Baker.

Since light received is proportional to (radius)^2, Abel revceives 1/3^1 = 1/9th of the light received by Baker.

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