Explanation:
Given:




Let
= mass of the asteroid and
= orbital radius of the asteroid around the sun. The centripetal force
is equal to the gravitational force 

or

where

with T = period of orbit. Rearranging the variables, we get

Taking the square root,



Answer:
C ) 1.53
Explanation:
The critical angle of a material is given by the formula

where
c is the critical angle
n is the refractive index
This formula is valid if the second medium is air (which is the case of the problem).
In this problem, we know the critical angle:

Therefore we can rearrange the equation to find the refractive index:

When a problem says a rigid vessel, it means that volume is constant. At constant V, pressure and temperature are indirectly proportional. We calculate as follows:
P1/T1 = P2/T2
P1/P2 = T1/T2
P1/P2 = 273.15 / 272.15
P1/P2 = 1.00
Hope this helps. Have a nice day.