In this problem you’ll consider objects at the extreme ends of astronomical density scale. you can assume that all objects given below are spherical and of uniform density. recall that volume of a sphere of radius r is v = 4r3π/3. the only formula you’ll need is m = rho∗v where rho is the density of the object, m is its mass and v its volume. (a) assume that the density of a neutron star is 5 ∗ 1017kg/m3. what is the mass of one teaspoon of neutron star matter? you can assume that the standard teaspoon volume is 5ml = 5 ∗ 10−6m3. (b) assuming the same density, what is the radius of a neutron star with mass equal to two solar masses? (c) molecular clouds are the birthplace of stars. a typical molecular cloud has density of rho = 1.67 ∗ 10−19kg/m3. what is the diameter of a cloud with mass equal to one solar mass? give your answer both in meters and in light years. (the answer in (c) will give you the minimal size of the part of the cloud needed for the creation of the solar system. a typical total size of the protostellar cloud is much, much larger.)

f=ma newton

f=100x2.5=250n

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.