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Collisions of planets and comets, redshift of galaxies

1. A planet orbiting a star is occasionally hit by comets. Each comet has a mass of 4.8 * 10^6 kg of which 30% is rock and 70% is water ice. Each time a comet hits the planet 40% of the mass of the comet is vaporized and the rest is added to the planet, increasing the mass of the planet. If 6 comets hit the planet every 10 years, by how much will the mass of the planet have increased in 1 million years? How much of the additional mass will be in the form of rock, assuming that the rock and ice evaporate in the same proportions as exist in the original comet? You should give both answers to one significant figure and in scientific notation.

Increase in mass of planet after 1 Million Yrs = ? kg

Additional mass of rock after 1 Million Yrs = ? kg

2. Galaxies, A and B, which have red shifts of:
Galaxy A = 0.01 and Galaxy B = 0.04. (a) Which galaxy is closest to us and what is its distance away from us?
You may assume that the Hubble constant is H0 = 75 km.s-1/Mpc and that the speed of light is c = 3.0 - 10E5 km.s-1.

a. The closest galaxy is A or B?

b. What is its distance in Mpc?

Assuming that Galaxy A is intrinsically of identical luminosity to Galaxy B, how does its apparent brightness on the night sky compare to that of Galaxy B?

c. How many times brighter or fainter is it?

Solution Preview

(1) Comet - Planet Collision Question

Mass of typical comet Mc = 4.8 x 10E.6 Kg (30% Rock, 70% Water Ice)

Each time a comet hits then 40% vaporises and assuming none of the vapourised debris adds to the
planets mass this then implies 60% of the comets mass is added to the planet.

Therefore we can work out How much mass is typically added to a planets mass by a comet collision which is
given as Delta(M)

Delta(M) = 60*Mc/100 = 60 x 4.8 x10E.6/100 = 2.88 x 10E.6 Kg (+ to a planets mass by 1 comet collision)

We are told that there are typically 6 comet collisions with said planet every 10 years so the number of
comet collisions occurring with the planet in 1 Million Years can be deduced simply as given by N below

N = 6 (collions every 10 years) * 1000000/10 = 6 x 10E.5 collision in 1 Million years

Therefore the mass added to the planet (Delta(Mp)) by comet collisiosn over 1 Million years would be given
as the product N*Delta(M)

ie. Delta(Mp) = N*Delta(M) ...

Solution Summary

This is a 2 part solution. The first part shows how using data on comet collisions with planets one can derive the additionl mass of a planet as the result of the collision and the additional mass of rock deposited. The second part looks at using Redshift data and the Hubble Constant to derive the distance of two galaxies and then compute their relative brightnesses based on the distance data. Known Astrophysical laws are used throughout in the derivations