water delivery: a) About 70% of the Earth is covered with water. Assuming the Ea
ID: 236965 • Letter: W
Question
water delivery:
a) About 70% of the Earth is covered with water. Assuming the Earth is a perfect sphere of radius 6,371 km and the typical ocean depth is 7 km, about how much mass of water is this (assume water is 1 kg / m^3)? How does this compare to the mass of the current asteroid belt, which is about 3 x 10^21 kg?
b) A typical comet nucleus is 1 km radius. Assuming a comet is 100% water and spherical, how many comets would it take to cover the Earth with water?
c) A high rate of impactors would be extremely disruptive to the development of multicellular life and probably photo-synthesis, but bacteria could probably survive. It is thought that the earliest water on earth was present for about 300 million years (starting 4.4 billion years ago) prior to the development of life. After this, for 600 million years single-celled life was present. How many comets per year must impact the earth in those 900 million years to deliver present day water to earth?
Explanation / Answer
a) mass of water = density*volume
=1000*0.70*4/3*pi*(6371000^3-7000^3)
= 7.582 × 10^23 kg
It is as much as 758e21/3e21= 253 asteroids.
B)mass of water comet = density*volume
= 1000*4/3*pi*1000^3
= 4.189e12 kg
Number of comets required =7.582e23/4.189e12
= 1.81 ×10^11
C) number of comets per year = 1.81e11/900e6
= 201 comets per year
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