Question

If the Oort cloud contains 1012 comets, and ten new comets are discovered coming close to the Sun each year, what percentage of the comets have been “used up” since the beginning of the solar system?

Answer 1

99.99 %

Step-by-step explanation:

We know that age of the Solar System = 4.57 Billion years = 4570000000 Years

Lets assume that the no. of comets coming towards Sun each year is uniform since the beginning. It means that if we backtrack from the current number of comets in the Oort's cloud we can find the answer to the given problem.

Present number of comets in Oort's cloud = 1012

No. of comets leaving Oort's cloud each year = 10

This implies, number of comets(N) in Oort's cloud 4.57 billion years back were:

`N = (10 * 4570000000) + 1012`

`N = 45700001012`

Percentage of comets used up in this period:

`= ((45700001012 - 1012))/(45700001012)*100`

`= (45700000000)/(45700001012)*100`

`= 0.9999*100`

`= 99.99%`

This means that 99.99 % of the comets since the beginning of the solar system have been used up.

Answer 2

4.57 %

Step-by-step explanation:

The age of the solar system in years is about

`4.57\cdot 10^9 y`

Each year 10 new coments enter the solar system, so the total number of comets "used up" since the beginning of the solar system is

`10 \cdot 4.57\cdot 10^9 = 4.57\cdot 10^(10)`

The number of comets contained in the Oort cloud is

`10^(12)`

Therefore, the percentage of comets that have been "used up" is

`(4.57\cdot 10^(10))/(10^(12)) \cdot 100 = 4.57\%`