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Answer both of the following questions:

1. Suppose that a typical comet has a mass of [tex]10^{14} \, \text{kg}[/tex], orbits the Sun once every 60 years, and during the 3 months it is closest to the Sun, it emits gases at a rate of [tex]10^3 \, \text{kg per second}[/tex]. Calculate how long it can survive before being entirely dissipated by the Sun. Describe the logic of the calculation you will use, and then carry out the calculation.

2. Suppose that the Oort Cloud contains 10 billion comets. What is the total mass of all these comets? Do they add up to more or less than the mass of the Earth? Describe the logic of the calculation you will use, and then carry out the calculation.

Answer :

The mass of the Earth is approximately 5.972 × 10²⁴ kg, so the total mass of all the comets in the Oort Cloud is less than the mass of the Earth.

How to calculate the value

Mass of gases emitted during this time:

Mass emitted = 10³ kg/s * (3 * 30 * 24 * 60 * 60 s) = 7.776 * 10¹¹ kg

Total orbits = Lifetime / Orbital period = Lifetime / 60

Total mass emitted = Mass emitted * Total orbits

Total mass = 10¹⁰* 10¹⁴ kg = 10²⁴ kg

The mass of the Earth is approximately 5.972 × 10²⁴ kg, so the total mass of all the comets in the Oort Cloud is less than the mass of the Earth.

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