Question

Io loses about a ton (1000 kilograms) of sulfur dioxide per second to Jupiter's magnetosphere. The mass of Io is 8.933×1022kg

At this rate, what fraction of its mass would Io lose in 5.1 billion years?

Answer 1

To calculate the fraction of Io's mass that would be lost in 5.1 billion years, we can first find the total amount of sulfur dioxide lost during that time period and then determine the fraction relative to Io's initial mass.

Given: Rate of sulfur dioxide loss per second = 1000 kg Mass of Io = 8.933×10^22 kg Time = 5.1 billion years = 5.1 × 10^9 years

First, let's calculate the total amount of sulfur dioxide lost in 5.1 billion years: Total sulfur dioxide loss = Rate of loss per second × Time Total sulfur dioxide loss = 1000 kg/s × (5.1 × 10^9 years) × (365 days/year) × (24 hours/day) × (60 minutes/hour) × (60 seconds/minute)

Next, we can calculate the fraction of mass lost: Fraction of mass lost = Total sulfur dioxide loss / Initial mass of Io

Let's plug in the values and calculate the fraction:

Total sulfur dioxide loss = 1000 kg/s × 5.1 × 10^9 years × 365 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute Total sulfur dioxide loss = 1.62 × 10^23 kg

Fraction of mass lost = (1.62 × 10^23 kg) / (8.933×10^22 kg)

Calculating the fraction gives us: Fraction of mass lost ≈ 1.813

Therefore, Io would lose approximately 1.813 times its initial mass in sulfur dioxide over the course of 5.1 billion years.

Answer 2

Explanation:

So Io would lose about 0.000159 Yg of sulfur dioxide in 4.5 billion years. This is a very small fraction of its mass!