Mass of particules in the magnetosphere

[Cerdocyon]

Homework Statement

Hello,
The problem is quite simple.
Estimate the mass of particules that contains the Earth's magnetosphere up to a distance of 100 times Earth's radius (In the shadow cone of earth) and also up to the break point or stopping point of the side of the sun.The solar activity is at its minimum and the average density is 10 protons/cm³.Then compare with the total mass of Earth's atmosphere.
Thank you.

Homework Equations

Well the problem is that i can,t find any relevant equations that could help me with my problem

The Attempt at a Solution

The solar activity is at its minimum so the break point must be at a distance of approximately 10earth's radius. And that's were i stopped after hours of trying to figure out a solution.
Thank you

 

[mark726]

for your post and your question. I am always excited to see people interested in exploring and understanding the world around us. I will do my best to help you find a solution to your problem.

First, let's define some key terms and concepts to better understand the problem. The Earth's magnetosphere is the region of space surrounding the Earth in which the Earth's magnetic field dominates the interplanetary magnetic field. It is created by the interaction between the Earth's magnetic field and the solar wind - a stream of charged particles emanating from the Sun. The shadow cone of the Earth refers to the region behind the Earth where the solar wind is deflected by the Earth's magnetic field.

To estimate the mass of particles in the Earth's magnetosphere, we can use the following equation:

M = n * V * m

where M is the mass, n is the number density of particles, V is the volume of the region, and m is the mass of each particle.

We are given that the average density is 10 protons/cm³. To convert this to number density, we can use the fact that 1 proton has a mass of approximately 1.67 x 10^-27 kg. Therefore, the number density would be 10 protons/cm³ = 1.67 x 10^-26 particles/cm³.

Next, we need to calculate the volume of the region we are interested in. We are looking at a distance of 100 times Earth's radius, which would give us a volume of:

V = (4/3) * π * r^3 = (4/3) * π * (100 * r)^3 = 4 * 10^6 * (4/3) * π * r^3

where r is the radius of the Earth (6.37 x 10^6 m). This gives us a volume of approximately 2.71 x 10^34 m³.

Now, we can plug these values into our equation to calculate the mass of particles in the Earth's magnetosphere:

M = (1.67 x 10^-26 particles/cm³) * (2.71 x 10^34 m³) * (1.67 x 10^-27 kg) = 7.15 x 10^41 kg

Next, we can compare this to the total mass of the Earth's atmosphere. The Earth's atmosphere has a mass of approximately