What is the total mass of the earth's atmosphere? The radius of the Earth is 6.37E6 m, and atmospheric pressure at the surface is 1.013E5 N/m^2 (or Pa).

I tried this:

1.013E5 Pa = Mg/ pi(6.37E6)^2

1.013E5 Pa (denominator)= 9.8 M

solve for M: I'm coming with different ans from book.

The surface area of a sphere is 4 pi R^2

Thank you so much! What an oversight!!!
Earth is a sphere and not a circle!!!! I have the answer now! It matches that of the book!!!!

You're welcome! I'm glad you realized the oversight. Indeed, Earth is a sphere, so when calculating the total mass of the Earth's atmosphere, we need to use the formula for the surface area of a sphere.

To find the total mass of the Earth's atmosphere, you can use the following steps:

1. First, calculate the surface area of Earth using the formula for the surface area of a sphere:

Surface Area = 4 * pi * R^2

Where R is the radius of the Earth, which is given as 6.37E6 m.

So, Surface Area = 4 * pi * (6.37E6)^2

2. Next, we know that the atmospheric pressure at the surface is given as 1.013E5 N/m^2 (or Pa). This pressure is the force exerted by the atmosphere over a unit area, so we can obtain the total force exerted by the atmosphere by multiplying the pressure by the surface area:

Total Force = Pressure * Surface Area

Total Force = 1.013E5 Pa * Surface Area

3. Now, we need to use Newton's second law of motion, which states that force (F) equals mass (M) multiplied by acceleration due to gravity (g):

Total Force = M * g

The acceleration due to gravity on Earth is approximately 9.8 m/s^2.

Therefore,

M = Total Force / g

4. Finally, substitute the values into the equation to find the total mass of the Earth's atmosphere:

M = (1.013E5 Pa * Surface Area) / g

Calculate the surface area using the given radius, substitute it in the equation, and then divide by the acceleration due to gravity (9.8 m/s^2). That will give you the total mass of the Earth's atmosphere in kilograms.

By following these steps correctly, you should obtain the correct answer that matches the one in the book.