Chapter 15.8, Problem 44E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A model for the density δ of the earth’s atmosphere near its surface is δ = 619.09 - 0.000097*ρ* where *ρ* (the distance from the center of the earth) is measured in meters and δ is measured in kilograms per cubic meter. If we take the surface of the earth to be a sphere with radius 6370 km, then this model is a reasonable one for 6.370 × 10^{6}
*ρ*
^{6}. Use this model to estimate the mass of the atmosphere between the ground and an altitude of 5 km.

To determine

**To estimate:** The mass of the atmosphere between the ground and an altitude of 5 km

Explanation

**Formula used:**

If
*E* given by

If
*z* then,

The spherical coordinates

**Given:**

The density model of the earth’s atmosphere is

Earth is of sphere in shape with radius 6370 km and

**Calculation:**

From the given condition, it is observed that

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