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Chapter 2: Problem 33

Using a protractor, you estimate an angle of \(40^{\circ}\) between your zenith and Polaris. What is the altitude of Polaris? What is your latitude? Are you in the continental United States or Canada?

Short Answer

Expert verified
The altitude of Polaris is \( 40^{\text{°}} \). Your latitude is \( 40^{\text{°}} \), which means you are in the continental United States.

Step by step solution

01

Understand the Angle Measurement

The angle measured between the zenith (the point directly overhead) and Polaris (the North Star) is given as \(40^{\text{°}}\). This angle is also known as the altitude of Polaris.
02

Altitude of Polaris

The altitude of Polaris is the same as the angle measured between the zenith and Polaris. Therefore, in this case, the altitude of Polaris is \(40^{\text{°}}\).
03

Determine Your Latitude

In the Northern Hemisphere, the altitude of Polaris above the horizon is approximately equal to your latitude. Therefore, the latitude is also \(40^{\text{°}}\).
04

Identify the Location

Check if the latitude of \(40^{\text{°}}\) falls within the continental United States or Canada. The latitude \(40^{\text{°}}\) is within the range of the continental United States, specifically spanning from approximately \(24^{\text{°}}\) to \(49^{\text{°}}\) N. Hence, you are in the continental United States.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Zenith
The zenith is the point in the sky that is directly above you, no matter where you are standing on the Earth's surface. Imagine a line going from your head straight up to the sky—where this line ends, that's your zenith. It is a fixed point that moves as you move. This concept is crucial in astronomy for measuring angles and locating objects in the sky.
Polaris
Polaris, also known as the North Star, is a star located nearly directly above the North Pole of the Earth. One of its most significant characteristics is that it remains relatively fixed in the sky compared to other stars, making it an excellent reference point for navigation. In the Northern Hemisphere, you can always find Polaris by looking almost due north. The altitude of Polaris (its angle above the horizon) is equal to the latitude of the observer, making it a useful tool for determining one's geographical location.
Latitude
Latitude refers to the measure of how far north or south you are from the Equator, which is the imaginary line that runs around the Earth’s middle. Latitude is measured in degrees, with the Equator at 0° and the North and South Poles at 90°N and 90°S, respectively. For instance, if the altitude of Polaris where you are standing is 40°, your latitude is 40°N. This concept is used extensively in navigation, cartography, and geography to pinpoint exact locations on Earth.

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Most popular questions from this chapter

If people on Earth were observing a lunar eclipse, what would you see from the Moon?

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