Longitude problem on a Terrestrial Sphere

In summary, the distance between two points on the equator with a difference of 1 degree in longitude is approximately 69.8 miles, assuming a radius of the Earth as 3959 miles. However, this value may vary slightly depending on the exact radius used.
  • #1
Equilibrium
82
0

Homework Statement


How far apart (in miles) are 2 points on the equator if their longitudes differ by 1 degree?
The correct answer is 69.8 miles, I'm not sure if typo

Homework Equations


[tex]S=r\theta[/tex]
radius of Earth = 3959 miles

The Attempt at a Solution


[tex]\theta = 1\deg*\frac{\pi}{180}[/tex]
[tex]S=3959*\frac{\pi}{180}[/tex]
[tex]S = 69.1 miles[/tex]
 
Physics news on Phys.org
  • #2
Nothing wrong with your working, except that you should be more clear that you're starting by converting theta into radian measure. But your answer is right.

The difference could be because of the value you're supposed to use for the Earth's equatorial (great circle) radius. Are you given a value you're supposed to use?

The value you quoted looks quite OK, but google's is slightly different: 3 963.1676 miles, and yields a slightly different answer (69.2mi, still closer to yours than the expected one).
 
  • #3
thanks for verifying
 

1. What is the longitude problem on a terrestrial sphere?

The longitude problem on a terrestrial sphere refers to the difficulty in accurately determining the longitude of a specific location on the Earth's surface. It is the counterpart to the latitude problem, which involves determining the north-south position of a location.

2. Why is the longitude problem important?

The accurate measurement of longitude is crucial for navigation, cartography, and scientific research. It allows us to accurately map the Earth's surface and determine the exact location of a place, which is essential for things like air and sea travel, global trade, and disaster management.

3. How was the longitude problem solved?

The longitude problem was solved through the development of various methods and instruments, such as the marine chronometer, lunar distance method, and satellite-based systems like GPS. These methods rely on precise timekeeping, astronomical observations, and advanced technology to accurately determine longitude.

4. What challenges did scientists face in solving the longitude problem?

Scientists faced many challenges in solving the longitude problem, including the need for accurate timekeeping, the difficulty of making precise astronomical observations at sea, and the high cost of developing and using advanced instruments. It also required a significant amount of collaborative effort and trial and error before an accurate solution was found.

5. Is the longitude problem completely solved today?

While the longitude problem has been solved to a large extent, there is still ongoing research and development to improve the accuracy and efficiency of longitude determination. New technologies and methods continue to be developed, and there may always be room for improvement in this area of study.

Similar threads

Replies
18
Views
3K
  • Precalculus Mathematics Homework Help
Replies
7
Views
2K
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
399
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • Precalculus Mathematics Homework Help
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
3K
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
562
Back
Top