<p>This is hardly an astronomy question, but I like drawing, so here you are:</p>

<p><img src="https://i.sstatic.net/1cGfH.png" alt="Earth from above"></p>

<p>Longitudes are measured from the Greenwich meridian, so the angle between Kampala and Quito is
$$\theta_\mathrm{Q} + \theta_\mathrm{K} = 82.5^\circ + 37.5^\circ = 110^\circ.$$
(remember that $0^\circ30' = 0.5^\circ$).
The shortest surface path is along Equator. Since $110^\circ$ is $\frac{110^\circ}{360^\circ} \simeq 0.3$ times the <a href="https://www.google.dk/#q=circumference+of+Earth+at+Equator" rel="nofollow noreferrer">circumference of Earth at Equator</a>, the length of path A (the dashed line) is
$$\mathrm{A}:\,\,d = 0.3 \times 40,075\,\mathrm{km} = 12,245\,\mathrm{km}$$</p>

<p>For path B (the solid line), you need a bit more  trigonometry. The radius of Earth is $R = 40,075\,\mathrm{km}\,/\,2\pi = 6,378\,\mathrm{km}$. The rest will be left as an exercise.</p>

CC BY-SA 3.0
2015-04-13T09:17:20.373Z
Strange mixture of significant figures. The radius to match the circumference you have used is 6378 km.
ProfRob
CC BY-SA 3.0
2015-04-13T10:38:36.143Z
@RobJeffries: That's because the 6371 km is an "average" over the whole Earth. At the equator, it is [6378 km](http://en.wikipedia.org/wiki/Earth_radius#Equatorial_radius), as you say. Thanks for pointing that out, I'll fix it.
pela
CC BY-SA 3.0
2015-04-13T09:00:10.070Z
2015-04-13T10:41:01.570Z
2015-04-13T10:41:01.570Z
pela
<p>Both Quito and Kampala lie on the Equator. The longitude of Quito is 82°30'W and that of Kampala is 37°30'E. What is the distance from Quito to Kampala?
A) along the shortest surface path
B) along a direct through the Earth path?
Please help me visualize it with a figure. How to do it?</p>

<earth><distances>
What is the distance between 2 cities?
1234567890
# What is the distance between 2 cities?

(Asked by: username_0 on 2015-04-13)

Both Quito and Kampala lie on the Equator. The longitude of Quito is 82°30'W and that of Kampala is 37°30'E. What is the distance from Quito to Kampala?
A) along the shortest surface path
B) along a direct through the Earth path?
Please help me visualize it with a figure. How to do it?

**Tags:** earth, distances


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## 1 answers

### Answer by username_1 on 2015-04-13. Score: 2 | Accepted answer

This is hardly an astronomy question, but I like drawing, so here you are:

![Earth from above](https://i.sstatic.net/1cGfH.png)

Longitudes are measured from the Greenwich meridian, so the angle between Kampala and Quito is
$$\theta\_\mathrm{Q} + \theta\_\mathrm{K} = 82.5^\circ + 37.5^\circ = 110^\circ.$$
(remember that $0^\circ30' = 0.5^\circ$).
The shortest surface path is along Equator. Since $110^\circ$ is $\frac{110^\circ}{360^\circ} \simeq 0.3$ times the [circumference of Earth at Equator](https://www.google.dk/#q=circumference+of+Earth+at+Equator), the length of path A (the dashed line) is
$$\mathrm{A}:\,\,d = 0.3 \times 40,075\,\mathrm{km} = 12,245\,\mathrm{km}$$

For path B (the solid line), you need a bit more trigonometry. The radius of Earth is $R = 40,075\,\mathrm{km}\,/\,2\pi = 6,378\,\mathrm{km}$. The rest will be left as an exercise.

> **Comments:**
> **username_2**: Strange mixture of significant figures. The radius to match the circumference you have used is 6378 km.  
> **username_1**: @RobJeffries: That's because the 6371 km is an "average" over the whole Earth. At the equator, it is [6378 km](http://en.wikipedia.org/wiki/Earth_radius#Equatorial_radius), as you say. Thanks for pointing that out, I'll fix it.  

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