Example

Both Torrens Creek (Queensland) and Kyabram (Victoria) are on the ${145^{\circ}}$ E meridian of longitude, but Torrens Creek is at ${20.77^{\circ}}$ S whereas Kyabram is at ${36.32^{\circ}}$ S

How far is it from Torrens Creek to Kyabram travelling along the ${145^{\circ}}$ E meridian, correct to the nearest km?

Solution

Each meridian is a great circle, with a radius of 6400 km.

The angle between the latitude of Torrens Creek and that of Kyabram is ${36.32^{\circ}}$ - ${20.77^{\circ}}$ = ${15.55^{\circ}}$.

(We find the difference since both places are on the same side of the Equator!)

From Torrens Creek to Kyabram

\begin{align*} l &=\frac{r\pi}{180^{\circ}}\times\theta\\ &=\frac{6400\pi}{180^{\circ}}\times 15.55^{\circ}\\ &=1736.95\ldots\\ &\approx 1737\text{ km} \end{align*}

Example

Both Cooktown (Queensland) and Kyabram (Victoria) are on the ${145^{\circ}}$ E meridian of longitude, but Cooktown is at ${15.47^{\circ}}$ S whereas Kyabram is at ${36.32^{\circ}}$ S.

How far is it from Cooktown to Kyabram travelling along the ${145^{\circ}}$ E meridian, correct to the nearest km?

Solution

Each meridian is a great circle, with a radius of 6400 km.

The angle between the latitude of Cooktown and that of Kyabram is ${36.32^{\circ}}$ - ${15.47^{\circ}}$ = ${20.85^{\circ}}$.

(We find the difference since both places are on the same side of the Equator!)

From Cooktown to Kyabram

\begin{align*} l &=\frac{r\pi}{180^{\circ}}\times\theta\\ &=\frac{6400\pi}{180^{\circ}}\times 20.85^{\circ}\\ &=2328.967\ldots\\ &\approx 2329\text{ km} \end{align*}

Example

Both Broken Hill (NSW) and Morioka (Japan) are on the ${141^{\circ}}$ E meridian of longitude, but Broken Hill is at ${31.95^{\circ}}$ S whereas Morioka is at ${39.70^{\circ}}$ N.

How far is it from Broken Hill to Morioka travelling along the ${141^{\circ}}$ E meridian, correct to the nearest km?

Solution

Each meridian is a great circle, with a radius of 6400 km.

The angle between the latitude of Broken Hill and that of Morioka is ${31.95^{\circ}}$ + ${39.70^{\circ}}$ = ${71.65^{\circ}}$.

(We find the sum since both places are on different sides of the Equator!)

From Broken Hill to Morioka

\begin{align*} l &=\frac{r\pi}{180^{\circ}}\times\theta\\ &=\frac{6400\pi}{180^{\circ}}\times 71.65^{\circ}\\ &=8003.31\ldots\\ &\approx 8003\text{ km} \end{align*}

Example

Both Shellharbour (NSW) and Magadan (Russia) are on the ${151^{\circ}}$ E meridian of longitude, but Shellharbour is at ${34.58^{\circ}}$ S whereas Magadan is at ${59.57^{\circ}}$ N.

How far is it from Shellharbour to Magadan travelling along the ${151^{\circ}}$ E meridian, correct to the nearest km?

Solution

Each meridian is a great circle, with a radius of 6400 km.

The angle between the latitude of Shellharbour and that of Magadan is ${34.58^{\circ}}$ + ${59.57^{\circ}}$ = ${94.15^{\circ}}$.

(We find the sum since both places are on different sides of the Equator!)

From Shellharbour to Magadan

\begin{align*} l &=\frac{r\pi}{180^{\circ}}\times\theta\\ &=\frac{6400\pi}{180^{\circ}}\times 94.15^{\circ}\\ &=10 516.655\ldots\\ &\approx 10 517\text{ km} \end{align*}

Example

Both Perth (WA) and Baoding (China) are on the ${115^{\circ}}$ E meridian of longitude, but Perth is at ${31.93^{\circ}}$ S whereas Baoding is at ${38.78^{\circ}}$ N.

How far is it from Perth to Baoding travelling along the ${115^{\circ}}$ E meridian, correct to the nearest km?

Solution

Each meridian is a great circle, with a radius of 6400 km.

The angle between the latitude of Perth and that of Baoding is ${31.93^{\circ}}$ + ${38.78^{\circ}}$ = ${70.71^{\circ}}$.

(We find the sum since both places are on different sides of the Equator!)

From Perth to Baoding

\begin{align*} l &=\frac{r\pi}{180^{\circ}}\times\theta\\ &=\frac{6400\pi}{180^{\circ}}\times 70.71^{\circ}\\ &=7898.38\ldots\\ &\approx 7898\text{ km} \end{align*}