Flashcards · 7 cards

Longitude & latitude

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Rule
What is latitude?
Answer
The angle at the centre of the earth between a place and the equator, north or south: $0^\circ$ to $90^\circ$ .
Latitude θ: the angle at the centre O between OP and the equator
From the lesson: Latitude, longitude and distances on the earth
Rule
What is longitude?
Answer
The angle east or west of the Greenwich meridian: $0^\circ$ to $180^\circ$ .
Longitude φ: the angle east or west of the Greenwich meridian
From the lesson: Latitude, longitude and distances on the earth
Know it
Two places are at $35^\circ$ E and $25^\circ$ W. What is their difference in longitude?
Answer
$35^\circ + 25^\circ = 60^\circ$ : they are on opposite sides of Greenwich, so add. Same side: subtract.
From the lesson: Latitude, longitude and distances on the earth
Know it
The distance between two places on the same meridian?
Answer
$\dfrac{\text{difference in latitude}}{360} \times 2\pi R$ , where $R$ is the radius of the earth. A meridian is a great circle.
From the lesson: Latitude, longitude and distances on the earth
Know it
The radius of the circle of latitude $\theta$ ?
Answer
$R\cos\theta$ . It gets smaller towards the poles.
From the lesson: Latitude, longitude and distances on the earth
Rule
The distance between two places on the same latitude $\theta$ ?
Answer
$\dfrac{\text{difference in longitude}}{360} \times 2\pi R\cos\theta$ . Only the equator has the full radius $R$ .
Parallels of latitude run east–west and shrink towards the poles; meridians run from pole to pole
From the lesson: Latitude, longitude and distances on the earth
Which method?
WAEC 2013 · Paper 2 · Q12
An aeroplane flies due north from a town $T$ on the equator at a speed of $950\text{ km}$ per hour for 4 hours to another town $P$ . It then flies eastwards to town $Q$ on longitude $65^\circ$ E. If the longitude of $T$ is $15^\circ$ E, (i) represent this information in a diagram; (ii) calculate the: (I) latitude of $P$ , correct to the nearest degree; (II) distance between $P$ and $Q$ , correct to 4 significant figures. $\left[\text{Take }\pi = \frac{22}{7}, \text{ radius of the earth} = 6400\text{ km}\right]$
Flying due north for 4 hours covers 3800 km. How do you find the new latitude?
Answer
Due north is along a meridian, a great circle of radius $R$ : $\dfrac{\theta}{360} \times 2\pi R = 3800$ gives the change in latitude $\theta$ .
From the lesson: Latitude, longitude and distances on the earth Try the question