please i need help with spherical geometry, i missed class lessons bc in hospital ! (1 Viewer)

[adrianforever69]

Hi guys,
I have an assignment over the hols and im really stuck. I missed the lessons (due to being hospitalised- not just waggin or being lazy) on geometry of the earth/ spherical geometry and now im so over my head. I would really really appreciate some help!!

Here are the questions..
(*= degrees)
1. why do the meridians of longitude measure 180* to the East and 180* to the west while the parrallels of latitude measure 90* to North and 90* to the south.

2.in spherical geography what is meant by terms great circle and small circle.

3. City A= paris 49N, 2E
City B= barcelona 41N, 2E
Calculate distance to nearest km between city A and B

4. Two unknown cities E and F lie on the same meridian of longitude. The distance between them is 5800kms.
a) calculatre the angle between cities correct to nearest degree.
b) if city E has a parallel of latitude of 19*N, calculate a possible parallel of latitude for city F.

Any help you can give me would be extemely appreciated.. i really need it

Thanks so much,
Sarah

 

[PC]

Hi guys,
4. Two unknown cities E and F lie on the same meridian of longitude. The distance between them is 5800kms.
a) calculatre the angle between cities correct to nearest degree.
b) if city E has a parallel of latitude of 19*N, calculate a possible parallel of latitude for city F.

(a) Use the arc length formula.
Distance = angle/360 x 2πr
We know the distance and we know the radius of the earth. So:
5800 = (angle/360) x 2 x π x 6400
5800 ÷ (2 x π x 6400) = angle/360
5800 ÷ 40212.38597 = angle/360
0.1442341672 = angle/360
angle = 0.1442341672 x 360
= 51.92430018
= 52°

(b) City F could be north or south of City E.
If City F is north then latitude = 19 + 52 = 71°N
If City F is south then latitude = 19 – 52 = -33 which means 33°S

 

[jason21]

Re: please i need help with spherical geometry, i missed class lessons bc in hospital

1. This is because all circles and spheres add up to 360* (i.e. 180 degrees to the east and 180* to the west = 360*) 90* north of the equator and 90* south of the equator =180* (but this is only one side of the Earth, so multiply by 2) =360*

2. A great circle is all lines of longtitude as they pass through the poles and cover the largest circumference of the Earth. All lines of latitude, except the Equator, are small circles as they do not cover the largest circumference over the surface of the Earth.

3. Both cities lie on the same line of longitude but different line of latitude. 49-41= 8 degrees difference (both cities lie to the North of the equator so you subtract the degrees).
use the Arc length formula- 8/360 2*pi*r

r=6380km

therefore= 893.61km
= 894km

 

[adrianforever69]

Thanks heaps guys really appreciate it