posted by .

How many parallels of latitude have a radius of 2500km?

  • Maths -

    Assuming the earth is a perfect sphere, and with a radius of 6400 km, there are exactly two parallels with a radius of 2500 km, located at approximately
    =67° N or S.

  • Maths -

    Show that the points (20°N,20°E) and (60°N,160°W) lie on the same great circle.Find their great circle distance apart.

  • Maths -

    There is at least one great circle that passes through any two non-coincident points lying on a sphere.

    If the two points are diametrically located, there is an infinite number of great circles that pass through the two points.

    The proof is relatively simple. The two points and the centre of the sphere form a plane that bisects the sphere into two hemispheres.

    As for the distance, we are into spherical trigonometry.
    There are various formulas to calculate the central angle subtended at the centre. The great circle distance is therefore the radius multiplied by this angle (in radians).

    There are three formulas
    1. spherical cosine formula.
    This formula does not apply to small distances between the two points (say less than 10 km) because numerical round-off errors are magnified by the difference of cosine of small angles.
    2. Haversine formula works well for almost all cases except for points which are, or almost, diametrically placed (which is our case in point).
    3. A more complicated formula applies to all cases, and that's the Vincenty formula.

    Here are the results, using R=6371 km.
    (1) 11119.49 km
    (2) 9623.09 km (rejected)
    (3) 11119.49 km

    The respective formulas are, using
    R=radius of the earth (assumed a sphere)
    p1=latitude of point 1 (radians)
    p2=latitude of point 2 (radians)
    L =difference in longitude of the two points (in radians)
    D=great circle distance


Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Social Studies

    1. What countries/continents are included in the Americas?
  2. science

    what are 4 countries found on the equator and their locations?
  3. geometry

    The towns A and B are on the circle of latitude 24 degrees N.The longitude of A is 108degrees E and longitude B is 75 degrees E. a. Calculate the radius of the circle of latitude 24 degrees N. b.The shortest distance between A and …
  4. Maths

    A geographical globe has a radius of 18cm.find the radius of the circleformed by the parallel of latitude 56 degrees south.
  5. Maths

    A geographical globe has a radius of 18cm.find the radius of the circleformed by the parallel of latitude 56 degrees south.
  6. Maths

    An aeroplane leaves a point on latitude 54degree south at 10 a.m. It flies due south at a steady speed of 800km/h. (a) what is its latitude at mid-point?
  7. Geometry

    find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (one city is due north of the other) Dallas, Texas Latitude: 32* 47' 39" Omaha, Nebraska Latitude: …
  8. Geology

    (Magnetic inclination vs. latitude graph). Two igneous rocks crystallized at different times at the same geographic location on a continent. One rock crystallized at 120 Ma and records a magnetic inclination of 68 degrees; the second …
  9. Maths

    The speed of a point A due to the rotation of the earth is twice that of a point B.If A is on latitude 22°N.calculate the latitude of B
  10. Maths

    An aeroplane leaves a point on latitude 54°S at 10 flies due south at a steady speed at 800km/h. (a)what is the latitude at mid-day(b) At what time does it pass over the south pole

More Similar Questions