Lesson 4: Answers/hints for exercises

  1. Assuming that Earth's equatorial radius is 6370 kilometers, calculate the distance from the equator along any meridian to the North Pole?

    distance = 1/4*2*pi*6370 kilometers or approximately 10001 kilometers
  2. Assuming that the Moon is a sphere with radius 1000 miles, compare its area with that of Earth.

    Area of Moon= 4*pi*1000^2 sq miles or approximately 12560000 sq miles
    Using 3970 miles as radius of Earth, area of Earth = 4*pi*3970^2 or approximately 198000000 square miles. Area of Earth is approximately 16 times that of Moon
  3. Using the assumption in exercise (2.), calculate the circumference of the Moon, i.e. the length of any of its great circles.
    Using 1000 miles as the radius of the moon,
    circumference = 2 * pi * 1000 = approximately 6280 miles
  4. Calculate the area of the portion of the Eastern hemisphere that is bounded by the Greenwich meridian and the meridian with longitude 45°E.
    In the Eastern hemisphere, meridians with longitudes 45°, 90° and 135° divide the hemisphere into four parts of equal area. So the area of the portion described is 1/4 the area of the hemisphere.
    Using radius of Earth = 3970 miles,
    area = (1/4) * (1/2) * 4 * pi * (3970)^2
    = approximately 24,744,613 square miles
  5. Given that the latitude of the city hall of San Francisco is 37° 46'N, calculate the distance of the city hall from the equator in nautical miles, in statute miles, and in kilometers.
    The distance to the equator is measured along a meridian, which is a great circle. So each minute of latutude represents one nautical mile.
    Distance = (number of minutes) nautical miles = 37 * 60 + 46 nautical miles = 2266 nautical miles
    = approximately 2266 (nautical miles)* 1.154 (miles/nautical mile)
    = approximately 2615 miles
    = approximately 2615 (miles) * 1.61 (km/mile)
    = approximately 4210 kilometers
  6. Assuming that the Moon is approximately 240,000 miles from Earth throughout its orbit, calculate the length of its orbit with respect to Earth. With respect to Earth's rotation about the Sun throughout a solar year, why is the Moon's path not a circle or an ellipse?
    The Moon's orbit is elliptical and nearly circular. Using 240,000 as the radius of the circle, length of orbit is approximately 2 * pi * 240,000 miles = approximately 1,507,200 miles

    While the moon's orbit around Earth is nearly circular with respect to Earth's center, the motion of Earth about the Sun causes the Moon's path of orbit to be a spiral that follows Earth's orbit around the Sun.

  7. Describe, in terms of place names, bodies of water, etc., the path on Earth occupied by a
    1. rhumb line from Los Angeles, California to Helsinki, Finland.
      From Los Angeles on a path of constant direction, east by northeast, slightly south of Denver, Colorado; over Detroit, Michigan; across the southern part of Newfoundland; over Glasgow, Scotland; over Stockholm, Sweden; then to Helsinki.
    2. great circle from Los Angeles to Helsinki
      From Los Angeles starting in a direction north by northeast, almost north, and slightly east of Las Vegas, Nevada; over Billings, Montana; diagonally across Sasketchewan, Canada; over the western tip of Hudson Bay, Canada; direction turns south over central Greenland at aproximately 45° west longitude; over Northern Sweden; then to Helsinki.

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Materials developed by-
Wm. Rundberg
College of San Mateo
1700 West Hillsdale Blvd
San Mateo, Ca. 94402
650.574.6258
rundberg@smcccd.cc.ca.us