What Is Latitude?

If I was flying in an airplane going 700mph at what latitude would I have to b to keep up with the setting sun?

• If I was flying in an airplane traveling 700mph, at what latitude would I have to be to keep up with the setting sun? Given- At the equator, latitude of 0 the earth is spinning at 1,000mph The circumference of the earth at the equator is 25,000ft At the poles, Latitude 90 the earth is spinning say 0 What are the equations involved in this answer and how did you figure it out?

• Answer:

  First a correction for you... We can take the circumference of the Earth ot be 25,000 MILES at the equator however you don't really need this to figure out your answer. Also to understand what is happening in your problem think of angular velocity and linear velocity. The Earth rotates with a constant angular velocity but the linear velocity of a point on the surface does vary in the manner you have described. The relationship used to find the Linear Velocity of a point at a given latitude can be easily determined via trigonometry. Here's a quick way... the velocity is at a maximum at latitude zero and a minimum at latitude 90. What simple trig function varies in that manner?....' cosine. So we have linear velocity varies as the cosine of the latitude. Take your approximate values and solve for inverse cosine: you'll get 700/1000 = 0.7 = cos(lat) or lat = 45.57 degrees Or we could have stated "around 45 degrees of latitude" from the beginning because we know cosine (45) is 0.707 So we have that somewhere very close to 45 degrees of latitude, if your 'ground speed' in the airplane is 700 MPH, it should inturn keep you stationary with respect to the Sun (if you are flying True West!)