How Do You Solve a Math Problem Using Spherical Coordinates?

[ThomasHW]

Homework Statement

http://tunerspec.ca/school/problem2.gif


I really have no idea where to start. Any help would be much appreciated.

 

[D H]

The problem asks you to use the dot product. A good place to start would be to express the points P and Q in cartesian coordinates so you can use the dot product.

 

[Meir Achuz]

The distance is R*theta/360, where cos(theta)=P.Q
Put P and Q into spherical coordinates and find the dot product to get cos(theta).

 

[ThomasHW]

I'm just not understanding how to use the angles, as I've only ever used metres, Newtons, etc.

Could you possibly show me how?

 

[Sourabh N]

I hope you know how to calculate dot product for two vectors. You can write P and Q in vector form and then in spherical form( this wiki article may help you - http://en.wikipedia.org/wiki/Spherical_coordinates ) and calculate the dot product.

 

[ThomasHW]

I know how to calculate a dot product, but I don't understand how I'm supposed to do it with four angles...

 

[D H]

What four angles? All you have two worry about is the angle between the two vectors from the center of the center of the Earth to each of the points P and Q.

 

[ThomasHW]

What four angles? All you have two worry about is the angle between the two vectors from the center of the center of the Earth to each of the points P and Q.

The two longitude's and the two latitude's...

I'm not seeing how you can use the dot product with four angles...

 

[D H]

The latitude and longitude of some point on the Earth's surface together with the Earth's radius are just the spherical coordinates of the point. Certainly you have been taught something about spherical coordinates ...

 

[ThomasHW]

No, we haven't. Either our professor is assuming we've been taught this before... or... I'm not sure.

That is why I really don't understand this question.

 

[dontdisturbmycircles]

Naw we haven't learned about spherical coordinates D H (I am doing same assignment as Thomas)

Draw out one of the vectors, the angles they supply are enough to determine the x y and z coordinates of each point. (P and Q)

 

[dontdisturbmycircles]

I haven't worked with spherical coords either but once you get the angle between P and Q and you know the radius, you can find the arc length.

 

[Sourabh N]

Read the wiki article. There 3 space coordinates are expressed in spherical coordinate form. Each vector is represented in terms of its latitude and longitude.