Recent content by haytil

I'm sorry, I'm not being very clear. The scenario I'm trying to handle is quite simple, I'm just not explaining it right. Let me try again: Imagine a straight line that passes through the point (r1, Θ1) and that the slope of the line at that point is sin(ΘT)/cos(ΘT). What is the value...

It's a simple conversion from polar to cartesian coordinates. The definition of the conversion (I'm sure this is in your textbook) is: x = r * cos Θ y = r * sin Θ However, you're given r as a function of Θ - i.e., r(Θ). So the conversion becomes: x = r(Θ) * cos Θ y = r(Θ) * sin...

In writing a computer raytracing simulation using polar coordinates, I've come across a simple problem: I need to calculate the value of dr/dΘ at an arbitrary point (in polar coordinates), pointing in an arbitrary direction (given as an angle). So if point 1 (p1) is given by the coordinates...

Though this isn't homework (haven't taken a class since I graduated), I checked the homework guidelines. If someone can confirm that this is a problem solvable at the undergraduate level (so then I at least know it can be attained easily), I wouldn't mind the topic being moved to the homework...

I'm trying to find the geodesic between any two points in 3D space, where the geodesic is constrained to a surface defined by z = A / (x^2 + y^2), where A is a constant. I've tried all sorts of variations on the Euler-Lagrange equations (after changing to cylindrical coordinates), but am...

I am interested in solving the null geodesic between two points in the presence of a gravitational mass, assuming that everything takes place in 2 dimensions (i.e., no Z coordinate). The following is known: -x and y coordinates of first point -x and y coordinates of second point -x and y...

I'm interested in the deflection angles of light rays passing by extremely dense gravitational objects, specifically black holes. First, I'd like to find the formula for the deflection angle of an incoming light ray. My googling (as well as a textbook from college, Hartle's "Gravity") states...