The location of the orbiting object at the current time t is located in the plane using vector calculus in polar coordinates both with the standard Euclidean basis and with the polar basis with the origin coinciding with the center of force. Let r be the distance between the object and the center and θ θ be the angle it has rotated. Let x ^ ^ and y ^ ^ be the standard Euclidean bases and let r ^ ^ = cos ⁡ ⁡ ( θ θ ) x ^ ^ + sin ⁡ ⁡ ( θ θ ) y ^ ^ and θ θ ^ ^ = − − sin ⁡ ⁡ ( θ θ ) x ^ ^ + cos ⁡ ⁡ ( θ θ ) y ^ ^ be the radial and transverse polar basis with the first being the unit vector pointing from the central body to the current location of the orbiting object and the second being the orthogonal unit vector pointing in the direction that the orbiting object would travel if orbiting in a counter clockwise circle. Then the vector to the orbiting object is