Using $L=mvr$ and conservation of angular momentum, if the radius is halved then the velocity must be doubled and vice versa. But in the case of planetary orbits, this is not the case.
To take the example of the earth orbiting the sun, if the distance is doubled and accounting for constant mass and angular momentum, then the velocity should half which is around 15km/s. But it actually turns out to be closer to 21km/s. This is dividing the initial velocity by the square root of 2 rather than 2.
Why is this?