Specify enity's path width in meters

I’m using Cesium to display the path of a space object, appearing on the ground. The satellite’s position is stored as a SamplePositionProperty.
To visualize the path I created an Entity that has the satellite’s position, but clamped to the ground. And I add the path like this:

         width: getPathWidth(),  
         material: Color.fromAlpha(Color.CHARTREUSE, 0.4),
         trailTime: duration,
         leadTime: 0

The problem is that I need to specify the path width in meters. I’ve tried using CorridorGraphics and RectanglesGraphics, but they are much slower (I render dozens of satellites).
My current option includes calculating the path width in pixels in an approximate formula that relies on the current camera’s height (zoom):

    const metersToPathWidth = (meters: number) => {
            return meters * 1580 / scene.camera.positionCartographic.height;

But that solution is clearly wonky and inaccurate. It works about right but the value depends on the current window size (in the browser). Is there any other way I can solve my problem?