As the force field is centered on the sun, the earth is displaced from its center by 8.33 light-minutes. This means, the closest point to Earth is at a distance
[tex]d = radius - displacement[/tex]
When the sphere is placed, the light that is inside the sphere must reach Earth before we can observe the light from the stars being blocked. So, from the closest point, the light must travel:
[tex]d = 6 light-hours - 8.33 light-minutes[/tex]
[tex]d = 6 light-hours - 8.33 light-minutes[/tex]
[tex]d = 5 light-hours + 51 light-minutes + 40.2 light-seconds[/tex]
So, if the sphere is placed at 9 pm, this must mean the opaque sphere starts to appear at 2:51:40.2 am of the following day.
The sphere wont appear all at one, as the earth is at different distance for different points.
The farthest point from earth is at :
[tex]d = radius + displacement[/tex]
[tex]d = 6 light-hours + 8.33 light-minutes[/tex]
This means, that it will be observed blocking light at 3:08:19.8 am of the following day.
Between this two events, it will appear that from the closest point a sphere grows enlarging, wrapping earth in the process.