Is it possible for an orbital "sun shade satellite" to have a geosynchronous equatorial orbit such that it is in an approximately straight line between the Sun and a fixed point on the Earth's equator?
If it is possible, what diameter would the satellite need to have to block all direct sunlight? (I do realise that diffuse sky radiation prevents shadowing.) Obviously, it would need to be 32 arc minutes at apogee, but it may need to be even larger to account for necessary misalignment due to its orbit.
I have looked for online orbital simulators to try this, but was unable to find any that both included the direction of the sun and also allowed tracking a fixed point on the Earth's surface. I envision an elliptical orbit where the satellite has higher orbital velocity in the Earth's shadow to "catch up" and be ready for sunrise at the fixed equatorial point. Something like this:
Sorry for the crude illustration: Yellow shading is sunlight entering from the left. Black dotted line is satellite's orbit. Black vertical bar with white area to the right is the satellite and its shadow. Blue ball with white area to the right is the Earth and its shadow. Red dot is the fixed point on the equator.