My question is specifically WHY CAN WE NOT USE Radar to measure the distance to the Sun? What is the reason for that? Sorry if this is a lame question, I'm not an expert on these things and just occurred to me why not use radar to measure the distance to the Sun directly rather than go through all the complications of doing it indirectly via Venus and then using trigonometry to work it out. What is the reason for that?
My question is specifically WHY CAN WE NOT USE Radar to measure the distance to the Sun?
By way of analogy, the path of a solar eclipse will cross the United States this summer. People are already being warned not to look directly at the Sun during the eclipse without protection. The reason of course is that looking at a partially eclipsed Sun may cause permanent damage to ones eyes. Most of that damage results from from the Sun's infrared rather than visible output. Just because one cannot see that infrared radiation does not mean it won't hurt you.
The same applies to radio antenna. While radio antenna are typically designed to be insensitive to visible and infrared, an unprotected radio antenna, like an unprotected eye, will suffer irreparable damage when pointed at the Sun.
What about a radio antenna protected by a radome? Those can be and are pointed directly at the Sun. What they see is a large body that radiates at an effective temperature well above the 5778 K of the surface of the Sun. The Sun's chromosphere can have an effective blackbody temperature in the microwave and radio frequencies in the tens of thousands of kelvins, and the solar corona, in the millions of kelvins.
This is particularly the case when the Sun is active, a one to four year long period during the Sun's eleven year solar cycle. Solar scientists aim radome-protected radio antenna directly at the Sun because the deviations from blackbody radiation at 10.7 centimeters are highly correlated with deviations at short wavelengths. Scientists use the Sun's radiation at 10.7 cm as a bellwether of the Sun's activity.
Suppose someone decides to ping the Sun with a radio antenna inside a radome while the Sun is quiet. Even during quiet periods, the Sun still outputs radiation in the microwave and radio frequencies with an effective temperature of nearly 10000 kelvins. The large output from the Sun in the microwave and radio frequencies will overwhelm that little ping, even when the Sun is at its quietest.
Once again by way of analogy, think of pointing a flashlight directly at a street light. Flashlights work great when pointed at a somewhat nearby dark patch of ground. They don't do much at all when pointed at a more remote source of light.
The strength of the radar signal falls rapidly with distance so for objects within the Solar System we are dealing with very faint reflected signals. That isn't a problem with objects like Venus because with suitable signal processing we can extract the radar reflection from the background noise. The problem with the Sun is that it's a (very) strong emitter of radio waves and this black body background completely swamps the radar reflection.