Re: How do we measure planets without having been to them?

The diameter of a planet can be measured if its distance from the earth is 
known. It's based on the idea that the farther an object is, the smaller 
it appears. For instance, a book at arm's length appears to be the size of 
a hand. But across the room it seems as big as a fingernail. The apparent 
width of a planet, a, is measured in "seconds of arc" (one second of an 
arc is 1/3600 of a degree), and its actual diameter, d, can be determined 
by the formula:

d = aD/206 265, where D = distance between planet and earth.

How did astronomers get D?

Well, first they used right-triangle geometry (basic trigonometry) to 
figure out the relative distances between the planets and  the sun. They 
waited for Venus to appear as a half-moon, and measured the angle between 
Venus and the sun. At that point in its orbit, Venus is the 90 degree 
vertex. By measuring the other angle you can figure out the ratio of Venus-
sun distance to that of the earth-sun distance. They did the same thing 
for Mercury, and something slightly more complicated for outer planets 
like Mars , Jupiter and Saturn and obtained very accurate values even by 
today's standards. 

When Cassini came along in the late 1600's, he calculated the actual 
distance to Mars using parallax. This is based on the idea that nearby 
objects seem to move more against their background if you change your 
point of view. Hold your finger in front of your face and stare at it with 
one eye shut. Then without moving your finger, close your other eye and 
open the closed one. The finger seems to move to the left or to the right, 
depending on which eye was opened first. Cassini two different seasons 
(the earth is at tow different positions), and  he measured Mars' apparent 
movement against the background of the stars. This allowed him to get an 
actual distance in miles. Since it was known from trigonometry that it was 
1.5 times as far from the sun as earth was, they just had to divide that 
distance by 1.5 and realized that the earth is 93 000 000 miles from the 
sun. 

Reference: (you may find it tough reading, but if you're still interested 
in astronomy a couple of years from now, it's a great book!)
Universe. Kaufmann, William J.  Freeman. 1985