This is all well and good, but we want absolute distances! so,

How to measure the Astronomical Unit

Method #1: Transits of Venus

• Rare events, happen twice a century.
• Observe transit from two different latitudes on Earth, seperated by B.
• Measure angular difference between transit lines.

• Geometry of similar triangles:

• This gives the linear size of Sun (diameter=1,400,000km)
• Know the angular size (0.5 degree)
• Get distance

Method #2: Radar Echoing of Venus

• Bounce a radar signal off Venus; travel time gives distance.
• Use trig to calculate Earth-Sun distance:

Now that we have absolute distances, we can compute:

• size of objects

• masses of objects (with the help of Kepler's laws), ie the Sun:

• densities of objects