How was the mass of Venus determined? The mass of Venus seems rather complicated to determine to me:

Venus doesn't have any satellites, so you can't just apply Kepler's third law (like you would with Jupiter or Saturn for instance) to determine its mass.
The gravitational tug of Venus on the Sun is very small compared to that of other Jupiter or Saturn, so it seems like it would be difficult to extract what part of the Sun's proper motion is caused by Venus.
There are few asteroids with orbits close to that of Venus, so not many objects who might have their trajectory modified by Venus.

Knowing Venus' radius, and assuming it has the same density as the Earth, you can get a pretty close estimate of its mass (85% of Earth's mass with this assumption, when the actual value is 82%). But that's a pretty strong assumption (the density of Earth and Venus only happen to be close by chance) and a rather unsatisfactory &quot;guesstimate&quot;.
Nowdays, there are a few probes that have flown by Venus, so by looking at their trajectory, you can infer what Venus' gravitational field looks like. But those fly-bys are pretty recent. Did we know about Venus' mass before those fly-bys?
How was the mass of Venus measured for the first time?
How was the mass of Venus measured for the first time?

In the mid 19th century, Urbain Le Verrier's predicted of the existence of a then unknown planet beyond the orbit of Uranus. He even predicted this planet's orbit. The discovery of Neptune based on his predictions was perhaps his greatest accomplishment.
Le Verrier then went on to investigate Mercury. He used observations of Mercury, Venus, the Sun (as a stand-in for the Earth) and Mars and calculated that Mercury should precess by 532 arc seconds per century based on Newtonian mechanics. Along the way, he had to (and did) estimate the mass of Venus. There was a problem here; the observed precession of Mercury's orbit is 575 arc seconds per century, 43 arc seconds per century greater than his calculated value. This led Le Verrier to conjecture that there was a planet even closer to the Sun than Mercury.
Despite the failure to discover the non-existent planet tentatively named Vulcan, Le Verrier's estimate for the mass of Venus was fairly close to the correct figure, within a couple of percent. Once the cause of this 43 arc second per century discrepancy was discovered by Einstein, the mass of Venus was determined with even greater accuracy. Of course, once probes were sent into orbit about Venus, its mass was determined with greater accuracy yet.
Reference:
Leverrier, M. &quot;On the masses of the planets, and the parallax of the Sun.&quot; Monthly Notices of the Royal Astronomical Society 32 (1872): 322.