The second part of this question is much easier to answer than the first. We will definitely get a different number for Eris’ size once a spacecraft visits it. Spacecraft measurements can be thousands of times better than measurements from Earth. The proximity means we don’t have to make as many assumptions. For example, New Horizons passed within 7,800 miles (12,500 kilometers) of Pluto’s surface on July 14, 2015, giving us the best-ever view of Pluto. Spacecraft imagery puts Pluto’s diameter at 1,474 miles (2,372 km). From Earth, about 5 billion miles away, the dwarf planet’s diameter was estimated to be 1,471 miles (2,368 km) by studying Pluto’s atmospheric haze as it passed in front of a distant star. This is not an easy thing to do, but it did result in a very accurate answer — yet different nonetheless from the spacecraft number.
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