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Chapter 4: Problem 21

Why does Venus have its largest angular diameter when it is new and its smallest angular diameter when it is full?

Short Answer

Expert verified
The angular diameter of Venus depends on its distance from Earth, which varies with its orbital phase. In the new phase, Venus is at its closest proximity to Earth, making its angular diameter large. Conversely, in the full phase, Venus is at its furthest from Earth, making its angular diameter smaller.

Step by step solution

01

Understanding Angular Diameter

The angular diameter of a celestial body is the angle between lines sight drawn from the observer to opposite edges of the body. Closer objects have a larger angular diameter as observed from the Earth, as they cover more of our field of view.
02

Venus's Phases and Distance from Earth

As Venus orbits the Sun, it goes through phases just like our Moon, which change its position relative to both Earth and the Sun. When Venus is in its new phase, it is between Earth and the Sun i.e., at its closest approach or inferior conjunction, so from Earth, we see it at its biggest angular size. When Venus is in its full phase, it is on the opposite side of the Sun, at its greatest distance from Earth i.e., in superior conjunction. In this position, we see Venus at its smallest angular size.
03

Drawing the Conclusion

Therefore, Venus has its largest angular diameter when it is new and closest to Earth, and its smallest angular diameter when it is full and farthest from Earth.

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Most popular questions from this chapter

What is an epicycle? How is it important in Ptolemy's explanation of the retrograde motions of the planets?

Imagine a planet like the Earth orbiting a star with 4 times the mass of the Sun. If the semimajor axis of the planet's orbit is \(1 \mathrm{AU}\), what would be the planet's sidereal period? (Hint: Use Newton's form of Kepler's third law. Compared with the case of the Earth orbiting the Sun, by what factor has the quantity \(m_{1}+m_{2}\) changed? Has \(a\) changed? By what factor must \(P^{2}\) change?)

How did the models of Aristarchus and Copernicus explain the retrograde motion of the planets?

It is quite probable that within a few weeks of your reading this chapter one of the planets will be near opposition or greatest eastern elongation, making it readily visible in the evening sky. Select a planet that is at or near such a configuration by searching the World Wide Web or by consulting a reference book, such as the current issue of the Astronomical Almanac or the pamphlet entitled Astronomical Phenomena (both published by the U.S. government). At that configuration, would you expect the planet to be moving rapidly or slowly from night to night against the background stars? Verify your expectations by observing the planet once a week for a month, recording your observations on a star chart.

Suppose that you traveled to a planet with 4 times the mass and 4 times the diameter of the Earth. Would you weigh more or less on that planet than on Earth? By what factor?
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