Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 2: The Rise of Astronomy

Problems

1
A small probe is exploring a spherical asteroid. As the probe creeps over the surface, it drills holes to take soil samples. Scientists on Earth notice that the Sun shines straight down into one of the holes. At the same time, 10 kilometers due "north," the shadow of the vertical antenna on the main landing craft allows the scientists to deduce that the Sun is 15° from directly overhead. What is the radius of the asteroid? How many times smaller or bigger than Earth's is its radius?
2
If the distance between Alexandria and Syene had been 15,000 stadia, what would Eratosthenes have calculated for the circumference and diameter of the Earth?
3
On average, Mercury is 0.387 times Earth's distance from the Sun, and Pluto is 39.53 times Earth's distance from the Sun. If the Sun has an angular diameter of 0.5° as seen from Earth, what is the Sun's angular diameter as seen from Mercury? from Pluto?
4
The great galaxy in Andromeda has an angular diameter along its long axis of about 5°. Its distance is about 2.2 million light-years. What is its linear diameter?
5
Suppose a planet is found with an orbital period of 64 years. How might you estimate its distance from the Sun? If its orbit is circular, what is its radius?
6
In 2003, astronomers discovered Sedna, an object in the outer Solar System with a semimajor axis of 526 AU. What is its orbital period?
7
Suppose a planet orbits a nearby star once every 125 years. If the star is identical to the Sun, how could you find the planet's distance from its star? If the planet's orbit is a perfect circle, how far from the star is the planet in AU?
8
Suppose that future observations with a new telescope reveal a planet about 16 AU from a star whose mass is the same as our Sun's. How long does it take the planet to orbit the star?
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