Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 21, Problem 24E
Kepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun
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Two exoplanets, UCF1.01 and UCF1.02 are found revolving around the same star. The period of planet UCF1.01 is 92.4 days, and that of planet UCF1.02 is 7.1 days.
If the average distance of UCF1.01 to the sun is 5,828.0 km, what is the average distance of UCF1.02 to the sun in km? Please keep four digits after decimal points.
(a)
Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result.
aIo = AU
(b)
One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result.
PIo = yr
(c)
Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result.
MJup(Io) = MSun
(d)
Based on this result, Jupiter's mass is about that of the Sun.
Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.
O Jupiter's third-largest natural satellite, lo, follows an
orbit with a semimajor axis of 422,000 km (4.22 × 105
km) and a period of 1.77 Earth days (Plo = 1.77 d). To
use Kepler's Third Law, we first must convert lo's orbital
semimajor axis to astronomical units. One AU equals
150 million km (1 AU = 1.50 x 108 km). Convert lo's a
value to AU and record the result.
alo =
AU
Chapter 21 Solutions
Astronomy
Ch. 21 - Give several reasons the Orion molecular cloud is...Ch. 21 - Why is star formation more likely to occur in cold...Ch. 21 - Why have we learned a lot about star formation...Ch. 21 - Describe what happens when a star forms. Begin...Ch. 21 - Describe how the T Tauri star stage in the life of...Ch. 21 - Look at the four stages shown in Figure 21.8. In...Ch. 21 - The evolutionary track for a star of 1 solar mass...Ch. 21 - Two protostars, one 10 times the mass of the Sun...Ch. 21 - Compare the scale (size) of a typical dusty disk...Ch. 21 - Why is it so hard to see planets around other...
Ch. 21 - Why did it take astronomers until 1995 to discover...Ch. 21 - Which types of planets are most easily detected by...Ch. 21 - List three ways in which the exoplanets we have...Ch. 21 - List any similarities between discovered...Ch. 21 - What revisions to the theory of planet formation...Ch. 21 - Why are young Jupiters easier to see with direct...Ch. 21 - A friend of yours who did not do well in her...Ch. 21 - Observations suggest that it takes more than 3...Ch. 21 - Suppose you wanted to observe a planet around...Ch. 21 - Why were giant planets close to their stars the...Ch. 21 - Exoplanets in eccentric orbits experience large...Ch. 21 - When astronomers found the first giant planets...Ch. 21 - An exoplanetary system has two known planets....Ch. 21 - Kepler’s third law says that the orbital period...Ch. 21 - Calculate the transit depth for an M dwarf star...Ch. 21 - If a transit depth of 0.00001 can be detected with...Ch. 21 - What fraction of gas giant planets seems to have...
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