Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 3, Problem 37E
What is the average distance from the Sun (in astronomical units) of a planet with an orbital period of 45.66 years?
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Planet X orbits the star Omega with a "year" that is 492 days long. Planet Y circles Omega at four times the orbital distance of planet X. How many earth days is a year on planet Y? Enter units as d.
A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of
12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU
..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.]
Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer
was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]
(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.
Chapter 3 Solutions
Astronomy
Ch. 3 - State Kepler’s three laws in your own words.Ch. 3 - Why did Kepler need Tycho Brahe’s data to...Ch. 3 - Which has more mass: an armful of feathers or an...Ch. 3 - Explain how Kepler was able to find a relationship...Ch. 3 - Write out Newton’s three laws of motion in terms...Ch. 3 - Which major planet has the largest . . . A....Ch. 3 - Why do we say that Neptune was the first planet to...Ch. 3 - Why was Brahe reluctant to provide Kepler with all...Ch. 3 - According to Kepler’s second law, where in a...Ch. 3 - The gas pedal, the brakes, and the steering wheel...
Ch. 3 - Explain how a rocket can propel itself using...Ch. 3 - A certain material has a mass of 565 g while...Ch. 3 - To calculate the momentum of an object, which...Ch. 3 - To calculate the angular momentum of an object,...Ch. 3 - What was the great insight Newton had regarding...Ch. 3 - Which of these properties of an object best...Ch. 3 - Pluto’s orbit is more eccentric than any of the...Ch. 3 - Why is Tycho Brahe often called “the greatest...Ch. 3 - Is it possible to escape the force of gravity by...Ch. 3 - What is the momentum of an object whose velocity...Ch. 3 - Evil space aliens drop you and your fellow...Ch. 3 - A body moves in a perfectly circular path at...Ch. 3 - As friction with our atmosphere causes a satellite...Ch. 3 - Use a history book, an encyclopedia, or the...Ch. 3 - Two asteroids begin to gravitationally attract one...Ch. 3 - How does the mass of an astronaut change when she...Ch. 3 - If there is gravity where the International Space...Ch. 3 - Compare the density, weight, mass, and volume of a...Ch. 3 - If identical spacecraft were orbiting Mars and...Ch. 3 - By what factor would a person’s weight be...Ch. 3 - Suppose astronomers find an earthlike planet that...Ch. 3 - What is the semimajor axis of a circle of diameter...Ch. 3 - If 24 g of material fills a cube 2 cm on a side,...Ch. 3 - If 128 g of material is in the shape of a brick 2...Ch. 3 - If the major axis of an ellipse is 16 cm, what is...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - In 1996, astronomers discovered an icy object...
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- Mars has an orbital radius of 1.523 AU and an orbital period of 687.0 days. What is its average speed v in SI units? (1 AU is the astronomical unit, the mean distance between the Sun and the Earth, which is 1.496×1011 m) a. 0.00221 AU/day b. 3838 m/s c. 0 d. 1.28×10−9 m/sarrow_forwardA planet revolves around a star at a distance of 88.5 x 1016 m away from it in a circular orbit. How much distance it travels in half a cycle around that star? Note: Write your answer in scientific representation with two decimal palces. Answer:arrow_forwardThe solar system has a planet with an orbital period T1b=1.51d and an orbital radius of R1b=1.6456x10^6km. Another planet in the system has an orbital radius of R1f=5.5352x10^6 km. Calculate its orbital period in days.arrow_forward
- 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.arrow_forwardConsider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?arrow_forwardOn the surface of the Moon an astronaut has a weight of Fg = 190 N. The radius of the Moon is Rm = 1.74 × 106 m, the gravitational constant is G = 6.67 × 10-11 N (m/kg)2 and the mass of the Moon is Mm = 7.35 × 1022 kg. Calculate the mass of the astronaut, m, in kilograms.arrow_forward
- According to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is approximately 3.82 x 105 km. The Moon orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month). Calculate the orbital velocity of the Moon in m/s.arrow_forwardThe mass of Mars is 6.42 × 10^23 kg. Its moon Phobos is 9.378 x 10^6 meters away from Mars, with a mass of 1.06 × 10^16 kg and a period of 7.66 hours. It's moon Deimos has a mass of 1.4762x10^15 kg and a period of 30.3 hours. a) Use Kepler's 3rd law to determine the orbital distance between Mars and Deimos? b) What is the tangential velocity of Phobos, using the formula v (tangential) = sqrt (G x m(central)/ r)? c) What is the gravitational force of attraction between Mars and Phobos.arrow_forwardOn the evening of an autumnal equinox day Siddhant noticed that Mars was exactly along the north-south meridian in his sky at the exact moment when the sun was setting. In other words, the Sun and Mars subtended an angle of exactly 90° as measured from the Earth. If the orbital radius of Mars is 1.52 au, What will be the approximate rise time of the mars on the next autumnal equinox day?arrow_forward
- A comet (see the figure below) approaches the Sun to within 0.570 AU, and its orbital period is 79.6 yr. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean Earth-Sun distance.) How far from the Sun will the comet travel before it starts its return journey?arrow_forwardThe periods of two satellites of Saturn is P,=16 days and P2=2 days around the planet. What is the ratio of the distances (d/d,) of the two moons from the planet ? 1Xarrow_forwardAccording to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is approximately 3.92 x 105 km. The Moon orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month). Calculate the orbital velocity of the Moon in m/s. Answer: Choose...arrow_forward
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