EBK UNDERSTANDING OUR UNIVERSE (THIRD E
3rd Edition
ISBN: 9780393631760
Author: Blumenthal
Publisher: VST
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Chapter 3, Problem 38QAP
To determine
The given statement is correct or incorrect.
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(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.
The table below illustrates data on Kepler's 3rd Law for the first six planets.
Use it to estimate the semi-major axis of the object Hathor 2340 which has an orbital period of 0.77 years
p (years) p2
a3 a (AU)
Mercury
0.24
0.058 0.058
0.39
Venus
0.62
0.38
0.38
0.72
Earth
1.00
1.00
1.00
1.00
Mars
1.88
3.54
3.54
1.52
Jupiter
11.9
141
141
5.20
Saturn
29.5
868
868
9.54
А. 13.7 AU
O B. 0.84 AU
ОС. 1.41 AU
D. 2.55 AU
O E. 1.05 AU
Congratulations! You just derived a version of Kepler's Third Law for Mars!
Using the mass of Mars in kilograms and converting the 4.5 hours to seconds, calculate the distance from the center of the planet.
GM kg
4π²
]s)²
3 =
And then determine the distance (in km) from the surface.
r = rm + rs
rs
km
=
km
Chapter 3 Solutions
EBK UNDERSTANDING OUR UNIVERSE (THIRD E
Ch. 3.1 - Prob. 3.1CYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3.5 - Prob. 3.5CYUCh. 3 - Prob. 1QAPCh. 3 - Prob. 2QAPCh. 3 - Prob. 3QAPCh. 3 - Prob. 4QAPCh. 3 - Prob. 5QAP
Ch. 3 - Prob. 6QAPCh. 3 - Prob. 7QAPCh. 3 - Prob. 8QAPCh. 3 - Prob. 9QAPCh. 3 - Prob. 10QAPCh. 3 - Prob. 11QAPCh. 3 - Prob. 12QAPCh. 3 - Prob. 13QAPCh. 3 - Prob. 14QAPCh. 3 - Prob. 15QAPCh. 3 - Prob. 16QAPCh. 3 - Prob. 17QAPCh. 3 - Prob. 18QAPCh. 3 - Prob. 19QAPCh. 3 - Prob. 20QAPCh. 3 - Prob. 21QAPCh. 3 - Prob. 22QAPCh. 3 - Prob. 23QAPCh. 3 - Prob. 24QAPCh. 3 - Prob. 25QAPCh. 3 - Prob. 26QAPCh. 3 - Prob. 27QAPCh. 3 - Prob. 28QAPCh. 3 - Prob. 29QAPCh. 3 - Prob. 30QAPCh. 3 - Prob. 31QAPCh. 3 - Prob. 32QAPCh. 3 - Prob. 33QAPCh. 3 - Prob. 34QAPCh. 3 - Prob. 35QAPCh. 3 - Prob. 36QAPCh. 3 - Prob. 37QAPCh. 3 - Prob. 38QAPCh. 3 - Prob. 39QAPCh. 3 - Prob. 40QAPCh. 3 - Prob. 41QAPCh. 3 - Prob. 42QAPCh. 3 - Prob. 43QAPCh. 3 - Prob. 44QAPCh. 3 - Prob. 45QAP
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- Suppose you are told that a satellite orbiting the Earth has a orbital period of 0.95 hours. Part (a) Using the orbital characteristics of the Moon (RM = 3.84 × 105km and TM = 0.0748 y), use Kepler's laws to calculate the orbital radius for the satellite, in kilometers.arrow_forwardA planet of mass 5.8 x 1024 kg orbits a star of mass 1.6 x 1030 kg in a circular orbit 10 x 1011 m from its center. Calculate the period of the orbit, in Earth years. Use G = 6.7 x 10-11 N m2/ kg2 and that one Earth year is 3.15 x 107 s. (Please answer to the fourth decimal place - i.e 14.3225)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_forward
- The table below illustrates data on Kepler's 3rd Law for the first six planets. Use it to estimate the orbital period of Asteroid Baade which has a semi-major axis of 2.55 AU | P (years) p2 a3 a (AU) Mercury 0.24 0.058 0.058 0.39 Venus 0.62 0.38 0.38 0.72 Earth 1.00 1.00 1.00 1.00 Mars 1.88 3.54 3.54 1.52 Jupiter 11.9 141 141 5.20 Saturn 29.5 868 868 9.54 A. 0.77 years B. 4.07 years C. 19.2 years D. 1.67 years Е. 50.2 yearsarrow_forwardA 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).]arrow_forwardPlanet 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.arrow_forward
- Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.arrow_forwardTwo 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_forwardMars 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_forward
- The Moon has a period of 27.3 days and a mean distance of 3.9x105 km from its center to the center of Earth. a)Use Kepler's laws to find the period of a satellite in orbit 6.70x 10 km from the center of Earth. b) How far above Earth's surface is this satellite?arrow_forwardConsider a planet of total mass 19.3 x 1024 kg, and radius 10.7 x 106 m. If the planet has a uniform density, calculate the gravitational field 2.7 x 106 m below the surface, in N/kg. Use G = 6.7 x 10-11 N m2/ kg2. (Please answer to the fourth decimal place - i.e 14.3225)arrow_forwardPlanet X orbits the star Omega with a "year" that is 450 earth days long. Planet Y circles Omega at four times the distance of Planet X. How long is a year on Planet Y? Express your answer in earth days.arrow_forward
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