21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 36QP
To determine
Prove that the planet with period of 3 years and distance from 2 AU is not possible.
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A)At what altitude would a geostationary sattelite need to be above the surface of Mars? Assume the mass of Mars is 6.39 x 1023 kg, the length of a martian solar day is 24 hours 39minutes 35seconds, the length of the sidereal day is 24hours 37minutes 22seconds, and the equatorial radius is 3396 km. The answer can be calculated using Newton's verison of Kepler's third law.
(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.
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
21st Century Astronomy
Ch. 3.1 - Prob. 3.1ACYUCh. 3.1 - Prob. 3.1BCYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3 - Prob. 1QPCh. 3 - Prob. 2QPCh. 3 - Prob. 3QPCh. 3 - Prob. 4QPCh. 3 - Prob. 5QP
Ch. 3 - Prob. 6QPCh. 3 - Prob. 7QPCh. 3 - Prob. 8QPCh. 3 - Prob. 9QPCh. 3 - Prob. 10QPCh. 3 - Prob. 11QPCh. 3 - Prob. 12QPCh. 3 - Prob. 13QPCh. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Prob. 16QPCh. 3 - Prob. 17QPCh. 3 - Prob. 18QPCh. 3 - Prob. 19QPCh. 3 - Prob. 20QPCh. 3 - Prob. 21QPCh. 3 - Prob. 22QPCh. 3 - Prob. 23QPCh. 3 - Prob. 24QPCh. 3 - Prob. 25QPCh. 3 - Prob. 26QPCh. 3 - Prob. 27QPCh. 3 - Prob. 28QPCh. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Prob. 32QPCh. 3 - Prob. 33QPCh. 3 - Prob. 34QPCh. 3 - Prob. 35QPCh. 3 - Prob. 36QPCh. 3 - Prob. 37QPCh. 3 - Prob. 38QPCh. 3 - Prob. 39QPCh. 3 - Prob. 40QPCh. 3 - Prob. 41QPCh. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Prob. 44QPCh. 3 - Prob. 45QP
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- In a distant star system there are many inhabitable planets. One of these planets is named Qomar. Qomar is 3.2 AU's from its star and takes 6.5 Earth years to go around its star once. There is another planet in the same star system called Ferenginar. Ferenginar is 0.9 AUs from the star. What is the length of a Ferengi year (on Ferenginar) in terms of Earth years?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_forwardThe 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 AUarrow_forward
- Assume the earth's mass is 55.818 x 1025 kg, and radius is 10.63 x 103 miles, what would be the gravitational acceleration on such an planet in unit of m/s2? Use G=6.67x 10 -11 Nm2/kg2.arrow_forwardKepler'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_forwardMars has two moons orbiting it. One moon is named Deimos ( terror/dread from Greek mythology). Deimos has a mass of 2(10)^15 kg and is 23,460 km from Mars. The mass of Mars is 6.42 (10) ^23 kg a) What is the gravitational force between Mars and Deimos? (give this answer in Scientific Notation with 2 decimal places) b) What is the velocity of Deimos as it orbits Mars? ( give this answer in decimal form to 2 decimal places) a) = FG __________________ N b) V = ________________ m/sarrow_forward
- Which of Kepler's law can be used to estimate the mass of a distant star system based on the period and semimajor axis of its planet?arrow_forwardSuppose 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_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
- 10 Jup Europa Figure I Ganymedearrow_forwardA newly discovered planet, Eagal, has two known moons, Dorainn and Bron. The table below gives some of the known information about Dorainn and Bron. Dorainn Bron Mass 1.427 x 1015 kg 1.427 x 1015 kg Radius 6.142 km Orbital Period 1.091 x 105 s Orbital Radius 23,640 km 27,650 km a. Determine the gravitational field strength at the surface of Dorainn. b. Using only the information provided for each moon and proportionality, determine Bron's orbital period. Clearly show or explain all workings. c. Use the data provided for Dorainn to determine the mass of Eagal. d. Determine the orbital speed of Bron.arrow_forwardTwo exoplanets, UCF1.01 and UCF1.02 are found revolving around the same star. The period of planet UCF1.01 is 4.8 days, and that of planet UCF1.02 is 5.2 days. If the average distance of planet A to the sun is 2,885.4 km, what is the average distance of planet B to the sun km? Please keep four digits after decimal points.arrow_forward
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