21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 35QP
(a)
To determine
Find the sidereal period of dwarf planet Ceres.
(b)
To determine
Find the sidereal period of dwarf planet Ceres using Kepler’s law.
(a)
To determine
Compare the sidereal period of the Ceres calculated from two different methods.
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A newly discovered planet orbits a star with the same mass as the Sun with a semi-major axis of 239.36 million kilometers. Its orbital eccentricity is 0.1.A. Find the planet's orbital period.B. Find the planet's perihelion distance.C. Find the planet's aphelion distance.
Kepler's third law of planetary motion describes a relationship between the__ *
a, shape of orbit and the location of the Sun.
b. orbital velocity and position in orbit
c. distance from the Sun and length of year.
d. path of epicycle and position.
BACKGROUND
An ingenious solution to the Earth's circumference occured in 230 BC. Eratosthenes, a Greek
geographer, mathematician, music theorist, poet, astronomer, and philosopher, was reading in the
Library of Alexandria when he noticed an account for a deep well near Syene (now Aswan),
some distance to the south (800 km) in which at high noon on the longest day of the year the
bottom of the well was fully illuminated by the Sun. Eratosthenes exclaimed "Ah-ah!" (or
something like that), "I can solve for the circumference of the Earth!". In his mind's eye,
Eratosthenes could see that at Syene, at the moment when the bottom of the well was fully lit, the
Sun must have been at the Zenith (directly overhead). Yet he knew that at the same moment in
Alexandria vertical objects (like a tower, pole) cast shadows.
Here is the experiment perfomed by Eratosthenes (see the picture below).
• He erected a vertical pole at Alexandria (A) and measured the angle of its shadow at the
moment when the…
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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- 1. The average orbital distance of Mars is 1.52 times the average orbital distance of the Earth. Knowing that the Earth orbits the sun in approximately 365 days, use Kepler's law of harmonies to predict the time for Mars to orbit the sun.arrow_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_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_forward
- A newly discovered planet orbits a star with the same mass as the Sun with a semi-major axis of 329.12 million kilometers. Its orbital eccentricity is 0.6. 13. Find the planet’s orbital period. 14. Find the planet’s perihelion distance. 15. Find the planet’s aphelion distance.arrow_forward1. How does the speed of revolution depend on its distance from the sun? 2. How were tycho brahe's observaions used by kepler to produce his laws of planetary motion?arrow_forwardAccording to Lunar Laser Ranging experiments the average distance LM from the Earth to the Moon is approximately 3.85 × 10° km. The Moon orbits the Earth and completes one revolution in approximately 27.5 days (a sidereal month). How can the mass of the Earth be calculated using the information above? Select the correct statements. Select one or more: O a. Use Newton's third law. O b. Use Newton's first law. c. Use Coulombs law. O d. Use Newton's second law.arrow_forward
- 9. Pluto's orbit around the Sun is highly elliptical compared to the planets in our Solar System. It has a perihelion distance of 29.7 AU and an aphelion distance of 49.5 AU. a) What is the semi-major axis of Pluto's orbit, in AU? b) What is Pluto's orbital period, in Earth years?arrow_forwardSuppose a Moon takes 15.8 days to orbit its host planet. Convert this orbital period into Earth years (365.25 =1 Earth year). a. 0.0431-0.0435 b. 0.0331-0.0335 c. 0.0231-0.0235 d. 0.0131-0.0135arrow_forwardTRUE OR FALSE only. 1. DIURNAL MOTION is caused by the daily motion of a planet on its axis. 2. Eudoxus was the first to propose that the sun is the center of the solar system. 3. The most perfect shape of the earth and universe according to Plato is cylindrical. 4. Ancient astronomers believed that the Earth did not move because there was no stellar parallax observed. 5. Galileo's observation of the planets supported the geocentric theory. 6. The planet closest to the sun has the shortest period of revolution about the sun. 7. In the proposed model by Copernicus, the earth was at the center of the universe. 8. Epicycles refer to the circular paths taken by planets. 9. The second law of planetary motion implies that the product of the velocity and the distance from the sun remain the same as a planet moves about the sun. 10. The first law implies that there is a common principle that governs the orbital motion of the planets.arrow_forward
- 1. Mars takes 1.88 years to complete one orbit around the sun. What is its average distance from the sun?arrow_forward9. A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 x 10° km away from the sun?arrow_forward8. The mean distance of Earth from the Sun is 149.6 x 10° km and the mean distance of Mercury from the Sun is 57.9 x 10° km. The period of Earth's revolutions is 1 year, what is the period of Mercury's revolution? a. 0.24 year on Earth b. 0.42 year on Earth C. 1.13 year on Earth d. 1.31 year on Earth 9. The planet Delta has 2 times the gravitational field strength and 3 times the radius of Earth. How does the mass of the planet Delta compare with the mass of Earth?arrow_forward
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