21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 45QP
(a)
To determine
Find the value of major axis and semimajor axis of Mars.
(b)
To determine
Find the distance from the center of the orbit to the Sun and eccentricity of Mars orbit and compare it with Earth’s eccentricity.
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Let's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures.
Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different.
When you have calculated them, only submit the value for Mercury.
Planet
Distance from the sun
Period of orbit around the sun
Earth
150 million km
___ Earth years
Mercury
58 million km
___ Earth years
Venus
108 million km
___ Earth years
Mars
228 million km
___ Earth years
M
M
1. What is the gravitational potential energy of the mass (m) in the picture? The mass is the same
distance awayr from the centers of both of the other masses, and both of the other masses have
the same mass, M. Give your answer in Joules.
r= 400 million meters
m = 7x1022 kg
M = 2x1027 kg
2. What is the net gravitational force for the mass m at this location? Give your answer in
Newtons.
A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 122 million kilometers. Its orbital eccentricity is 0.5.
1. Find the planet's orbital period. Express your answer in years to three significant figures.
2. Find the planet's nearest and farthest orbital distances from its star. Express your answers in millions of kilometers to three significant figures separated by a comma.
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 1993 the Galileo spacecraft sent home an image of asteroid "243 Ida" and a tiny moon "Dactyl" orbiting the asteroid. Assume that the small moon orbits in a circle with a radius of r = 100 km from the center of the asteroid with an orbital period of T = 27 hours. a. Show and explain how we derived Kepler's 3rd law using Newton's 2nd Law, the definition for centripetal acceleration, and the equation for gravitational force. b. Use your result for Kepler's 3rd Law to determine the mass of the asteroid. c. If the asteroid has a radius of about 16 km calculate the approximate value for the acceleration due to gravity, g, on its surface. d. What velocity would you need to achieve in order to lift off and leave this asteroid? e. Use Newton's 2nd Law, the definition for centripetal acceleration, and the equation for gravitational force to determine an expression for circular orbital velocity. f. What is the orbital velocity of the small moon if we assume it is in a circular orbit?arrow_forwardLet's use Kepler's laws for the inner planets. Use the following distances from the sun to calculate the orbital period for each of these planets. Express your answer in terms of Earth years to two significant figures. Answer for the highlighted planet in each question. Note: Use Kepler's law directly. Don't just Google the answers, as they will be a little bit different. When you have calculated them, only submit the value for Earth. Planet Distance from the sun Period of orbit around the sun Earth 150 million km ___ Earth years Mercury 58 million km ___ Earth years Venus 108 million km ___ Earth years Mars 228 million km ___ Earth yearsarrow_forwardUse the diagram and the fact that Planet A has a nearly circular orbit while Planet B has a highly elliptical orbit to answer the following questions. Use examples of Newton’s and Kepler’s laws in your answers. a. Does Planet B travel faster or slower when it is closest to the Sun than at other times? Explain your answer. b. Which planet takes longer to orbit the Sun? Explain your answer. c. Does the gravitational attraction between these planets increase or decrease as their orbits move them closer together? Explain your answer. d. Which planet has the highest average orbital speed? Explain your answer. e. Which planet travels at about the same speed throughout its orbit? Explain your answer.arrow_forward
- 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.arrow_forwardUntil recently, the term "planet" had no clear-cut definition. In August of 2006, leading astronomers established new guidelines and declared that Pluto is no longer a planet. Which of the following is either false or least consistent with the new guidelines? Group of answer choices Pluto is by far the largest known object in the Kuiper belt, while Eris is the largest known object in the asteroid belt. A planet must have cleared the neighborhood around its orbit. Pluto is automatically disqualified from being a planet because its oblong orbit overlaps with Neptune's. A planet must have sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a nearly round shape. Pluto and the asteroid Ceres are both now classified as dwarf planets.arrow_forwardThe dwarf planet Pluto has an elliptical orbit with a semi-major axis of 5.91×10^12 m and eccentricity 0.249. Calculate Pluto's orbital period. Express your answer in seconds. Calculate Pluto's orbital period. Express your answer in earth years. During Pluto's orbit around the sun, what is its closest distance from the sun? Express your answer with the appropriate units. During Pluto's orbit around the sun, what is its farthest distance from the sun? Express your answer with the appropriate units.arrow_forward
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