The Solar System
10th Edition
ISBN: 9781337672252
Author: The Solar System
Publisher: Cengage
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Chapter 4, Problem 21RQ
To determine
The value of
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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.
I. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius.
Average
Radius of
Orbit
Times of
Planet
R3
T2
T?/R3
Revolution
Mercury
5.7869 x 1010
7.605 x 106
Venus
1.081 x 1011
1.941 x 107
Earth
1.496 x 1011
3.156 x 107
1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?
II. Solve the given problems. Write your solution on the space provided before each number.
1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the
following:
a) Speed
b) Period
c) Radial Acceleration
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Given:
Unknown:
Formula:
Solution:
Answer:
Mars is 1.53 times as far from the Sun as Earth is. Use Keller’s third law to predict the required for Mars to orbit the sun in Earth days.
Chapter 4 Solutions
The Solar System
Ch. 4 - Prob. 1RQCh. 4 - Why did early human cultures observe astronomical...Ch. 4 - Prob. 3RQCh. 4 - Name one example each of a famous politician,...Ch. 4 - Why did Plato propose that all heavenly motion was...Ch. 4 -
On what did Plato base his knowledge? Was it...Ch. 4 - Which two-dimensional (2D) and three-dimensional...Ch. 4 - Prob. 8RQCh. 4 - In Ptolemys model, how do the epicycles of Mercury...Ch. 4 - Describe in detail the motions of the planets...
Ch. 4 - Prob. 11RQCh. 4 - Prob. 12RQCh. 4 - Prob. 13RQCh. 4 -
When Tycho observed the new star of 1572, he...Ch. 4 - Assume the night is clear and the Moons phase is...Ch. 4 - Does Tychos model of the Universe explain the...Ch. 4 - Name an empirical law. Why is it considered...Ch. 4 -
How does Kepler’s first law of planetary motion...Ch. 4 - Prob. 19RQCh. 4 - Prob. 20RQCh. 4 - Prob. 21RQCh. 4 - Prob. 22RQCh. 4 - Prob. 23RQCh. 4 - Prob. 24RQCh. 4 - Prob. 25RQCh. 4 - Prob. 26RQCh. 4 - Prob. 27RQCh. 4 - Prob. 1PCh. 4 -
If you lived on Mars, which planets would exhibit...Ch. 4 - Prob. 3PCh. 4 - If a planet has an average distance from the Sun...Ch. 4 - If a space probe is sent into an orbit around the...Ch. 4 - Prob. 6PCh. 4 - An object takes 29.5 years to orbit the Sun. What...Ch. 4 -
One planet is three times farther from the Sun...Ch. 4 - Galileos telescope showed him that Venus has a...Ch. 4 - Which is the phase of Venus when it is closest?...Ch. 4 - Prob. 11PCh. 4 - Prob. 1SPCh. 4 - Prob. 2SPCh. 4 - Prob. 1LLCh. 4 - Prob. 2LLCh. 4 - What three astronomical objects are represented...Ch. 4 - Use the figure below to explain how the Ptolemaic...
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- Why might Tycho Brahe have hesitated to hire Kepler? Why do you suppose he appointed Kepler his scientific heir? What is limited about Keplers third law P2 = a3, where P is the time in units of years a planet takes to orbit the Sun and a is the planets average distance from the Sun in units of AU? (Hint: Look at the units.) What does this tell you about Kepler and his laws?arrow_forwardAccording to Kepler’s second law, where in a planet’s orbit would it be moving fastest? Where would it be moving slowest?arrow_forwardHow Do We Know? Describe the differences between a hypothesis, a theory, and a law. Give an example of each.arrow_forward
- Suppose a planet sweeps out an area, call it A, in one day. In terms of A, Kepler's second law tells us it would sweep out how large an area in five days?arrow_forwardThe table below presents the semi-major axis (a) and Actual orbital period for all of the major planets in the solar system. Cube for each planet the semi-major axis in Astronomical Units. Then take the square root of this number to get the Calculated orbital period of each planet. Fill in the final row of data for each planet. Table of Data for Kepler’s Third Law: Table of Data for Kepler’s Third Law: Planet aau = Semi-Major Axis (AU) Actual Planet Calculated Planet Period (Yr) Period (Yr) __________ ______________________ ___________ ________________ Mercury 0.39 0.24 Venus 0.72 0.62 Earth 1.00 1.00 Mars 1.52 1.88 Jupiter…arrow_forward3arrow_forward
- In your own words, describe the meaning of Kepler's Third Law of Planetary Motion. Do not use any equations, do not describe the equations in words, just tell me the conceptual meaning.arrow_forwardWhat is planetary motion through Kepler's law?arrow_forwardWrite down an expression for the gravitational filed strength of a planet of radius R and density ρ. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate without the quotes). For Greek letters such as ?ρ and ?π use rho and pi. Please use the "Display response" button to check you entered the answer you expectarrow_forward
- The moon has a period of 27.3 days and a mean distance of 3.9 x 10 ^5 km from the center of the earth. a) Use Kepler's laws to find the period of a satellite in orbit 6.7x 10^3 km from center of earth. ( Round your answer to the nearest thousandth of a day) b) Convert your answer to minutes. (Round your answer to the nearest tenth). c) Given the earth's radius is 6.4 × 10^6 m, determine how far above earth's surface is the satellite in meters, km and miles.arrow_forwardThe average Earth-Moon distance is 3.84 X 10^5 km, while the Earth-Sun is 1.496 X 10^8 km. Since the radius of the Moon is 1.74 X 10^3 km and that of the Sun is 6.96 X 10^5 km. a) Calculate the angular radius of the Moon and the Sun, qmax, according to the following figure. D Bax R b) Calculate the solid angle of the Moon and the Sun as seen from Earth. (c) Interpret its results; Would this be enough to explain the occurrence of total solar eclipses?arrow_forwardThe moon has a period of 27.3 days and a mean distance of 3.9 x 10 ^5 km from the center of the earth. a) Use Kepler's laws to find the period of a satellite in orbit 6.7 x 10^3 km from center of earth. ( Round your answer to the nearest thousandth of a day) b) Convert your answer to minutes. ( Round your answer to the nearest tenth). c) Given the earth's radius is 6.4 x 10^6 m, determine how far above earth's surface is the satellite in meters, km and miles.arrow_forward
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