The Solar System
9th Edition
ISBN: 9781305804562
Author: Seeds
Publisher: Cengage
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Chapter 4, Problem 11RQ
To determine
Whether epicycle or deferent travels in uniform circular motion as viewed from particular point. Whether the uniform circular motions have same speed and in same directions.
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Describe three propositions, now known as Kepler’s laws of planetary motion?
Which of the following statements is supported by Kepler's laws of planetary motion?
Earth orbits the Sun at a constant speed, never speeding up or slowing down.
Earth's orbit is a perfect circle, with the Sun located at the center of the circle.
Earth orbits the Sun at a slightly faster speed every year.
Earth has an elliptical orbit, with the Sun located at one focus of the ellipse.
Kepler's Third Law and Newton's Law of Universal Gravitation
(a) Use Newton's Universal Law of Gravitation and what you know about centripetal acceleration/force to
derive Kepler's Third Law for a planet in a circular orbit about the sun:
T² = Kr³
K = constant = 4²/GM
where T is the orbital period of the planet (the time for one complete orbit), r is the radius of the planet's
orbit, M is the mass of the sun, and G is the universal gravitational constant.
(b) Determine the metric system units of K and show that they make the units of T² – Kr³ work out
correctly.
(c) The earth orbits the sun once per year (365 days) and its average orbital radius is 1.50 x 10¹¹ m. Use
this information and Kepler's Third Law to estimate the mass of the sun in kilograms.
[answer: about 2 x 10³⁰ kg]
(d) The radius of the sun is about 7 x 108 m. Use this radius and the mass of the sun estimated in part (c)
to estimate the acceleration of an object near the surface of the sun. [answer: about 300 m/s²]
F₂ =G…
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 - Why might Tycho Brahe have hesitated to hire...Ch. 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 -
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. 1LTLCh. 4 - Prob. 2LTLCh. 4 - What three astronomical objects are represented...Ch. 4 - Use the figure below to explain how the Ptolemaic...
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- Which of Keplers or Newtons laws best describes Aristotelean violent motions?arrow_forwardPlease answer this question in full steps using proper formulas for universal circular motion. Send ASAP.arrow_forwardWhich of the following are, or follow directly from, Kepler's Laws of planetary motion? Check all that apply. More distant planets move at slower speeds. The force of attraction between any two objects decreases with the square of the distance between their centers. The orbit of each planet about the Sun is an ellipse with the Sun at one focus. A planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. As a planet moves around its orbit, it sweeps out equal areas in equal times.arrow_forward
- ) A boy is flying a drone in a circular path at 35 miles per hour. If the drone is experiencing a centripetal acceleration of 0.70 m/s2, what is the diameter (in meters) of the circle that the boy’s drone is flying?arrow_forwardExplain and analyse the simiilarities and difference between circular motion and planetary motion.arrow_forward1) Give the following numbers to four significant figures in scientific notation: a) 0.0056542b) 93 842 773c) 0.000000100092d) 0.0095435 2) Repeat part (1), but this time give the numbers to two significant figures. 3) The radial acceleration, a, of a body rotating in a circle of radius r at constant speed v is given by ? =v2/rIf v = (3.00±0.05) m/s and r = (1.5±0.1) m, a) calculate a,b) the maximum values of a, c) minimum values of a, d) the uncertainty in a. 4) Linearize the following equations (rearranged in the form y = mx + c): a) ? = ?? , where F is the dependent variable, N is the independent variable and µ is the constant. b) ? = 2?√(?⁄?) where T is the dependent variable, l is the independent variable and g is the constant.i) What would you plot in order to obtain a straight line)? (Answer for a) and b)ii) How are the slope and intercept related to the constants in the equation? (Answer for a) and b)arrow_forward
- For circular orbits, relate Kepler’s third law of planetary motion to Newton’s law of gravitation and centripetal acceleration to the configuration system or any situational scenarios. Explain and justify. Cite an example to support your answer.arrow_forwardIf an airplane pilot is told to fly 123 km in a straight line to get from San Francisco to Sacramento, explain why he could end upanywhere on the circle . What other information would he need to get to Sacramento?arrow_forwardUsing Kepler's 3rd law, how long will it take a new planet that is 3.68 x 107 km to travel around the Earth?arrow_forward
- Consider the Earth's orbit around the Sun to be circular with radius R = 9.30 x 107 mi and it takes 365 days to complete one revolution. What is the distance Earth traveled for one revolution (circumference of a circle is 2??2πR )?arrow_forwardA planet is about 7.79 x 108 km (orbital radius) from the sun. It takes 1,425 days for the planet to go around its orbit (assume circular orbit). What is the orbital velocity in km/sec of the planet along its orbital path? What is its acceleration toward the sun in km/sec2? (Force attraction of sun = ma = mv2); r = orbital radius rarrow_forwardWe found the centripetal acceleration of the Earth as it revolves around the Sun. Compute the centripetal acceleration of a point on the surface of the Earth at the equator caused by the rotation of the Earth about its axis. (Enter the magnitude. The radius of the Earth is 6,371 km.) m/s²arrow_forward
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