Astronomy
Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Chapter 3, Problem 2E

Why did Kepler need Tycho Brahe’s data to formulate his laws?

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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.
The mass of Mars is 6.42 × 10^23 kg. Its moon Phobos is 9.378 x 10^6 meters away from Mars, with a mass of 1.06 × 10^16 kg and a period of 7.66 hours. It's moon Deimos has a mass of 1.4762x10^15 kg and a period of 30.3 hours. a) Use Kepler's 3rd law to determine the orbital distance between Mars and Deimos? b) What is the tangential velocity of Phobos, using the formula v (tangential) = sqrt (G x m(central)/ r)? c) What is the gravitational force of attraction between Mars and Phobos.
(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.

Chapter 3 Solutions

Astronomy

Ch. 3 - Explain how a rocket can propel itself using...Ch. 3 - A certain material has a mass of 565 g while...Ch. 3 - To calculate the momentum of an object, which...Ch. 3 - To calculate the angular momentum of an object,...Ch. 3 - What was the great insight Newton had regarding...Ch. 3 - Which of these properties of an object best...Ch. 3 - Pluto’s orbit is more eccentric than any of the...Ch. 3 - Why is Tycho Brahe often called “the greatest...Ch. 3 - Is it possible to escape the force of gravity by...Ch. 3 - What is the momentum of an object whose velocity...Ch. 3 - Evil space aliens drop you and your fellow...Ch. 3 - A body moves in a perfectly circular path at...Ch. 3 - As friction with our atmosphere causes a satellite...Ch. 3 - Use a history book, an encyclopedia, or the...Ch. 3 - Two asteroids begin to gravitationally attract one...Ch. 3 - How does the mass of an astronaut change when she...Ch. 3 - If there is gravity where the International Space...Ch. 3 - Compare the density, weight, mass, and volume of a...Ch. 3 - If identical spacecraft were orbiting Mars and...Ch. 3 - By what factor would a person’s weight be...Ch. 3 - Suppose astronomers find an earthlike planet that...Ch. 3 - What is the semimajor axis of a circle of diameter...Ch. 3 - If 24 g of material fills a cube 2 cm on a side,...Ch. 3 - If 128 g of material is in the shape of a brick 2...Ch. 3 - If the major axis of an ellipse is 16 cm, what is...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - What is the average distance from the Sun (in...Ch. 3 - In 1996, astronomers discovered an icy object...
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Kepler's Three Laws Explained; Author: PhysicsHigh;https://www.youtube.com/watch?v=kyR6EO_RMKE;License: Standard YouTube License, CC-BY