Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 3, Problem 4E
Explain how Kepler was able to find a relationship (his third law) between the orbital periods and distances of the planets that did not depend on the masses of the planets or the Sun.
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Question 4:
Use Kepler's 3rd law to find the orbital periods (assume circular orbits) for the inner planets given
that their orbital radii are:
Mercury: 5.8 x 107 km
Venus: 1.08 x 108 km
A 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).]
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.
Chapter 3 Solutions
Astronomy
Ch. 3 - State Kepler’s three laws in your own words.Ch. 3 - Why did Kepler need Tycho Brahe’s data to...Ch. 3 - Which has more mass: an armful of feathers or an...Ch. 3 - Explain how Kepler was able to find a relationship...Ch. 3 - Write out Newton’s three laws of motion in terms...Ch. 3 - Which major planet has the largest . . . A....Ch. 3 - Why do we say that Neptune was the first planet to...Ch. 3 - Why was Brahe reluctant to provide Kepler with all...Ch. 3 - According to Kepler’s second law, where in a...Ch. 3 - The gas pedal, the brakes, and the steering wheel...
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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- Comet Halley (Fig. P11.21) approaches the Sun to within 0.570 AU, and its orbital period is 75.6 yr. (AU is the symbol for astronomical unit, where 1 AU = 1.50 1011 m is the mean EarthSun distance.) How far from the Sun will Halleys comet travel before it starts its return journey?arrow_forwardWhich of Keplers laws gives an indication of the semimajor axis? (16.1) (a) law of elliptical orbits (b) law of equal areas (c) harmonic lawarrow_forwardWhy did Kepler need Tycho Brahe’s data to formulate his laws?arrow_forward
- Which of Keplers or Newtons laws best describes Aristotelean violent motions?arrow_forwardWhy did Copernicus want to develop a completely new system for predicting planetary positions? Provide two reasons.arrow_forwardSaturn has an angular size of 16”, and an observed Synodic Period of 1.035yrs. Saturn’s moon, Titan orbits the planet with an angular separation of 192”, with a period of 15.9days. From these observations we can determine Saturn’s mass. Use the Sidereal Period of Saturn above to find the distance to Saturn from the Sun.arrow_forward
- 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.arrow_forwardScientist once hypothesized the existence of a planet called vulcan to explain Mercury's precession. Vulcan is supposed to be between mercury and the sun with a solar distance equal to 2/3;of that mercury. What would be its supposed periodarrow_forwardOn the evening of an autumnal equinox day Siddhant noticed that Mars was exactly along the north-south meridian in his sky at the exact moment when the sun was setting. In other words, the Sun and Mars subtended an angle of exactly 90° as measured from the Earth. If the orbital radius of Mars is 1.52 au, What will be the approximate rise time of the mars on the next autumnal equinox day?arrow_forward
- Determine what the period of revolution of the Earth would be if its distance from the Sun were 3.5 AU rather than 1 AU. Assume that the mass of the Sun remains the same. The final unit should be y in the answer.arrow_forwardUsing the m, = 1.99 x 1030 kg and the mę = 5.98 x 1024 kg and the distance between them as 1.00 AU (astronomical unit), what would be the orbital period of an object orbiting the sun at a distance of 2.12 AU? (please give answer in years) Number Unitsarrow_forwardNewton’s law of gravitation and the formula for centripetal acceleration can be used to show that: T^2=(4π^2/Gms)R^3 where G is the universal constant of gravitation and MS is the mass of the Sun. Take logarithms to base 10 of both sides of the equation to complete the expression for 2 lg T.2 lg T = ……………… × lg R + ……………………arrow_forward
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