2. (This is a problem from Physics 211 (Mechanics). Of course it has an electrical analog in the hydrogen atom, due to the analogy between gravity and electricity.) You are to make use of Kepler's laws of planetary motion to solve this problem. The orbit of Mercury around the sun is actually an ellipse with a very small eccentricity. For elliptical motion the location of the distance of closest approach of a planet to the sun is called the perihelion, and the location of the furthest distance of planet from the sun is called the aphelion. You are given the following data: mass of the sun: 1.98 × 10³0 kg; distance of Mercury from the sun at the perihelion: 24 X 100 km; speed of Mercury at the perihelion: 50 km/sec; speed of Mercury at the aphelion: 34 km/ sec; G = 6.67 X 10-¹1 m³/(kg sec²). Determine: 1) the distance of Mercury from the sun when it is located at the aphelion; 2) the length of a Mercurian year in seconds.

2. (This is a problem from Physics 211 (Mechanics). Of course it has an electrical analog in the hydrogen atom, due to the analogy between gravity and electricity.) You are to make use of Kepler's laws of planetary motion to solve this problem. The orbit of Mercury around the sun is actually an ellipse with a very small eccentricity. For elliptical motion the location of the distance of closest approach of a planet to the sun is called the perihelion, and the location of the furthest distance of planet from the sun is called the aphelion. You are given the following data: mass of the sun: 1.98 × 10³0 kg; distance of Mercury from the sun at the perihelion: 24 X 100 km; speed of Mercury at the perihelion: 50 km/sec; speed of Mercury at the aphelion: 34 km/ sec; G = 6.67 X 10-¹1 m³/(kg sec²). Determine: 1) the distance of Mercury from the sun when it is located at the aphelion; 2) the length of a Mercurian year in seconds.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 3PQ: For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the...

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For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet
Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.
Suppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter. (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)
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According to the National Academy of Sciences, the Earths surface temperature has risen about 1F since 1900. There is evidence that this climate change may be due to human activity. The organizers of World Jump Day argue that if the Earth were in a slightly larger orbit, we could avoid global warming and climate change. They propose that we move the Earth into this new orbit by jumping. The idea is to get people in a particular time zone to jump together. The hope is to have 600 million people jump in a 24-hour period. Lets see if it will work. Consider the Earth and its inhabitants to make up the system. a. Estimate the number of people in your time zone. Assume they all decide to jump at the same time; estimate the total mass of the jumpers. b. What is the net external force on the Earthjumpers system? c. Assume the jumpers use high-tech Flybar pogo sticks (Fig. P8.32), which allow them to jump 6 ft. What is the displacement of the Earth as a result of their jump? d. What happens to the Earth when the jumpers land?
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On a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?
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Model the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)
In what frame(s) of reference are Kepler's laws valid? Are Kepler's laws purely descriptive, or do they contain causal information?