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Chapter 13: Q. 11 (page 353)
Saturn鈥檚 moon Titan has a mass of and a radius of What is the free-fall acceleration on Titan?
The free-fall acceleration on Titan is
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Two spherical asteroids have the same radius . Asteroidhas mass and asteroid has mass The two asteroids are released from rest with distance between their centers. What is the speed of each asteroid just before they collide?
Hint: You will need to use two conservation laws.
You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be and its rotation period to be role="math" localid="1648535932335" You have previously determined that the planet orbits from its star with a period of . Once on the surface you find that the free-fall acceleration is What is the mass of (a) the planet and (b) the star?
The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0 x 108 m/s. Astronomers have determined
that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.
a. Assuming the orbit is circular, what is the period of the solar
system鈥檚 orbit? Give your answer in years.
b. Our solar system was formed roughly 5 billion years ago. How many orbits has it completed?
c. The gravitational force on the solar system is the net force due to all the matter inside our orbit. Most of that matter is concentrated near the center of the galaxy. Assume that the matter has a spherical distribution, like a giant star. What is the approximate mass of the galactic center?
d. Assume that the sun is a typical star with a typical mass. If galactic matter is made up of stars, approximately how many stars are in the center of the galaxy?
Astronomers have spent many years trying to determine how many stars there are in the Milky Way. The number of stars seems to be only about 10% of what you found in part d. In other words,
about 90% of the mass of the galaxy appears to be in some form other than stars. This is called the dark matter of the universe. No one knows what the dark matter is. This is one of the outstanding scientific questions of our day.
The gravitational force of a star on orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2. What is the ratio F1/F2?
A binary star system has two stars, each with the same mass as our sun, separated by A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a trajectory that passes through the midpoint between the two stars. What is the comet鈥檚 speed at the midpoint?
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