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Chapter 13: Q. 30 (page 354)
An earth satellite moves in a circular orbit at a speed of . What is its orbital period?
The orbital period is
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A newly discovered planet has a radius twice as large as earth鈥檚 and a mass five times as large. What is the free-fall acceleration on its surface?
An object of mass is dropped from height above a planet of mass and radius Find an expression for the object鈥檚 speed as it hits the ground.
A proposed space elevator would consist of a cable stretching from the earth鈥檚 surface to a satellite, orbiting far in space, that would keep the cable taut. A motorized climber could slowly carry rockets to the top, where they could be launched away from the earth using much less energy. What would be the escape speed for a craft launched from a space elevator at a height of ? Ignore the earth鈥檚 rotation.
What is the total gravitational potential energy of the three masses in
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.
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