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Chapter 13: Q. 18 (page 353)
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?
The minimum speed that the probe needs to escape the solar system is
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Two meteoroids are heading for earth. Their speeds as they cross the moon鈥檚 orbit are
a. The first meteoroid is heading straight for earth. What is its speed of impact?
b. The second misses the earth by What is its speed at its closest point?
What is the escape speed from Jupiter?
Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton鈥檚 third law, the forces that
push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The
gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to
form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of 鈮� 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars.
a. Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the speed of a point on the equator of the star?
b. What is g at the surface of this neutron star?
c. A stationary 1.0 kg mass has a weight on earth of 9.8 N. What would be its weight on the star?
d. How many revolutions per minute are made by a satellite orbiting 1.0 km above the surface?
e. What is the radius of a geosynchronous orbit?
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?
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.
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