A Near Miss! In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained undetected until three days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth—about a third of the distance to the Moon. (a) Find the speed of the asteroid at closest approach, assuming its speed at infinite distance to be zero and considering only its interaction with the Earth. (b) Observations indicate the asteroid to have a diameter of about 0.730 km. Estimate the kinetic energy of the asteroid at closest approach, assuming it has an average density of 3.33 g/cm 3 . (For comparison, a 1-megaton nuclear weapon releases about 4.2 × 10 15 J of energy.)
A Near Miss! In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained undetected until three days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth—about a third of the distance to the Moon. (a) Find the speed of the asteroid at closest approach, assuming its speed at infinite distance to be zero and considering only its interaction with the Earth. (b) Observations indicate the asteroid to have a diameter of about 0.730 km. Estimate the kinetic energy of the asteroid at closest approach, assuming it has an average density of 3.33 g/cm 3 . (For comparison, a 1-megaton nuclear weapon releases about 4.2 × 10 15 J of energy.)
A Near Miss! In the early morning hours of June 14, 2002, the Earth had a remarkably close encounter with an asteroid the size of a small city. The previously unknown asteroid, now designated 2002 MN, remained undetected until three days after it had passed the Earth. At its closest approach, the asteroid was 73,600 miles from the center of the Earth—about a third of the distance to the Moon. (a) Find the speed of the asteroid at closest approach, assuming its speed at infinite distance to be zero and considering only its interaction with the Earth. (b) Observations indicate the asteroid to have a diameter of about 0.730 km. Estimate the kinetic energy of the asteroid at closest approach, assuming it has an average density of 3.33 g/cm3. (For comparison, a 1-megaton nuclear weapon releases about 4.2 × 1015 J of energy.)
(a) Evaluate the gravitational potential energy (in J) between two 6.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm.
(b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of
5.20 cm.
m/s
A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a
clue to the size of this black hole.
(a) One of these stars is believed to be in an approximātely circular orbit with a radius of about 1.50 x 10° AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is
orbiting.
kg
(b) What is the speed of this star?
V
star
m/s
How does it compare with the speed of the Earth in its orbit?
V star
VEarth
How does it compare with the speed of light?
V
star
A rocket is launched straight up from the earth's surface at a speed of 1.90×10^4 m/s. What is its speed when it is very far away from the earth?
Chapter 12 Solutions
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