Summary

• Newton's Universal Law of Gravity
• Kepler's laws of orbits
• Newton's explanation of Kepler's law

• Written Quiz Ch.11-12







• Gravitation inside Earth
Example #1


• potential energy
Example #2


• orbit energy
Example #3
Example #4


• escape speed
Example #5
Example #6



• Interactive Example about escape speed



• circular and elliptical orbits
Example #7

HRW10e 13.26
A uniform solid sphere of radius R produces a gravitational acceleration a_g on its surface. At what distances from the sphere's center is the gravitational acceleration a_g/3?
A. R/9 and 9R
B. R/3 and 3R
C. R/√3 and 3R
D. R/3 and √3 R
Answer



















pse6 13.27
How much energy is required to move a 1000 kg mass from the Earth's surface to an altitude twice the Earth's radius (r = 3R_E)?
A. 3.13 GJ
B. 209 MJ
C. 41.7 GJ
D. 6.26 TJ
Answer



















PoP5 11.32
How much work is required to move a 625-kg Earth satellite from a circular orbit of radius 2R_E to one of radius 3R_E?
A. 3.26 GJ
B. 6.52 GJ
C. 9.77 GJ
D. 19.5 GJ
Answer



















PoP5 11.26
A spaceship is fired from earth with an initial speed of 20.0 km/s. What will its speed be when it is very far from Earth?
A. 128 m/s
B. 16.6 km/s
C. 8.33 km/s
D. 275 km/s
Answer



















PoP5 11.34a
What is the minimum speed, relative to the Sun (M_Sun = 1.99×10³⁰ kg), necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit (r = 1.50×10¹¹ m)?
A. 42.1 km/s
B. 72.9 km/s
C. 538 km/s
D. 1770 km/s
Answer



















PoP5 11.25
What is the maximum radius of an asteroid from which an astronaut can escape by jumping straight upward? The density of the asteroid matches that of the Earth, and on Earth the astronaut can jump 0.500 m upward.
A. 38.4 m
B. 385 m
C. 525 m
D. 1783 m
Answer



















PoP5 11.44
A spacecraft of mass 1.00×10⁴ kg is in a circular orbit at an altitude of 500 km above the Earth's surface. How much energy is required to get it into an elliptical orbit with an apogee distance of 2.00×10⁴ km?
A. 8850 J
B. 1.42×10¹¹ J
C. 1.34×10⁴ J
D. 4.00×10⁸ J
Answer







































answer

D. R/3 and √3 R





















answer

C. 41.7 GJ




















answer

A. 3.26 GJ




















answer

B. 16.6 km/s




















answer

A. 42.1 km/s




















answer

D. 1783 m




















answer

B. 1.42×10¹¹ J