Astronomy 122&, Fall 2009

Homework B Answers

Part I: Multiple choice. One point each.

1. "Velocity" implies both
b) speed and direction

2. If you were to triple the mass of the Earth but keep the radius the same you would weigh
b) 3 times as much as you do now (The force of gravity on Earth goes as mass/radius squared.)

3. If you were to triple the radius of the Earth but keep the mass the same you would weigh
e) 1/9 as much as you do now (See question 2.)

4. Where does the Earth's gravity actually end?
e) nowhere

5. As you descend in an elevator in a tall building at constant speed, your weight
b) increases (since you are getting closer to the center of the Earth)

6. Orbiting astronauts are weightless because the
e) astronauts and the cabin are both free-falling bodies.

7. If you could cut off the gravity of the Sun and planets (which you cannot), Mars would
b) go flying away from the Solar System in a straight line (Newton's first law)

8. What is at one focus of the orbit of a planet?
d) the Sun

9. For the Solar System, the period of a planet in years equals the semi-major axis in AU raised to what power?
c) 3

10. As a planet approaches perihelion from aphelion, it
c) moves faster (in kilometers per second)

11. Which observation by Galileo supports the Copernican theory?
e) the phases of Venus

12. A body in a hyperbolic orbit relative to the Sun
c) will never return to the Sun

13. Which planet was discovered by William Herschel in the 18th century?
d) Uranus

14. The orbits of planets cannot actually be perfect ellipses because
c) of the gravitational pulls of the other planets

15. The motion of Uranus led to the discovery of
d) Neptune

16. If you could suddenly shrink the Earth (make the Earth smaller in radius but keep the same mass), the length of the day would
b) decrease (conservation of angular momentum)

17. Kepler's third law as generalized by Newton allows you to find
a) the mass of the Sun

18. Pluto was discovered by
d) Clyde Tombaugh

19. Kepler's second law of planetary motion is essentially the conservation of
a) angular momentum

20. Your weight on a planet depends
c) on both the planet's mass and radius

Part II. Ten points each.

1. Weight is proportional to the product of your mass times the mass of the Earth divided by the radius of the Earth squared.
a) If you double the mass of the Earth and keep the radius constant, you would weigh 200 lbs.
b) If you double the radius of the Earth and keep the mass constant, you would weigh 2 squared (4 times) less, or 25 lbs.
c) If you double them both, you would weigh 2/4 times as much, or 50 lbs.

2. For Solar System objects, P (yr)**2 = a(AU)**3. For an asteroid with a period of 8 years a**3 = 8**2 = 64, so a (the semimajor axis of the orbit) is the cube root of 64 = 4 AU.

3. In any two-body problem, P**2 is proportional to a**3. If you increase the distance from the center of the Earth by a factor of 10, a**3 goes up by a factor of 1000. P then goes up by a factor of the square root of 1000 = 31.6. The new period is then 100 minutes X 31.6 = 3160 minutes = 2.19 days.