## Answers to Example Questions for the Third Exam

1. d. Remeber that the escape velocity is equal to the circular velocity times "root 2" which is 1.414

2. False. An object moving AT the escape velocity follows a PARABOLIC orbit (an object moving FASTER than the escape velocity would follow a hyperbolic orbit).

3. True. Declination is the celestial equivalent of latitude, and just as the latitude of the north pole is +90, so the declination of the north celestial pole is also +90.

4. -23.5 degrees. Recall that the annual motion of the sun along the ecliptic carries the sun as far north as DEC = +23.5 (which occurs on the summer solstice, June 21) and as far south as DEC = -23.5 (which occurs on the winter solstice, Dec 22).

5. c. The only month the star is "above the horizon all day" is when it has the same Right Ascension as the sun. The sun is on the vernal equinox on March 21 and therefor has RA = 0 hours at this time (recall the zero point of the RA system is the vernal equinox). Hence, the sun will be at RA = 12 hours (where the star is) six months later, at september 21 (ie the fall equinox). Hence the star cant be seen in september.

6. a. Recall that the height of the celestial equator above the southern horizon is 90 - latitude. Thus, on the summer solstice, the sun is a further 23.5 degrees higher, which is +88.5 degrees for a latitude of +25 degrees (ie, 90 - 25 + 23.5 = 90 - 1.5 = 88.5 which is close to 88).

7. a. In June the sun's declination is +ve (it is in the northern celestial hemisphere) and so the rise and set points on the horizon are to the north of due east and due west.

8. Latitudes : Arctic (+66.5, ie 90 - 23.5); Antarctic (-66.5, ie -90 + 23.5); Tropic of Cancer (+23.5); and Tropic of Capricorn (-23.5). At the Arctic and Antarctic latitudes there is a 24 hour day(night) on the summer(winter) solstices. Further towards the poles, the number of days of continuous daylight(darkness) increases. At the poles, we have a 6 month day and a 6 month night. The Tropics of Cancer and Capricorn mark the limits of latitude within which the sun can pass through the zenith. At these exact latitudes, the zenith noon occurs on the summer solstice.

9. There are TWO reasons it is warmer in summer. First, the days are longer so there is more time to heat up during the day and less time to cool down at night. Second, the sun takes a higher path in the sky during the day, so the illumination is more vertical so each square meter receives more sunlight energy.

10. True. Recall that during the day, the sun moves about 1 degree to the east, so that after one SIDEREAL day (when the stars are back to their former positions in the sky) we need a bit MORE time (4 minutes, or about 1/360 of a day) of extra diurnal motion to bring the sun back to its former location in the sky, to make a complete SOLAR day. Hence the sidereal day is a bit shorter than a solar day. (See fig 3.9 in the text).

11. d. 90 degrees is 6 times 15 degrees, so it is 6 time zones between the two cities (alternatively, 90 degrees is a quarter of 360 so a quarter of a day or 6 hours). Paris is East of Chicago, so its time is LATER than in Paris (remember east coast US time is LATER than west coast time). Hence, if it is noon in Chicago it is 6pm in Paris.

12. a. False. Although the normal rule for a leap year would give a leap year in AD 1900 (ie, it is divisible by 4), remember that under the Gregorian reform calender, we skip the century leap years unless the year is divisible by 400. Since 1900 is not cleanly divisible by 400 we skip it as a leap year. (note, the year 2000 WILL be a leap year).

13. Sunrise (c). Recall that facing the sun, a third quarter moon is 90 degrees to the RIGHT (ie west) of the sun. If you are facing south and the third quarter moon is high in the sky, then the sun is about 90 degrees to the east, or just on the eastern horizon. Hence it is sunrise.

14. False. Recall that the moon goes around the earth in the same direction that the earth goes around the sun, so that the interval between two New moons is LONGER than the true (sidereal) orbital time of the moon. The correct statement is that the synodic month is about 1/12 month LONGER than a sidereal month.

15. The moon exerts a tidal force on the earth, which is a STRETCHING force, and this pulls the earth into a "football" shape with a high point towards the moon and a high point away from the moon. Although the solid rocky earth cannot move much, the earth's oceans can, and so the oceans move onto these two bulge areas. These would be the regions of high tide. As the earth spins, any part of the earth is carried past both bulges during one revolution, or day. Hence there are two high tides each day.

16. False. Lunar eclipses MUST occur at full moon, when the moon has a chance of falling under the earth's shadow.

17. In a total eclipse of the Sun, the moon FULLY COVERS the sun's disk, bringing full darkness. In an annular eclipse of the sun, the moon FITS INSIDE the sun, with some of the sun's disk visible all the way around, hence appearing like a bright RING (hence annular, from Latin). The reason for the difference depends on the APPARENT SIZES of the moon and sun which in turn depend on their DISTANCES. Total eclipses occur when the moon is close and appears big (at perigee) and the sun is far and appears small (aphelion); while Annular eclipses occur when the moon is far (apogee) and the sun is close (perihelion). Of these two effects, the changing distance of the MOON is the greater, since the eccentricity of its orbit is larger (0.05) than the earth's orbit (0.016).

18. d. The moon's orbital plane is tilted by 5 degrees to the plane of the ecliptic. Hence at many full or new moons, the moon is way above or below the ecliptic which is where the earth and its shadow lie. Only when the moon is close to one of its NODES (the points where its orbit intersects the ecliptic) is there a chance for an eclipse.

19. Jovian planets are LARGER have MORE satellites and are FURTHER from the sun, than terrestrial planets. There are a bunch of properties which distinguish the Jovians from the terrestrials, other include : mass, composition, (and also rotation rate).

20. Both earth and Sun are 4.5 giga-years old (4.5 billion years). They have the SAME age. The age dating is done in a couple of ways --- Rocks from the earth, moon, and meteorites can be age dated using careful measurements of radioactive elements found in them. These measurements all point to an age of around 4.5 giga years. The age of the sun is more difficult to measure, but involves creating computer models of a star with the properties of the sun, and seeing how old it is when it matches the properties of the present day sun. The answer is again 4.5 giga years.

21. c. It is the temperature in the young disk which determines the composition of the planets which are built in a particular place (high temps = iron/silicate; cold=ice/hydrogen). Hence it is the gradient in temperature in the disk which causes the terrestrial planets to form close to the sun, while the jovians form further out.