PART B(Please provide your answers to this part in the space provided in page 4)

21.Describe the Titius Bode law and estimate the distance to planet Saturn from the Sun inAstronomical Units (AU).

The Titius Bode law is the law that estimates how far a planet is from the sun. The formula is

d(n) = 0.4 + 0.3 * {2^(n-2) for (n => 2)0 for (n=1)

Where n is the nth planet. Saturn is seven, so plugging in 7 the distance is estimated to be 10AU.

22. Draw a sketch of the celestial sphere and label i) ecliptic, ii) celestial equator, iii) Vernal andAutumnal equinoxes. On the same diagram or a separate diagram indicate the equatorialcoordinate system: Right Ascension and Declination.

25. If the Moon’s tides pull the water away from the Earth, why are there two high tides a day?

The Moon pulls on the near side’s oceans more than the Earth and the far side’s oceans less thanthe Earth. This creates two high tides, one on the near side and one on the far side.

26. Do the tides cause the Earth’s rotation to speed up or slow down? Why?

The tides cause Earth’s rotation to slow down. The Moon orbits the Earth much more slowlythan the Earth rotates, and the tides follow the Moon’s orbit around the Earth. This relativemotion between the Earth and tides creates friction that reduces the speed of the Earth’s

rotation.

27. How many solar eclipses can you have in a year? Can they all be total?

The maximum number of solar eclipses in one year is five. This is because you can have amaximum of two eclipses per solar season, and a calendar year consists of a little more than twosolar seasons (when the Sun is near a node, which is an intersection between the Moon’s orbitalplane and the ecliptic). For a total solar eclipse, the Moon and Sun need to almost perfectlyalign, and the Moon needs to be close enough to the Earth in its elliptical orbit to completelycover the Sun. In other words, the Moon’s synodic period (time between new moons), theMoon’s draconic period (time between corresponding nodes), and the Moon’s anomalisticperiod (time between perigees) need to align. The Moon’s synodic period is 29.53 days, itsdraconic period is 27.21 days, and its anomalistic period is 27.55 days. If a total eclipse occursat some point one year, then one new moon later, 1.08 draconic periods will have elapsed, so theMoon will no longer be precisely aligned with the node. During the next eclipse season 6 newmoons after the total eclipse, 6.511 draconic months will have elapsed, so the Moon and Sunwill no longer be perfectly aligned with the other node (off by about 1/3°, compared to theMoon’s 1/2° angular diameter). In addition, 6.431 anomalistic months will have elapsed, so theMoon may not be close enough to perigee to produce a total eclipse.