1.
The fastest plane can travel at about 4400 kilometers/hour. How long would it take to travel to the Sun?
Convert your answer to the number of days and then the number of years. (The time it takes to travel a given distance = (distance travelled)/speed, or in the notation used in the chapter: t = D/v.)
The distance to the Sun from the Earth is (on average) 1 Astronomical Unit (AU) or 150 million kilometers. t
 d v

150

10
6 km
4,400 km hr

34 , 090 hr

1,420 days
So flying at 4,400 km/hr, the trip to the Sun would take 3.89 years.

3.89
yr
Just for interest, the Earth in that same 3.89 years would travel almost four complete trips around the
Sun. The approximate distance the Earth travels around the Sun in 3.89 years is 3.66 billion kilometers.
So you can see that the Earth is traveling about 24 times (ratio of 3.66 billion to 150 million) the speed of the fastest plane This means that right now, as you read this solution, your are traveling at about
106,000 km/hr around the Sun. No wonder people questioned the idea that the Earth actually moved back during the Renaissance.
2.
How far away is the nearest star outside of the solar system in kilometer units and light year units?
The nearest star beyond the Sun is Proxima Centauri, the closest star in the triple star system commonly known as Alpha Centauri. Proxima Centauri is about 4.3 light years distant or, equivalently
4 .
3 ly

4 .
3 ly



9 .
46

10
12 km ly



4 .
07

10
13 km

40 .
7

10
12 km

40.7
Trillion km
Again, just for interest, the Sun is about 8.1 light minutes away – that means that light leaving the Sun requires 8.3 minutes to reach the orbit of the Earth. The nearest star beyond the Sun is about 270,000 times farther from the Sun that we are. If the scale of the Universe were shrunk so that the Sun was just one foot from the Earth, Proxima Centauri would be about 270,000 feet or a bit over 51 miles away!
3.
How many kilometers would a light year be if it was discovered that the speed of light was two times slower than previously thought?
If it was discovered that the speed of light was two times slower than previously thought then a light year would be only half as long as it is now or 4 .
73

10
12 km. The speed of light in a vacuum is
3 .
00

10
5 km s
. Mathematically, it would look like this:

d
 v
 t

0 .
5

3 .
00

10
5 km s


 365 .
241 days
 hr
24 day

6 0 min hr

6 0 s min



4 .
73

10
12 km
4.
Where is our solar system in the Milky Way Galaxy?
Astronomer’s only learned of the Sun’s position in the Milky Way in the early part of the 1900’s. We now believe that the Sun is very nearly in the mid-plane of the galaxy and 28,000 light years from the center of the galaxy. This places the Sun about ½ way out from the center of the galaxy.
5.
How old is the Earth compared to the age of the universe?
This is a ratio problem where we compare the age of the Earth (4.6 billion years) to the age of the
Universe (13.8 billion years).
Age of Earth
Age of Universe

4 .
6 billion
1 3.8
billion years years

0 .
33
So the Earth is about 33% or 1/3 the age of the Universe.
Note: The Earth is really quite old. It is life on the Earth that is relatively recent. The first fossil life forms on Earth are about 3.5 billion years old. This means that life on Earth has been around for only
25% of the Age of the Universe. More dramatically, people (Homo Sapiens) have been on Earth, according to the fossil record for only 200,000 years. This means that people have existed for only
0.0015% of the age of the Universe. We are truly a new phenomena.
6.
How many times older is the Earth than the first civilizations?
This is a ratio problem where we compare the age of the Earth (4.6 billion years) to the age of the first civilization. A little web surfing indicates that the first civilization was known as Sumer in Babylonia.
Sumer flourished about 7,000 years ago.
Age of Earth
Age of First Civilizati aon

4 .
6 billion
7 ,000 years years

657 , 000
So the Earth is about 657,000 times older than the first civilization.
7.
What would be the altitude and azimuth of Polaris for observers at the following locations:*
Altitude of Polaris Azimuth of Polaris
1.
Syracuse, NY (43°N, 76°W)
2.
Moscow, Russia (56°N, 37°E)
3.
Havana, Cuba (23°N, 82°W)
4.
Fairbanks, Alaska, (65°N, 147°W)
5.
Quito, Ecuador (9°S, 78°W)
43°
56°
23°
65°
-9°
0°
0°
0°
0°
0°

6.
Buenos Aries, Argentina (35°S, 58°W) -35°
0°
8.
How many degrees does the Earth rotate on its axis each hour? If a star crosses an observer’s meridian in Syracuse, NY at 9:00 p.m. on Monday, at what time will it cross the meridian for an observer in
Moscow, Russia? Remember that the Earth rotates eastward on its axis.*
The Earth rotates 360° on its axis in 24 hours so that in one hour it rotates
360


15 deg hr
. Since the
24 hr stars appear to move westward as seen on the eastward rotating Earth, a star transiting (to “transit” is to cross the meridian) in Syracuse, NY at 76°W longitude must appear to move 247° around the Earth to be transiting in Moscow at 37°E longitude. The time required for the star to appear to rotate 247° is just
247

15 deg hr

16 .
47 hrs

16 hr 28 min . So a star transiting Syracuse’s meridian at 9:00 p.m will transit
Moscow.s meridian 16h 28 m later at 1:28 p.m. the next day (Syracuse time).