PHYSICS 1050 – SOLAR SYSTEM ASTRONOMY FALL 2003

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Problem 6, Chapter 1

Physics 1050 – Solar System Astronomy

Fall 2003 - Dr. Mike Fanelli

Solutions to Assigned Problems

Problems are taken from Chaisson and McMillan, fourth edition.

CHAPTER 1

Problem 1:

In one second light leaving Los Angeles reaches about how far ? Five possibilities are listed.

ANSWER: Light travels at 300,000 kilometers per second, a large but not infinite speed. Of the five choices, the correct one is (c) the Moon, since the moon’s average distance from Earth is given as 384,000 km. Light takes about 1.3 seconds to reach the Moon.

Problem 2:

This problem complements the worksheet available under “Handouts” on the class webpage.

(a) 1000 = 10³, 0.000001 = 10^-6, 1001 = 1.001 x 10³

1,000,000,000,000,000 = 10¹⁵, 123,000 = 1.23 x 10⁵, 0.000456 = 4.56 x 10^-4

(b) 3.16 x 10⁷ = 31,600,000, 2.998 x 10⁵ = 299,800

6.67 x 10^-11 = 0.0000000000667, 2 x 10⁰ = 2

(1.99 x 10³⁰) / (5.98 x 10²⁴) = 3.328 x 10⁵

(3.16 x 10⁷) x (2.998 x 10⁵) = 9.47 x 10¹²

Problem 6:

Through how many degrees, arcminutes, and arcseconds does the Moon move in (a) one hour, (b) one minute, (c) one second ? How long does it take the Moon to move a distance equal to its own diameter on the sky ?

ANS: Here you are asked to think about angular motion — the motion of an object across the sky with respect to the background of stars. The Moon takes 27.3 days to complete 1 orbit of the Earth with respect to the stars, a period known as a sidereal month. Through a telescope, the moon’s motion is readily apparent, but to the eye, it requires careful observation over several hours to notice the Moon’s changing position against the background of stars. This problem exercises your understanding of (1) angular units, degrees, minutes, and seconds, (2) how to convert one set of units into another, and (3) the use of ratios.

Note that the symbol for arcminutes is  and the symbol for arcseconds is .

(a) How far does the moon move in an hour ?

The moon completes one orbit in about a month, or more quantitatively, moves through 360 degrees in 27.3 days. 360 divided by 27.3 = 13.19 degrees per day. Each day the moon will appear about 13 to the east of its position at the same time on the previous day.
Now convert to motion per hour. 13.19 degrees/day divided by 24 hrs/day = 0.55 degrees/hr. The moon passes through a little more than ½ of a degree in one hour of time.
Since 1 = 60 arcminutes, then 0.55 = 33 arcminutes (this is a ratio, 1:60 as 0.55:33). Therefore the moon moves through 33 arcminutes per hour of time.
Since 1 arcminute = 60 arcseconds, then the moon moves through 33 times 60 arcseconds in a hour = 1978 per hour of time.

(b) How far does the Moon move across the sky in 1 minute ?

Moving 0.55 degrees / hr divided by 60 minutes per hr = 0.0092 degrees / min. The moon moves through a small fraction of a degree in one minute of time.
As 1 = 60 arcminutes, then 0.0092 = 0.55 arcminutes. The moon moves through 0.55 arcminutes per minute of time.
Since 1 arcminute = 60 arcseconds, the moon moves through 33 arcseconds per minute of time. This motion is easily visible through a small telescope.

Moving 0.55 degrees per hour divided by 3600 seconds per hour = 0.000153 degrees in a second of time.
If the moon moves 0.55 arcminute per minute of time (from part b) then the moon will move 0.55 / 60 = 0.0092 arcminutes in one second of time.
0.0092 arcminutes X 60 arcseconds per arcminute = 0.55 per second of time.

(d) How long does it take the Moon to move a distance equal to its own diameter ?

The diameter of the moon = 30 arcminutes = 0.5 degree (given in the notes).
From part (b), the moon moves through 0.55 arcminutes per minute of time
The time in takes to move a specific distance = that distance divided by the rate of motion. An analogy is estimating travel time on a car trip. The time it takes to travel 100 miles at 50 mph = distance (100 miles) divided by the rate (50 mph) = 2 hours. By analogy, the time it take the Moon to move one lunar diameter = distance traveled (30 arcminutes) / divided by rate (0.55 arcminutes per minute) = 54.5 minutes, just under an hour.

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