Michael:

Physics 9 The Solar System with Prof. D. Tytler Oct. 2000

Homework 5, due Nov 9 in class
Note: second midterm is on Nov 14, Tue. Same style as first midterm.

We encourage you to work together, to discuss the topics and solutions, but your answers must use all of your own words, calculations and diagrams.

You must not hand in work copied from someone else.

Please write down the code numbers of all in your study group.

The first two problems are to encourage you to categorize information in preparation for the second midterm. The others encourage you to examine and absorb your class notes, except the last, which deals with the question: how do we learn about planets.

Make a table which compares and contrasts comets, asteroids and meteoroids, in terms of mass, age, size, orbits and composition.

Comets

Asteroids

Meteoroids

Mass

Typical comets are larger and hence more massive than typical asteroids, but not by much. Some asteroids are larger than most comets.

Lighter than a comet since there are no volatiles. Collisions break up asteroids.

Lightest, those entering Earth’s atmosphere range from 10^-10g to 1000g

Age

4.5Byr formed along with rest of solar system. Pristine.

4.5 Byr like comets, but changed by later collisions.

Fragments of asteroid collisions and parts of disrupted comets. Age = time since last major change, which was probably a collision billions of years ago.

Orbits

Very eccenteric. Long-period comets follow almost parabolic paths, while short-period comets follow elongated elliptical orbits about Jupiter.

Most found between Earth and Jupiter. Orbits are slightly eccentric, but much less than those of comets.

Orbits similar to asteroids, except that those which hit the Earth must cross the Earth’s orbit, which is rare for asteroids.

Composition

Ice and primitive rock mixture

Mostly rock. Specifically: carbonaceous chondrites, stone/silicates, and metallic. Some believed to be exhausted comets.

Same as Asteroids, from which they originate.

As question 1, but for the terrestrial planets.

	Mercury	Venus	Earth	Mars
Mass	Lightest of the Inner Planets 3.3 x 10²³kg	About the same as Earth 48.7 x 10²³kg	About the same as Venus 59.7 x 10²³kg	Twice mercury: 6.4 x 10²³kg
Age	All the same as the age of the Sun and rest of solar system: 4.5 Byr, but surface has been changed by later cratering.	4.5 Byr, but surface is about 800 Myr old (book sais 500)	4.5 Byr The youngest surface.	4.5 Byr
Orbit	Closest to Sun	Between Mercury and Earth	Between Venus and Mars	Furthest from Sun
Composition	Iron, Nickel, (Metals) and Silicates (Rocks); Smallest density	Silicates, Iron and Nickel.	Same as Venus	Silicates, Iron, and Sulfur. Smallest proportion of Iron

Why do we not expect many comets or asteroids with circular orbits at distances between 5 and 30 AU from the Sun?

The gravity of large outer planets changes orbits in this part of the solar system, and ejects objects, e.g the origin of the Oort cloud comets.

Why do we expect small moons, asteroids and comets to lack volcanoes and (earth)quakes?

Because these bodies are small enough that they should be cool throughout, and hence static, unlike a large body like the Earth or Venus which have retained internal heat. As the heat travels out to the surface, it moves the rocks, leading to continental drift, and other activity (volcanoes, earthquakes).

What’s the difference between a long period comet and a member of the Oort cloud?

A long period comet was once a member of the Oort cloud, the only difference is that its’ path was once directed into the solar system, where it was again modified to an orbit which brings it back to the sun again. It will not return to the Oort cloud. Long period comets loose mass each time they pass near the sun, and eventually, after about 10,000 years they run out of volatiles.

How long is the lunar day? Night?

For the Earth, we use the word day to mean two things: the spin period of 24 hours, and the time when the sun is above the horizon, which is 12 hours on average. For the moon these two times are one month and two weeks.

Why was the rate of impacts much higher when the solar system was young?

Long ago there were more objects moving in the solar system that had not yet been ejected, destroyed by impact or accumulate into larger bodies, so the impact rate was much higher.

If in the distant past, the impact rate was 10,000 times higher than the current level, estimate the rate at which 20 kiloton, 50 Megaton, 1 Gigaton (Giga = 10⁹) and 1 Teraton (Tera = 10¹²) impacts occurred. Use values given in Lecture 11. Rates will be number per unit time. Choose units of time such that the rates are always of order unity (e.g., 1 per hour, rather than 30 per day).

20k: 10,000 x 1 impact / year = 27.4 / day = 1.14 / hour = 1 / 1 hour, 8 minutes,31 seconds (Or just 1 / hour)

50M: 10,000 x 1 impact / 300 years = 33.33 / year = 2.8 / month = 1 / 10 days, 19 hours, 12 minutes (Or just 3 / month –OR- 1 / 11 days)

1G: 10,000 x 1 impact / 30,000 years = 1 / 3 years

1T: 10,000 x 1 impact / 1,000,000 years = 1 / 100 years

Your car radio tuner breaks, and can only pick up 101.5 Megahertz. If you want to hear 105.3 Megacycles, what should you do? If you want to hear 95.7 Megahertz, what should you do?

The idea is move towards or away from the radio station, so that the Doppler effect moves the apparent frequency to that of your radio. You must also move very fast to notice the effect – this is why radio stations don’t bleed into each other when driving around.

To actually observe these effects would require either moving towards the source at 6 percent the speed of light (18,000 kilometers per second) or moving away from it at 4% the speed of light (11,000 kilometers per second). These distances are comparable to the diameter of the Earth.

So basically you should just get your radio fixed. The Doppler shifts are tiny, and not noticed without special instrument (eg. spectrographs) except when objects are moving at near the speed of light. Still, the Doppler effect is extremely important, and gives the velocities of all objects in astronomy.

When are tides highest?

The tides are highest during a Full Moon or a New Moon, when the pull of the Moon is combined with the pull of the Sun to create a large net effect.

A billion years from now will one year contain more than, less than, or exactly 365 days?

In a billion years the Earth’s spin will have slowed because of its tidal interactions with the Moon. Thus, the Earth will rotate more slowly, so there will be fewer days during the time the Earth goes around the sun.

The numbers are:

1 x 10⁹ yrs x 0.002 sec/100 yrs = 2.0 x 10⁴ sec x 1 hr/3600sec = 5.6 hours, giving a day of 24 hours + 5.6 hours = 30 hours.

The revolution of the Earth takes 3 x 10⁷ seconds, and this won’t change. There are then 365.25x(24/29.6) days per year = 292 days per year.

Interestingly, tides also slow the moon, pushing it further out. The moon will be 30,000 kilometers farther from the Earth then.

There have been many missions to Mars. Pick one. Summarize the mission. Which scientific instruments were on the satellite? What were the scientific goals? What was learned.

The answer should describe, either in complete sentences or in table form, the name, goal, design, country and results of the mission. For complete listing of missions to Mars visit either of the following web sites: http://nssdc.gsfc.nasa.gov/planetary/chronology_mars.html

http://observe.ivv.nasa.gov/nasa/exhibits/mars/missions/mission1a.html

	Comets	Asteroids	Meteoroids
Mass	Typical comets are larger and hence more massive than typical asteroids, but not by much. Some asteroids are larger than most comets.	Lighter than a comet since there are no volatiles. Collisions break up asteroids.	Lightest, those entering Earth’s atmosphere range from 10^-10g to 1000g
Age	4.5Byr formed along with rest of solar system. Pristine.	4.5 Byr like comets, but changed by later collisions.	Fragments of asteroid collisions and parts of disrupted comets. Age = time since last major change, which was probably a collision billions of years ago.
Orbits	Very eccenteric. Long-period comets follow almost parabolic paths, while short-period comets follow elongated elliptical orbits about Jupiter.	Most found between Earth and Jupiter. Orbits are slightly eccentric, but much less than those of comets.	Orbits similar to asteroids, except that those which hit the Earth must cross the Earth’s orbit, which is rare for asteroids.
Composition	Ice and primitive rock mixture	Mostly rock. Specifically: carbonaceous chondrites, stone/silicates, and metallic. Some believed to be exhausted comets.	Same as Asteroids, from which they originate.