Department of Physics, University of Colorado at Denver Physics 1052 (General Astronomy)

Experiment #5 — The Planets and Their Orbits: Size and Scale

This exercise focuses on exploring the differences in size and physical makeup of the planets, and character in their orbits and motion in the Solar System.

You need to carefully review this material and text book as needed to answer the all questions in each of the following sections.

Section 1: Size and composition of Jovian and Terrestrial planets

A. In figure 1, planets are arranged in their relative order from the Sun. Please anwser the following question from the help of the figure and book if needed.

1.1. Which is the biggest planet?

1.2. Which is the smallest planet?

1.3. Which are the four largest planets? Write in the order of largest to smallest.

1.4. Which are the four smallest planets? Write in the order of smallest to largest.

Please use the table on the next page to answer following questions.

1.5. How many times bigger than earth is Jupiter in terms of ratio of diameters ?

1.6. How many times bigger than Jupiter is the sun in terms of ration of diameters?

1.7. What is the ratio of the largest planet’s diameter to that of the smallest planet?

1.8. Do the planets seem to fall into groups based on size?

1.9. Which planets fall into each group?

B. Examinetheinformationonsurfacematerialsgivenintable1.(Notethatthetabledoesnotindicate likely surface materials for Uranus and Neptune; it is generally believed that their surfaces are probably composed of liquid and frozen gases).

1.10. Do the groups you found above based on size also seem to have different surface composition ? 1.11. If so, what are the differences between the groups?

1.12. Could you divide these groups into terrestrial and jovian? Which planet fall into which groups?

Figure 1

?

Department of Physics, University of Colorado at Denver Physics 1052 (General Astronomy)

Diameter of the Sun = 1,391,400 km; Earth’s mass = 5.98 x 1024 kg

??????????Mercury

?V enus

Earth

??Mars

?Jupiter

?Saturn

??Uranus

?Neptune

?diameter (Earth=1)

??0.382

?0.949

1

??0.532

?11.209

?9.44

??4.007

?3.883

?diameter (km)

??4,878

?12,104

12,756

??6,787

?142,800

?120,000

??51,118

?49,528

?mass (Earth=1)

??0.055

?0.815

1

??0.107

?318

??95

??15

?17

?mean distance from Sun(AU)

??0.39

?0.72

1

??1.52

5.20

??9.54

??19.18

?30.06

?orbital period (Earth years)

??0.24

?0.62

1

??1.88

11.86

?29.46

??84.01

?164.8

?eccentricity

??0.2056

?0.0068

0.0167

??0.0934

?0.0483

??0.0560

??0.0461

?0.0097

?mean orbital velocity(km/sec)

??47.89

?35.03

29.79

??24.13

13.06

?9.64

??6.81

?5.43

?rotation period (in Earth days)

??58.65

?-243*

1

??1.03

?0.41

??0.44

??-0.72*

?0.72

?inclination of axis (degrees)

??0.0

?177.4

23.45

??23.98

3.08

?26.73

??97.92

?28.8

?mean temperature at surface (oC)

??-180 to 430

?465

-89 to 58

??-82 to 0

?-150

?-170

??-200

?-210

?Surface nature

??rocky

?rocky

rocky

??rocky

?gaseous

??gaseous

??-

?-

?escape

velocity (km/sec)

??4.25

?10.36

11.18

??5.02

59.54

?35.49

??21.29

?23.71

?mean

density (water =1)

??5.43

?5.25

5.52

??3.93

?1.33

?0.71

??1.24

?1.67

?atmospheric composition

??none

?CO2

N2 + O2

??CO2

?H2 + He

?H2 + He

??H2 + He

?H2 + He

?number of moons

??0

?0

1

??2

?63

??62

??27

?13

?rings?

??no

??no

?no

???no

?yes

??yes

??yes

??yes

Negative values of rotation period indicate that the planet rotates in the direction opposite to that in which it orbits the Sun. This is called retrograde rotation.

Section 2: The relative scales of the orbits of the planets and their arrangements.

While planetary orbits are in fact ellipses, the perspective use in some illustrations tends to exaggerate their apparent eccentricity, or the degree of flateninning of the orbits. Planets orbits can be approximated by circles. But the orbits of Mars and Mercury are less circular than others. There is a regularity to the planets distances from the Sun which was recognized and stated as “rule” by astronomers Titius and Bode in 1772. Bode’s rule predicts planetary distaces from the Sun in the following way: write down for each planet the number 4, then add to it number 0 for Mercury, 3 for Venus, 6 for Earth, 12 for Mars, and so on for each successive planet. Include the asteroid belt located between Mars and Jupiter as planetary position. (Asteroid belt was in fact discovered by this means.) The add the numbers (e.g. 4 + 6 for Earth) and divide the result by 10. This number is then an estimate of each planet’s distance from the Sun in AU. Using the Bode’s Rule, calculate and write your estimate for each palnet in the bottom row in chart below. Show your work.

2.1. How closely do your predictions using Bode’s Rule mach the actual distances? 2.2. Do any of the planets fall well outside your predicted location?

2.3. Can you think of a possible cause for these regularities in planetory orbits?

????Planet

Mercury

?Venus

?Earth

??Mars

Asteroids

?Jupiter

??Saturn

?Uranus

??Neptune

??Distance

0.4

?0.7

?1.0

??1.5

2.8

?5.2

??9.5

?19.2

?30.0

??Estimate

Department of Physics, University of Colorado at Denver Physics 1052 (General Astronomy)

Section 3: Kepler’s law and shape of the planet’s orbits.

From the Kepler’s law we know that orbits of the planets are ellipses but not circle, the Sun being one of the foci of the elipses. As indicated in Figure 2, use a cardboard, two push pins and a string to draw two ellipses on the graph paper grid below. Use about six inches of srtings for each ellipse. For the first, separate pins by one inch and for the second separte them by two inches. Number your ellipses 1 and 2.

The eccentricity of planets’ orbit varies from about 0.0097 to 0.20565. A circle has eccentricity = 0 (both pins at the same point on the drawing board), while a straight line (no slack in the string) has ecenntricity = 1. We can calculate the eccentricity of the ellipses 1 and 2 by measuring distances for each ellipse, the shortest distance from one focus ( the apocenter distance, B). These distances lie along the major axis of the ellipse. The eccentricity is then

e?B B?2A

Record the A and B of the ellipses you drew below and calculate eccentricities of both ellipses.

Ellipse 1: A = _______ B = _________ ; eccentricity 1 = ———- = ——–

Ellipse 2: A = _______ B = _________ ; eccentricity 2 = ———- = ——–

Does the eccentricity you calculated for each ellipse corresponds to the flatness of the ellipse you drew; that is, bigger eccentricity, flatter ellipse?

B

A

Note: Please write a report according to general instructions for all labs. Write question and then write answer in the data and calculation section.

Department of Physics, University of Colorado at Denver Physics 1052 (General Astronomy)

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