PHYSICS 1040 - ELEMENTARY ASTRONOMY - HOMEWORK #7

1. Jupiter data: Average distance from Sun = 5.203 A.U.

Orbital period = 11.86 years

Rotational period = 9 hours 50 minutes

Diameter = 11.2 x Earth=s diameter

Average density = 1.326 x water=s density

Average temperature = -108 oC (at cloudtops)

Saturn data: Average distance from Sun = 9.572 A.U.

Orbital period = 29.4 years

Rotational period = 10 hours 14 minutes

Diameter = 9.4 x Earth=s diameter

Average density = 0.687 x water=s density

Average temperature = -180 oC (at cloudtops)

 

2. About 71 percent of Jupiter=s mass is hydrogen, 24 percent is helium, and 5 percent is heavier elements. (The numbers I gave in class were older estimates.  Sorry for the confusion!)  The great abundance of the two lightest elements explains why Jupiter=s average density is so high/low (circle one). Jupiter=s atmospheric weather pattern has a banded appearance. The light-colored zones consist of high-altitude clouds, and the dark-colored belts consist of low-altitude clouds. Jupiter=s Great Red Spot is a 300-year-old storm; it has some of the planet=s highest/lowest (circle one) clouds. The motion of Jupiter=s atmosphere is controlled by three factors:

a. Jupiter=s rapid rotation.

b. energy from the Sun.

c. energy from Jupiter=s interior that is left over from its formation.

In fact, Jupiter radiates about twice as much energy as it receives from the Sun!

 

3. Jupiter rotates so fast it is not spherical but oblate (slightly flattened). The study of Jupiter= s oblateness shows that, at its center, Jupiter has a dense, rocky core about the size of Earth but with 8 times Earth= s mass. Surrounding this is a hot liquid layer of water, methane, and ammonia. Above this, and reaching nearly to the surface, it a layer of helium and liquid metallic hydrogen. The outermost layer consists of ordinary hydrogen and helium. Jupiter=s strong magnetic field is generated by currents in the liquid metallic hydrogen layer.

 

4. Jupiter satellite data:

 

distance
from Jupiter(Jupiter radii)

orbital period
(days)

diameter(km)

density
(x water=s density)

Io

5.905

1.769

3642

3.529

Europa

9.397

3.551

3120

3.018

Ganymede

14.99

7.155

5268

1.936

Callisto

26.37

16.689

4800

1.851

Moon

-----

-----

3476

3.344

Jupiter

-----

-----

142,984

1.326

Mercury

-----

-----

4880

5.430

a. Which two satellites have a density nearest our Moon=s density?

Io and Europa

b. Which two satellites have a density nearest Jupiter=s density?

Ganymede and Callisto

c. Which satellite is nearest the size of Earth=s Moon?

Io

d. Which satellite is nearest the size of Mercury? Callisto

e. Which satellite is largest? Ganymede

 

5. According to Kepler=s 3rd law, a3/P2 = a constant; the constant = 1 for planets orbiting the Sun if R (the semimajor axis) is measured in AU and P (the orbital period) is measured in years. Fill out the table below and show that the Galilean satellites also obey a law similar to Kepler=s 3rd law. Don= t worry about the units; just use the numbers provided to calculate a3/P2 for each satellite. The first one has been done for you.

 

a(Jupiter radii)

P
(days)

a3

P2

a3/P2

Io

5.905

1.769

205.9

3.129

65.80

Europa


9.397


3.551


829.8

 
12.61 

 
65.80 

Ganymede

 
14.99


7.155


3368

 
51.19 

 
65.79

Callisto


26.37


16.689


18,337

 
278.5 

 
65.84 

 

6. The number of surface craters found on the four Galilean satellites of Jupiter decreases steadily from Callisto, the outermost moon, to Io, the innermost moon. The reason for this is that Callisto has the oldest surface, and Io has the youngest surface. Processes that are capable of covering craters, such as volcanic eruptions, are most important on the surface of Io, but are not as important on the more distant moons.

 

7. Io is covered with a yellowish/reddish layer of sulfur compounds deposited by eruptions from volcanic geysers on Io=s surface. Every 100 years Io ejects enough material to cover its surface to a depth of one meter, and any impact craters would quickly be covered. Recall from Homework #4 that the smaller/larger (circle one) the world, the less internal heat it is likely to have retained, and thus, the less geologic activity it will display on its surface. Tiny Io remains hot because tidal forces from Jupiter=s gravity squeeze Io as it moves about its elliptical orbit. This tidal heating is responsible for keeping Io=s interior hot and its surface active.

 

8. Europa is the smoothest object in the solar system. There are almost no craters on its surface; only three craters larger than 5 km across have been found. This means that Europa=s surface must be very young/old (circle one) and active. Europa=s surface is almost pure frozen water. Europa=s slushy ice crust is about 10 km thick. Below the crust there may be a layer of liquid water, perhaps 50 km deep. Below this ocean is Europa=s rocky core, which makes up 85 - 90 percent of Europa=s mass. Like Io, Europa=s interior is warmed by the effects of Jupiter's tidal force.

 

9. Saturn=s rings are made of snowball-size particles of ice and ice-covered rock. These ring particles orbit Saturn in their own individual orbits that obey Kepler's laws. If all of the ring particles were collected together to form a moon, the moon would be only 100 km in diameter! However, this will not happen. A planet=s Roche limit is the closest distance a large moon can be to a planet. If the moon gets any closer than the Roche limit, it will be torn apart by the planet=s gravitational tidal force. All of Saturn=s large moons are inside/outside (circle one) of Saturn=s Roche limit, and all of the rings are inside/outside (circle one). This prevents Saturn=s ring particles from ever coming together to form a moon.

 

10. An orbital resonance occur in Saturn's rings when a ring particle orbits Saturn an integral number of times faster than one of Saturn's large moons (2 times faster, 3 times faster, and so on). For example, a ring particle in the Cassini division between the A and B rings would orbit Saturn twice as fast as Saturn's moon Mimas. This means that the ring particle would line up with Mimas every two orbits. The repeated tugs of Mimas' gravity thus keeps the Cassini division between the A and B rings clear of particles.

 

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