Download Accelerated patterns in the solar system

ACCEL: PATTERNS OF MASS AND DENSITY IN THE SOLAR SYSTEM
Name: ____________________________________
Date: ______________
Purpose: To investigate the patterns of mass, density, and size of planets in the solar system and
compare the terrestrial and giant planets.
Background: Mass is a measure of the amount of matter an object contains. The masses of the
planets on the Planet Data Table are given in relation to Earth’s mass. For example, mercury’s
mass is given as 0.056, which means that it contains only a small fraction of the matter that Earth
contains. On the other hand, the giant planets contain several times more matter than Earth.
Density is the amount of matter in a given amount of space, or the mass per unit volume of a
substance. The average densities on the Planet Data Table are expressed in grams per cubic
centimeter (g/cm3). For density, the density of pure water is approximately 1 g/cm3.
Hypothesis: What relationship do you think you will observe between the mass, density, and
size of planets.
Procedure: Refer to the Planet Data Table handout to find the information needed to answer the
following questions. Answer in complete sentences unless answer is a fill-in.
1.
2.
3.
The planet ____________________ is the most massive planet in the solar system. It is
_______________ times more massive than Earth.
The least massive planet (excluding Pluto) is _________________________, which
contains only _______________ as much mass as Earth.
How many times more massive than Mercury is Jupiter?
times
The gravitational attraction of a planet is directly related to its mass. In other words, as a
planet’s mass increases, its gravitational attraction increases. Your weight is a function of the
gravitational attraction of an object acting on your mass.
4. Which planet exerts the greatest pull of gravity? Explain your answer.
5.
On which planet would you weigh the least? Explain your answer.
6.
Which of the two groups of planets: terrestrial or giant, would have the greatest ability to
hold large quantities of gas as part of their composition? Explain your answer.
7. Write a general statement comparing the masses of the terrestrial planets to the masses of the
giant planets.
8.
Plot a point on the graph below for each planet (excluding Pluto). The point should be
plotted where the planet’s diameter intersects its density. Use the diameter measurements
in kilometers from the Planet Data Table. Label each point with the planet’s name. Use a
different color for the terrestrial planets and the giant planets. Give the graph a title and
include a key.
DIAMETER (km X 1000)
150
100
50
0
0
1.0
2.0
3.0
4.0
5.0
6.0
DENSITY (g/cm3)
9.
What general relationship exists between a planet’s diameter and its density?
Circle your answers for the next two questions.
10. The densities of the two rock types that form the majority of Earth’s surface, the igneous
rocks granite and basalt, are each about 3.0 g/cm3. The average densities of the terrestrial
planets are (greater than, less than) the density of Earth’s surface rocks. The average
densities of the giant planets are (greater than, less than) the density of Earth’s surface
rocks.
11. The term (rocky/gaseous) best describes the terrestrial planets.
12. The average density of Earth is about 5.5 g/cm3. Considering that the densities of Earth’s
surface rocks are much less than Earth’s average density, you could infer that the center of
the Earth is made of _____(rock/gas) that is (more than /less than) 5.5g/cm3________.
13. Which of the planets has a density less than water and could therefore “float” (if you could
find a large enough container!)? ______________________________
14.
Explain why it is possible for Jupiter to be such a massive object and yet have such a low
density.
15.
Write a general statement comparing the densities of the terrestrial planets to the densities
of the giant planets.
16.
Why are the densities of the terrestrial and giant planets so different?
17.
Examine the estimated mass, diameter and density of Pluto. Complete the following
statements by circling the correct response.
The mass of Pluto is most like the masses of the (terrestrial, giant) planets, while the
density is similar to that of the (terrestrial, giant) planets. This suggests that Pluto is a
(small, large) body made of (rock, ice and frozen gas).
17. Pluto makes up the Kuiper belt. What do you think the other objects in the Kuiper belt
would be like in terms of density and composition (use the data in the chart and the patterns seen
to support your statement)?
18. If the material in the asteroid belt (2.8AU) had coalesced to form a planet, what do you think
it would have been like in terms of density and compostion? Would it likely have become a
terrestrial planet or a Jovian planet? Explain your reasoning
OTHER PATTERNS IN THE SOLAR SYSTEM – Use the information in the Planet Data
Table to explore some of the other relationships between the planets.
19. Describe the relationship between:
(a) distance from the sun and a planet’s period of revolution
(b) distance from the sun and a planet’s orbital velocity.
20. Describe the relationship between the number of moons (satellites) a planet has and
(a) its mass.
(b) its general distance from the sun.
21. How do the patterns you see between inner and outer planets fit in with the Nebular
Hypothesis?What accounts for their differences?
PART 2 Density of Moons
We know that rocks have an average density of 3.5g/cm3 and ice has a density of 0.9 g/cm3. We
can calculate the density of a moon by using the following formula:
(3.5 x percentage of rock) + (0.9 x percentage of ice) = density
100
Scientists can estimate the mass of something by its gravitational pull and they can estimate its
size using techniques like angular size. From this we can determine a density of objects in space.
If we wanted to know the percentage that was ice or rock we would need to use the formula
above except the problem is that there are now two unknowns (both the % ice AND the % rock).
However because the two together must equal 100%, we can assume that the percentage of 1ce is
always equal to 100 minus % rock. So we can rewrite the equation as follows:
(3.5 x % rock) + (0.9 x (100 - %rock) = density
100
Now you can simply solve for the % rock to figure out the portion of the objects density that is
ice versus that which is water.
1. Use this formula to determine the % of rock for Jupiter’s moon Callisto, which has a density
of 1.8g/cm3 Show your calculations and circle your answer.
2. What would be the % ice for Callisto?
When dealing with lots of moons its is easiest to make a graph since there is a relationship
between the % of rock and % ice and the density. Use the formula to complete the chart:
(3.5 x percentage of rock) + (0.9 x percentage of ice) = density
100
Percent rock
Percent Ice
100
80
60
40
20
0
0
20
40
60
80
100
Density of
moon g/cm3
3.5
Make a line graph on the next page of the density of moon vs. the percent Rock. Give it a title.
DENSITY OF MOON
3.0
2.0
1.0
% ROCK
1. Jupiter’s moon Ganymede has a density of 1.9 g/cm3. Based on your graph what percentage
of it is rock?
2. Neptune’s moon Triton has a density of 2.1 g/cm3 and would therefore be ____% rock.
3. Jupiter’s moon Europa has a density of 3.0g/cm3. What is its % of rock?
4. How do you think the rock and ice is distributed inside the moons? Give the reason for your
answer.