Download Kepler assignment 2012

Physics Assignment
2012
Criteria
1. demonstrate personal skills to organise and complete activities
3. collect, process and communicate information
4. demonstrate understanding of the application and impact of physics in society
5. *demonstrate knowledge and understanding of Newtonian Laws including gravitational fields
Due:
Question 1
3 main scientists Tycho Brahe, Isaac Newton and Johannes Kepler were instrumental in the
understanding of planetary motion
Tycho Brahe
Johannes Kepler
Isaac Newton
What did each of these men contribute to the theories on planetary motion
Question 2
a)
What is the difference between a geostationary, asynchronous and
polar orbit satellite?
b)
What applications would each satellite type have?
c)
An asynchronous satellite wishes to orbit the earth at a height of 700 km above the surface of
the earth. Determine the speed, acceleration and orbital period of the satellite. (Given: Mearth = 5.98 x
1024 kg, Rearth = 6.37 x 106 m)
Question 3
If a geostationary satellite wishes to orbit the earth in 24 hours (86400 s), then how high above
the earth's surface must it be located? (Given: Mearth = 5.98x1024 kg, Rearth = 6.37 x 106 m)
Question 4
One of Saturn's moons is named Mimas. The mean orbital distance of
Mimas is 1.87 x 108 m. The mean orbital period of Mimas is
approximately 23 hours (8.28x104 s). Use this information to estimate a
mass for the planet Saturn
Question 5
Orbital radius and orbital period data for the four biggest moons of Jupiter are listed in the table below.
The mass of Jupiter is 1.9 x 1027 kg.
a)
b)
Jupiter's Moon
Period (s)
Radius (m)
Io
1.53 x 105
4.2 x 108
Europa
3.07 x 105
6.7 x 108
Ganymede
6.18 x 105
1.1 x 109
Callisto
1.44 x 106
1.9 x 109
T2/R3
Determine the T2/R3 ratio (last column) for Jupiter's moons.
Which law of Kepler's does this seem to support?
c)
Using your graphics calculator, plot T2 vs. R3 (T2 should be plotted along the vertical axis) and
to determine the equation of the line. Write the equation in y =mx +c form.
d)
How does the T2/R3 ratio for Jupiter (from table) compare to the T2/R3 ratio found in (c) (i.e.,
the slope of the line
e)
How does the T2/R3 ratio for Jupiter you’ve calculated compare to the T2/R3 ratio found using
the following equation? (G=6.67x10-11 N*m2/kg2 and MJupiter = 1.9 x 1027 kg)
Question 6
a)
Galileo also studied the four largest of Jupiter's
moons. The moons orbiting Jupiter follow the same laws
of motion as the planets orbiting the sun. One of the
moons is called Io - its distance from Jupiter's center is
4.2 units and it orbits Jupiter in 1.8 Earth-days. Another
moon is called Ganymede; it is 10.7 units from Jupiter's
center. Make a prediction of the period of Ganymede
using Kepler's law of harmonies.
b)
Find and compare your answer to the theoretical value.
Question 7
a)
Suppose a small planet is discovered that is 97 times as far from the sun as the Earth's distance
is from the sun. Use Kepler's law to predict the orbital period of such a planet. GIVEN: T2/R3 = 2.97 x
10-19 s2/m3
b)
Does this planet exist?