More Gravitation & Kepler’s Laws, Conversions – 8B
Mass of Sun: 1.99 x 1030
Mass of Earth: 5.98 x 1024
Name: ____________________
Show your work (what you typed into your calculator, what equations you used, etc)!!!
1.
Saturn is 9.54 times further from the Sun than the Earth is. Calculate the period of Saturn’s orbit in years (Earth years).
2.
Uranus has an orbital period of 84 years. How many times larger is Uranus’ orbital radius than Earth’s?
b.
c.
3.
If Earth’s orbital radius about the sun is 1.4957 x 1011 meters, what is Uranus’ orbital radius?
Calculate the linear speed of Uranus’ orbit in meters/second
Venus has an orbital period of 225 days. Calculate Venus’ orbital radius as a multiple of the Earth’s?
b.
What is Venus’ orbital radius in meters (use info given in #2 part b)
c.
Calculate the linear speed of Venus in meters/second?
d.
How many times further from the sun is Uranus than Venus?
4.
Consider your answers to 2 c) and 3 c). We know that as the radius increases so does the period. As the radius increases, what
happens to the linear speed (increases or decreases)?
5.
In many instances, for things such as communication satellites and spy satellites, it is useful for satellites to remain right above the
same spot on Earth. These satellites are known as geosynchronous satellite, meaning they are in sync with the Earth and it takes
them the same amount of time to orbit the Earth as it does for the Earth to rotate once (which is why they stay above the same
spot above Earth. Calculate the necessary orbital radius for such as satellite. You need to convert its period to seconds. You
answer is distance from the center of the Earth. How far is this above the surface of the Earth in miles (there are 1609
meters/mile)?
6.
How many times more mass does the sun have than the Earth?
7.
The center of the moon is 3.9 x 105 km from the Earth’s center. Suppose you could run to the moon. How many years would it
take somebody running 4:20 per mile to get to the moon. Use the fact that there are 1609 meters in a mile, and pretend you are
running the entire 3.9 x 108 meters (not surface to surface, but center to center).
8.
Mimas, a moon of Saturn, has an orbital radius of 1.87 x 108 meters and an orbital period of 23 hours (convert to seconds). Use
this information to determine the mass of Saturn.
9.
The radius of the moon is 1.74 x 106 meters. It has a mass of 7.35 x 1022 kg. What would the period be (in minutes) of a satellite
that orbited the moon just above its surface?
10. The center of the moon is 3.9 x 108 m from the Earth’s center. Also, recall that the radius of the Earth is 6.37 x 106 m. How many
times harder does the moon pull on the near side of the Earth than it does on the far side? A good question to first answer is how
many times further away the far side of the Earth is to the moon compared the near side of the Earth.
11. How many times harder does the sun pull on the Earth than the moon? All necessary information is given in previous questions or
at the top of the page (highlighted in gray).
12. An asteroid orbits the sun with a linear speed of 8,146 m/s (over 16,600 miles per hour). Calculate the average orbital radius of
this asteroid.
13. The average radius of the sun is 6.96 x 108 meters. How many times more dense is the Earth than the sun? Recall, density =
mass/volume. The volume of a sphere = (4/3)πr3.
Answers:
1. 29.46 years
2. 19 times larger, 2.87 x 1012 m, 6800 m/s
3. .724, 1.08 x 1011 m, 35057 m/s, 26.5 times
4.
5. 42,250,474 m ; 22,299 miles
6. About 332,776
7. 1.99 years
8. 5.65 x 1026 kg
9. 108.5 minutes
10. 1.0675 times harder (recall Newton’s Law of Universal Grav. F ~1/r2, not 1/r.)
11. 183.6 times
12. 2 x 1012 m
13. About 3.92 times more dense.