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Planet Problem Set
Please solve the following problems and include clear explanations of how you found your answers. Include diagrams! Use 3 as
an approximate for π unless otherwise instructed. It is encouraged that you work together with others to solve these problems,
however, you should only submit your own work on this paper.
1. Fill in the circumference column in the Planet table, then give a general formula for how to find the circumference of a planet.
Show all your work here, including a diagram and clearly show how you solved the problem for Mercury.
2. Fill in the orbital speed column in the Planet table, then give a general formula for how to find the orbital speed of a planet in
km/hr. Assume that the planets travel at a constant rate around the sun. (Is this a reasonable assumption?) In your own words,
explain orbital speed, then clearly show you solved the problem for Mercury with the units clearly shown. Include a diagram.
3. Fill in the rotational speed column in the Planet table, then give a general formula for how to find the rotational speed of a
planet. In your own words, explain rotational speed then clearly show you solved the problem for Mercury with the units clearly
shown. Include a diagram.
4. The moon-Earth distance is approximately 385,000 km. If we want to find the distance the moon travels in its orbit around the
earth, we need to find its orbital radius. Because the moon is so much closer to the earth than the planets are to the sun, we need to
include the radius of the earth to find the orbital radius of the moon. Find the orbital radius of the moon and determine the distance
it travels around the earth, then find the speed at which the moon travels around the earth in km/hour. Include a diagram and
clearly show how you derived your units. (The moon revolves around the earth once every 28 days.)
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a. If you could fly to the Moon at a constant speed of 1000 kilometers per hour, which is the speed of a fast passenger jet,
how many days would it take to get there? Show work and units here.
b. If Apollo astronauts reached the Moon in just less than four days, how fast were they travelling in km/hour? How fast
is that in miles/hour? Show work and units here.
5. Around the World in 80 days, written by French author Jules Verne recounts the journey of Phineas Fogg as he
circumnavigates the earth in 80 days. At what speed would Phineas need to travel in order to successfully complete his journey?
Give your answer in km/hr and miles/hr. Show how you derived your units.
6. Astrology: The earth travels through all 12 zodiac (sun signs) signs each year. Draw a diagram of the earth’s orbit around the
sun as it passes through the 12 signs and use your diagram to answer the following questions. Show diagram here.
Sign
Aries
Taurus
Gemini
Cancer
Leo
Virgo
Libra
Scorpio
Sagittarius
Capricorn
Aquarius
Pisces
Symbol
Ram
Bull
Twins
Crab
Lion
Virgin
Balance
Scorpion
Archer
Goat
Water Bearer
Fish
Dates
March 21 - April 19
April 20 - May 20
May 21 - June 20
June 21 - July 22
July 23 - Aug 22
Aug 23 - Sept 22
Sept 23 - Oct 22
Oct 23 - Nov 21
Nov 22 - Dec 21
Dec 22 – Jan 19
Jan 20 - Feb 18
Feb 19 - March 20
a. How far does the earth travel during the sign of the goat (Capricorn)? How far does the earth travel during the spring as
it moves through the signs of Aries, Taurus and Gemini? Give your answers in degrees (arc measure) and in km (arc
length). Show all work here.
b. If the earth moves through 73 degrees of its orbit, how many zodiac signs does it move through? How far does it travel
in km? Show your work and incllude a diagram.
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c. If the earth travels through100 million km of its orbit around the sun (arc length), determine the arc measure of its path.
How many zodiac signs will the earth move through during this time? Show work and a diagram.
7. You are assigned to make a scale drawing of the planets in the solar system where the earth is approximately the size of a tennis
ball. Since you can’t actually measure the diameter of a tennis ball (why not?) you manage to meaure the circumference, which is
19.0 cm. Find the diameter of the tennis ball. Use 3.14 for an approximation for π and give your answer to the nearest .1cm.
Show how you arrived at the following answers.
a. How big would the planet Jupiter be in your drawing (diameter)?
b. If you were making a 3D model, what object might you use to represent Jupiter?
c. What would Mercury’s diameter be in your drawing?
d. If this were 3D model, what object might you use to represent Mercury?
8. If the earth’s gravity was suddenly turned off, the moon would continue on a tangent path out into space. Draw a diagram that
shows the orbital path the moon would take as the earth’s gravity is turned off and find the speed it would travel. Would it travel
at a constant speed? How long would it take the moon to visit Pluto? Show all work here.
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9. You set up your super powered telescope on the surface of the sun (impossible, I know) with a 57 degree viewing range. Draw a
diagram and clearly explain how you solve the following problems. Make sure your answers make sense, given your data.
a. What fraction (out of 360) of Jupiter’s orbital path are you able to see in your viewing range?
b. What is the total length of Jupiter’s orbital path?
c. How many kilometers of Jupiter’s total path (arc lengtha) are you able to see in your range?
d. How long would it take Jupiter to pass through the viewing range of your telescope.
10. Answer questions a – d, for Uranus.
11.Planet X moves through 250 million km of its orbital path (arc length) as it passes through 65º (arc measure) of its orbit. How
far is planet X from the sun? Show your work. Hint: Find the total distance traveled around the sun first.
12. Planet Y moves through 330 km of its orbital path (arc length) as it passes through 75º (arc measure) of its orbit. How far is
Planet Y from the sun?
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