21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3.2, Problem 3.2CYU
To determine
Order the following from largest to smallest semi major axis.
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The planet Earth has a semi-major axis of a = 1.00 AU and an orbital period of
P= 1 sidereal year = 365.25 days = 3.156 x 10^7 s. Compute the orbital periods of bodies
orbiting the Sun with each of the following semi-major axes.
a)
a = 0.1 AU
b)
a = 10 AU
c)
a = 100 AU
d)
a = 1000 AU
e)
a = 10,000 AU
1 AU = 1.496 x 10^8 km = 1.496 x 10^11 m = 1.496 x 10^13 cm.
GM(sun) = 1.327 x 10^20 m^3/s^2 = (Newton's Constant) x (Mass of Sun)
%3D
%3D
You land on Mars and observe that one of its moons (Phobos) has an orbital period of 7.66 hours. If the Phobos were farther from Mars than it is now, it’s period would be
a) less than 7.66 hrs.
b) about 7.66 hrs.
c) more than 7.66 hrs.
d) difficult to predict without more information.
Directions: Complete the given table by finding the ratio of the planet’s time of the revolution to its radius.
Planet
Average
Radius of
Orbit
Times of
Revolution
R3
T2
T2 /R3
Mercury
5.7869 × 1010
7.605 ×106
Venus
1.081 × 1011
1.941 ×107
Earth
1.496 × 1011
3.156 ×107
What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?
Chapter 3 Solutions
21st Century Astronomy
Ch. 3.1 - Prob. 3.1ACYUCh. 3.1 - Prob. 3.1BCYUCh. 3.2 - Prob. 3.2CYUCh. 3.3 - Prob. 3.3CYUCh. 3.4 - Prob. 3.4CYUCh. 3 - Prob. 1QPCh. 3 - Prob. 2QPCh. 3 - Prob. 3QPCh. 3 - Prob. 4QPCh. 3 - Prob. 5QP
Ch. 3 - Prob. 6QPCh. 3 - Prob. 7QPCh. 3 - Prob. 8QPCh. 3 - Prob. 9QPCh. 3 - Prob. 10QPCh. 3 - Prob. 11QPCh. 3 - Prob. 12QPCh. 3 - Prob. 13QPCh. 3 - Prob. 14QPCh. 3 - Prob. 15QPCh. 3 - Prob. 16QPCh. 3 - Prob. 17QPCh. 3 - Prob. 18QPCh. 3 - Prob. 19QPCh. 3 - Prob. 20QPCh. 3 - Prob. 21QPCh. 3 - Prob. 22QPCh. 3 - Prob. 23QPCh. 3 - Prob. 24QPCh. 3 - Prob. 25QPCh. 3 - Prob. 26QPCh. 3 - Prob. 27QPCh. 3 - Prob. 28QPCh. 3 - Prob. 29QPCh. 3 - Prob. 30QPCh. 3 - Prob. 31QPCh. 3 - Prob. 32QPCh. 3 - Prob. 33QPCh. 3 - Prob. 34QPCh. 3 - Prob. 35QPCh. 3 - Prob. 36QPCh. 3 - Prob. 37QPCh. 3 - Prob. 38QPCh. 3 - Prob. 39QPCh. 3 - Prob. 40QPCh. 3 - Prob. 41QPCh. 3 - Prob. 42QPCh. 3 - Prob. 43QPCh. 3 - Prob. 44QPCh. 3 - Prob. 45QP
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- The solar system has a planet with an orbital period T1b=1.51d and an orbital radius of R1b=1.6456x10^6km. Another planet in the system has an orbital radius of R1f=5.5352x10^6 km. Calculate its orbital period in days.arrow_forwardKepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.arrow_forwardA pendulum makes 10 swings every 15 seconds on Earth. You take the same pendulum to the surface of a different planet and you notice that the pendulum makes 15 swings in 15 seconds. Which of the following could be true? (Select two right answers) 1. The mass of the planet is larger than Earth 2. The mass of the planet is smaller than Earth 3. The radius of the planet is larger than Earth 4. The radius of the planet is smaller than Eartharrow_forward
- Average distance from Mars to the Sun: 1.524 x 106 A) using the fact that the sun subtends an angle of 0.5 degrees from the Earth, determine the angular size of the Sun from Mars.arrow_forward1. Mars takes 1.88 years to complete one orbit around the sun. What is its average distance from the sun?arrow_forwardWhich of the following is true in our solar system? 1. The planets travel in a circular path, with the sun being in the very center. 2. The planets travel in an elliptical path, with the sun being in the very center. 3. The planets travel in an elliptical path, with the sun at one of the focus points. 4. The planets travel in a helical path, with the sun located along the central axis.arrow_forward
- 18. Which of the following heavenly bodies might you be standing upon if you are experiencing a weight of 16, 500N, knowing that you have a mass of 60kg? Assume that you can stand atop the said heavenly body. Hint: Use common sense, or refer to the table of acceleration due to gravity of each planets and the Sun. Group of answer choices Mars No answer Sun Moon Mercuryarrow_forwardIf you know the radius of a planet, what additional information besides universal constants do you need to calculate its mass? a) Acceleration of a falling object near its surface b) Distance to a nearby star c) Mass of its moon d) Orbital period around its sunarrow_forwardA new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of 12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU ..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.] Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]arrow_forward
- Distance Orbital Period 88 days 225 days Mercury 0.39 AU Venus 0.72 AU Earth 1.00 AU 365 days Mars 1.52 AU 687 days (a) Calculate the average distance of Mercury, Venus and Mars to the Earth. Which one of these planets is the closest to Earth on average? (b) Calculate the average distance of Mercury, Venus and Earth to Mars. Which one of these planets is the closest to Mars on average? (c) What do you expect for the other planets? Hint: Assume circular orbits and use symmetries to make the distance calculation easier. You can approximate the average distance by using four well-chosen points on the planet's orbit.arrow_forward2. An unknown planet was accidentally discovered by NASA. It has a mean distance of 2.15 E11 meters from the sun. Assuming it has a mass of 6.02 E24 kg, how long (in Earth Years) will it take for the said planet to revolve around the sun?arrow_forwardThe planet Saturn has a mass of 5.68×10^26 kg and a radius of 58,200 km. Janus, a moon of Saturn, has a mass of 1.9×10^18 kg and it orbits Saturn a distance of 151,400 km from the center of Saturn. - How many hours does it take for Janus to orbit Saturn?arrow_forward
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