21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 3, Problem 40QP
(a)
To determine
Draw the comet’s orbit and find when it is moving fast and slow.
(b)
To determine
Find the value of semimajor axis and time it will take to go around the Sun.
(c)
To determine
Find the distance from the Sun to the center of the ellipse and the eccentricity of the comer’s orbit.
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Suppose you're in a circular orbit around Saturn (M = 5.683 x 1026 kg) with a semi-major axis
of a = 237,948 km.
a. What is your orbital velocity?
b. Using the "Vis-viva" equation (which can be derived from the total energy)
v = GM
What is the delta-V you would need to get from your current orbit, into an elliptical orbit
that has an apoapsis near Titan (a = 1,221,870 km)?
The distance between the center of the earth and the
center of the ellipse = 40 000 km, the apogee distance is
the five times of the perigee distance of a satellite in an
elliptical orbit.
Determine the following:
1-
Semi-major axis of the elliptical orbit.
2-
Orbit eccentricity
3-
The apogee distance and perigee distance.
4. The orbital period
5. If the elliptical orbit is changed to be circular orbit,
determine the orbital period for the new orbit (circular
orbit)
Comet Halley has a semi-major axis of 17.7 AU. (The AU, or Astronomical Unit, is the distance from the Sun to the Earth. 1 AU = 1.50x1011 m.) The eccentricity of Comet Halley is 0.967.
a. How far is Comet Halley from the sun at Aphelion, the farthest position from the sun? (Give your answer in AU.)?
b. What is comet Halley's orbital time? (Give your answer in years.) Note: Using Kepler's third law in the form: P2 = a3 is convenient. This equation works for any object orbiting the sun when the orbital period is in years and the semi major axis is in AU. The reason this works is because this equation is normalized to earth. The AU and year are both 1 for Earth.
c. In what year will Comet Halley start to move back toward the sun?
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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- When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently, it is moving toward the inner solar system. Its period is 10,500 years. Its perihelion distance is 75 AU. a. What is its semimajor axis in astronomical units? b. What is its aphelion distance?arrow_forwardKepler’s third law says that the orbital period (in years) is proportional to the square root of the cube of the mean distance (in AU) from the Sun (Pa1.5) . For mean distances from 0.1 to 32 AU, calculate and plot a curve showing the expected Keplerian period. For each planet in our solar system, look up the mean distance from the Sun in AU and the orbital period in years and overplot these data on the theoretical Keplerian curve.arrow_forward(a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter, (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 109 m and a period of 7.16 days. Calculate the mass of Jupiter from this data, (c) Are your results to parts (a) and (b) consistent? Explain.arrow_forward
- Ma years, what is 2. Saturn has an orbital period of 29.46 years, and its average distance to the sun is 9.54 A.U. If Venus has an orbital period of 0.62 its average distance to the sun in astronomical units (A.U.)? M stance A.U., Conceptual Physics Reading and Study Workbook Chapter 14arrow_forward1. Suppose you have an Oort cloud comet on an orbit with pericenter distance 10,000 AU, and apocenter distance 20,000 AU. a. What are the semi-major axis and eccentricity of the orbit? b. What are the specific energy (energy per unit mass), and specific angular momentum (angular momentum per unit mass) of the comet? c. How fast is the comet moving at apocenter (relative to the Sun)?arrow_forward13. The diagrams represent Saturn and one of its moons, Titan. Which diagram shows the distance between the two points that should be used to calculate the gravitational attraction between Saturn and Titan?arrow_forward
- Our understanding of the elliptical motion of planets about the Sun spanned several years and included contributions from many scientists. a. Which scientist is credited with the collection of the data necessary to support the planet's elliptical motion? b. Which scientist is credited with the long and difficult task of analyzing the data? c. Which scientist is credited with the accurate explanation of the data?arrow_forwardI. Directions: Complete the given table by finding the ratio of the planet's time of revolution to its radius. Average Radius of Orbit Times of Planet R3 T2 T?/R3 Revolution Mercury 5.7869 x 1010 7.605 x 106 Venus 1.081 x 1011 1.941 x 107 Earth 1.496 x 1011 3.156 x 107 1. What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support? II. Solve the given problems. Write your solution on the space provided before each number. 1. You wish to put a 1000-kg satellite into a circular orbit 300 km above the earth's surface. Find the following: a) Speed b) Period c) Radial Acceleration Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer: Given: Unknown: Formula: Solution: Answer:arrow_forwardPluto’s orbit around the Sun is highly elliptical compared to the planets in our Solar System. It has a perihelion distance of 29.7 AU and an aphelion distance of 49.5 AU. a) What is the semi-major axis of Pluto’s orbit, in AU? b) What is Pluto’s orbital period, in Earth years?arrow_forward
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