Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 11, Problem 11OQ
To determine
The comet’s maximum distance from the sun in astronomical units.
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(a)
Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result.
aIo = AU
(b)
One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result.
PIo = yr
(c)
Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result.
MJup(Io) = MSun
(d)
Based on this result, Jupiter's mass is about that of the Sun.
Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.
A comet (see the figure below) approaches the Sun to within 0.570 AU, and its orbital period is 79.6 yr. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean Earth-Sun distance.) How far from the Sun will the comet travel before it starts its return journey?
A 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).]
Chapter 11 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 11.1 - A planet has two moons of equal mass. Moon 1 is in...Ch. 11.3 - An asteroid is in a highly eccentric elliptical...Ch. 11.4 - Prob. 11.3QQCh. 11.5 - Prob. 11.4QQCh. 11 - Prob. 1OQCh. 11 - The gravitational force exerted on an astronaut on...Ch. 11 - Prob. 3OQCh. 11 - Prob. 4OQCh. 11 - A system consists of five particles. How many...Ch. 11 - Suppose the gravitational acceleration at the...
Ch. 11 - Prob. 7OQCh. 11 - Prob. 8OQCh. 11 - Prob. 9OQCh. 11 - Rank the following quantities of energy from...Ch. 11 - Prob. 11OQCh. 11 - Prob. 12OQCh. 11 - Prob. 13OQCh. 11 - Prob. 14OQCh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - In his 1798 experiment, Cavendish was said to have...Ch. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - A 200-kg object and a 500-kg object are separated...Ch. 11 - Prob. 4PCh. 11 - Prob. 5PCh. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - A spacecraft in the shape of a long cylinder has a...Ch. 11 - (a) Compute the vector gravitational field at a...Ch. 11 - Prob. 13PCh. 11 - Two planets X and Y travel counterclockwise in...Ch. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - Prob. 18PCh. 11 - Plasketts binary system consists of two stars that...Ch. 11 - As thermonuclear fusion proceeds in its core, the...Ch. 11 - Comet Halley (Fig. P11.21) approaches the Sun to...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - Prob. 25PCh. 11 - A space probe is fired as a projectile from the...Ch. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Prob. 30PCh. 11 - Prob. 31PCh. 11 - Prob. 32PCh. 11 - Prob. 33PCh. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - Prob. 38PCh. 11 - Prob. 39PCh. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - Prob. 42PCh. 11 - Prob. 43PCh. 11 - Prob. 44PCh. 11 - Prob. 45PCh. 11 - Prob. 46PCh. 11 - Let gM represent the difference in the...Ch. 11 - Prob. 48PCh. 11 - Prob. 49PCh. 11 - Two stars of masses M and m, separated by a...Ch. 11 - Prob. 51PCh. 11 - Prob. 52PCh. 11 - Prob. 53PCh. 11 - Prob. 54PCh. 11 - Prob. 55PCh. 11 - Prob. 56PCh. 11 - Prob. 57PCh. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Prob. 61PCh. 11 - Prob. 62PCh. 11 - Prob. 63PCh. 11 - Prob. 64PCh. 11 - Prob. 65P
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- A comet has a period of 72.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.540 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. HINT (a) the semimajor axis of the comet (in AU) AU (b) an estimate of the comet's maximum distance (in AU) from the Sun AUarrow_forwardA comet has a period of 81.8 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.540 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. (a)the semimajor axis of the comet (in AU) AU (b)an estimate of the comet's maximum distance (in AU) from the Sun AUarrow_forward(a) A reasonably accurate value for the AU is 1.50 × 101 m. If the year is a × 107 s, (2) (a good approximation, and one easy to remember) calculate Earth's speed in km/s assuming a circular orbit about the Sun. (b) The experimental determination (first attempted by Cavendish in 1797/98) yields G = 6.67×10-11 N-m²/kg?. Calculate the mass of the Sun. (c) On the other hand, when we measure distances in AU and speeds in km/s, the constant in the Vis-Viva Equation is GM = 900. Explain why this is the case. (d) Once we know the distance to the Sun, using its angular size one could determine that the radius of the Sun is approximately Rsun = 7 × 10* m. Calculate the ratio of the Sun's density to that of water.arrow_forward
- Needs Complete typed solution with 100 % accuracy.arrow_forwardA comet has a period of 75.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.640 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. (a) the semimajor axis of the comet (in AU) (b) an estimate of the comet's maximum distance (in AU) from the Sunarrow_forwardA comet has a period of 70.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.620 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. (a) the semimajor axis of the comet (in AU) (b)an estimate of the comet's maximum distance (in AU) from the Sunarrow_forward
- A)At what altitude would a geostationary sattelite need to be above the surface of Mars? Assume the mass of Mars is 6.39 x 1023 kg, the length of a martian solar day is 24 hours 39minutes 35seconds, the length of the sidereal day is 24hours 37minutes 22seconds, and the equatorial radius is 3396 km. The answer can be calculated using Newton's verison of Kepler's third law.arrow_forwardThe average Earth-Moon distance is 3.84 X 10^5 km, while the Earth-Sun is 1.496 X 10^8 km. Since the radius of the Moon is 1.74 X 10^3 km and that of the Sun is 6.96 X 10^5 km. a) Calculate the angular radius of the Moon and the Sun, qmax, according to the following figure. D Bax R b) Calculate the solid angle of the Moon and the Sun as seen from Earth. (c) Interpret its results; Would this be enough to explain the occurrence of total solar eclipses?arrow_forwardObservations and trigonometry can be used to determine that Earth's moon has an orbital period of 27.32 days and a mean orbital radius of 384,400 km. Using this information, calculate the mass of the Earth.arrow_forward
- If the satellite was placed in an orbit three times farther away, about how long would it take to orbit the Earth once? Answer in days, rounding to one significant figure.days Mars rotates on its axis once every 1.02 days (almost the same as Earth does). (a) Find the distance from Mars at which a satellite would remain in one spot over the Martian surface. (Use 6.42 1023 kg for the mass of Mars.)m(b) Find the speed of the satellite.m/sarrow_forwardOn the evening of an autumnal equinox day Siddhant noticed that Mars was exactly along the north-south meridian in his sky at the exact moment when the sun was setting. In other words, the Sun and Mars subtended an angle of exactly 90° as measured from the Earth. If the orbital radius of Mars is 1.52 au, What will be the approximate rise time of the mars on the next autumnal equinox day?arrow_forward3. The Moon has a period of 27.3 days and a mean distance of 3.90×105 km from the center of Earth. a. Use Kepler's laws to find the period of a satellite in orbit 6.70x103 km from the center of Earth. b. How far above Earth's surface is this satellite?arrow_forward
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