Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 13, Problem 11OQ
To determine
The maximum distance from the sun.
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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)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.
The 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?
Chapter 13 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 13.1 - A planet has two moons of equal mass. Moon 1 is in...Ch. 13.2 - Prob. 13.2QQCh. 13.4 - Prob. 13.3QQCh. 13.6 - Prob. 13.4QQCh. 13 - Prob. 1OQCh. 13 - Prob. 2OQCh. 13 - Prob. 3OQCh. 13 - Prob. 4OQCh. 13 - Prob. 5OQCh. 13 - Prob. 6OQ
Ch. 13 - Prob. 7OQCh. 13 - Prob. 8OQCh. 13 - Prob. 9OQCh. 13 - Prob. 10OQCh. 13 - Prob. 11OQCh. 13 - Prob. 1CQCh. 13 - Prob. 2CQCh. 13 - Prob. 3CQCh. 13 - Prob. 4CQCh. 13 - Prob. 5CQCh. 13 - Prob. 6CQCh. 13 - Prob. 7CQCh. 13 - Prob. 8CQCh. 13 - Prob. 9CQCh. 13 - Prob. 1PCh. 13 - Determine the order of magnitude of the...Ch. 13 - Prob. 3PCh. 13 - During a solar eclipse, the Moon, the Earth, and...Ch. 13 - Prob. 5PCh. 13 - Prob. 6PCh. 13 - Prob. 7PCh. 13 - Prob. 8PCh. 13 - Prob. 9PCh. 13 - Prob. 10PCh. 13 - Prob. 11PCh. 13 - Prob. 12PCh. 13 - Review. Miranda, a satellite of Uranus, is shown...Ch. 13 - (a) Compute the vector gravitational field at a...Ch. 13 - Prob. 15PCh. 13 - A spacecraft in the shape of a long cylinder has a...Ch. 13 - An artificial satellite circles the Earth in a...Ch. 13 - Prob. 18PCh. 13 - Prob. 19PCh. 13 - A particle of mass m moves along a straight line...Ch. 13 - Prob. 21PCh. 13 - Prob. 22PCh. 13 - Prob. 23PCh. 13 - Prob. 24PCh. 13 - Use Keplers third law to determine how many days...Ch. 13 - Prob. 26PCh. 13 - Prob. 27PCh. 13 - (a) Given that the period of the Moons orbit about...Ch. 13 - Suppose the Suns gravity were switched off. The...Ch. 13 - Prob. 30PCh. 13 - Prob. 31PCh. 13 - How much energy is required to move a 1 000-kg...Ch. 13 - Prob. 33PCh. 13 - An object is released from rest at an altitude h...Ch. 13 - A system consists of three particles, each of mass...Ch. 13 - Prob. 36PCh. 13 - A 500-kg satellite is in a circular orbit at an...Ch. 13 - Prob. 38PCh. 13 - Prob. 39PCh. 13 - Prob. 40PCh. 13 - Prob. 41PCh. 13 - Prob. 42PCh. 13 - Prob. 43PCh. 13 - Prob. 44PCh. 13 - Prob. 45PCh. 13 - Prob. 46PCh. 13 - Ganymede is the largest of Jupiters moons....Ch. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50APCh. 13 - Prob. 51APCh. 13 - Voyager 1 and Voyager 2 surveyed the surface of...Ch. 13 - Prob. 53APCh. 13 - Why is the following situation impossible? A...Ch. 13 - Let gM represent the difference in the...Ch. 13 - A sleeping area for a long space voyage consists...Ch. 13 - Prob. 57APCh. 13 - Prob. 58APCh. 13 - Prob. 59APCh. 13 - Two spheres having masses M and 2M and radii R and...Ch. 13 - Prob. 61APCh. 13 - (a) Show that the rate of change of the free-fall...Ch. 13 - Prob. 63APCh. 13 - Prob. 64APCh. 13 - Prob. 65APCh. 13 - A certain quaternary star system consists of three...Ch. 13 - Studies of the relationship of the Sun to our...Ch. 13 - Review. Two identical hard spheres, each of mass m...Ch. 13 - Prob. 69APCh. 13 - Prob. 70APCh. 13 - Prob. 71APCh. 13 - Prob. 72APCh. 13 - Prob. 73APCh. 13 - Two stars of masses M and m, separated by a...Ch. 13 - Prob. 75APCh. 13 - Prob. 76APCh. 13 - As thermonuclear fusion proceeds in its core, the...Ch. 13 - The Solar and Heliospheric Observatory (SOHO)...Ch. 13 - Prob. 79CPCh. 13 - Prob. 80CP
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- 3. 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_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_forwardMars' period (its "year") was noted by Kepler to be about 687 days (Earth days), which is (687d / 365 d) = 1.88 yr. Determine the distance of Mars from the Sun using the Earth as reference. (The distance of Earth from the Sun is 1.50 x 10 m) !3! Thu TMS IMS TE TES TES TE 2 28 x 10 m TES yr After reading and understanding the concept Gravity, please do the following problems: 1. What keeps a satellite up in its orbit around the Earth?arrow_forward
- Please help mearrow_forwardAccording to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is approximately 3.82 x 105 km. The Moon orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month). Calculate the orbital velocity of the Moon in m/s.arrow_forwardTo model a moon in the solar system, consider a sphere with radius R and uniform mass density p. Let gm = the acceleration due to gravity on the surface of the sphere. Calculate gm for these values of R and p: R = 2.0×106 m; p= 2.7x103 kg/m^3; (in m/s^2) OA: OB: 1.509 2.007 OC: 2.669 OD: 3.549 OE: OF: 4.721 6.279 OG: 8.351 OH: 1.111x101arrow_forward
- According to Lunar Laser Ranging experiments the average distance L M from the Earth to the Moon is approximately 3.85 X 105 km. The Moon orbits the Earth and completes one revolution in approximately 27.5 days (a sidereal month). Calculate the mass of the Earth and provide your answer in units of 1024 kg. For example, if your answer is 2.7×1024 enter 2.7.arrow_forwardCalculate the period of a satellite orbiting the Moon, 100 km above the Moon's surface. Ignore effects of the Earth. The radius of the Moon is 1740 km. Express your answer using two significant figures. ΑΣφ ? T S E ||arrow_forwardAccording to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is approximately 3.92 x 105 km. The Moon orbits the Earth and completes one revolution relative to the stars in approximately 27.5 days (a sidereal month). Calculate the orbital velocity of the Moon in m/s. Answer: Choose...arrow_forward
- Kepler's third law states that the relationship between the mean distance d (in astronomical units) of a planet from the Sun and the time t (in years) it takes the planet to orbit the Sun can be given by d^3 = t^2. (A). It takes Venus 0.616 years to orbit the Sun. Find the mean distance of Venus from the Sun (in astronomical units). (B). The mean distance of Jupiter from the Sun is 5.24 astronomical units. How many years does it take Jupiter to orbit the Sun?arrow_forwardEstimation: The orbital period of the moon is 27.3 d, the average center-to-center distance center distance between the moon and earth is 3.82 * 10^8m, the length of an Earth year 365.25d, and the average center to center distance between earth and the sun is 1.50 x 10^11m. Use this data to estimate the ratio of the mass of the Sun to the mass of Earth. Compare this estimation to the measured ratio of 3.33 x 10^5. List some neglected factors that might account for any discrepancy.arrow_forwardO Jupiter's third-largest natural satellite, lo, follows an orbit with a semimajor axis of 422,000 km (4.22 × 105 km) and a period of 1.77 Earth days (Plo = 1.77 d). To use Kepler's Third Law, we first must convert lo's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 x 108 km). Convert lo's a value to AU and record the result. alo = AUarrow_forward
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