Show that the orbital period of a satellite close to the surface of a spherical object depends on the mean density of the object, but not on its size. Find this period for the Earth (density 5.51 g cm 3).

Show that the orbital period of a satellite close to the surface of a spherical object depends on the mean density of the object, but not on its size. Find this period for the Earth (density 5.51 g cm 3).

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter13: Universal Gravitation

Section: Chapter Questions

Problem 13.6OQ: An object of mass m is located on the surface of a spherical planet of mass M and radius R. The...

See similar textbooks

Related questions

Q: A spherical planet has an outer radius R; its density p varies as a function of distance r given by…

A: Given data: The density function is, ρr=3-2r2R2.

Q: An artificial satellite is traveling 8.0 x 10 m/s in a circular orbit. Assuming g= 9.7 m/s at that…

Q: Spacecraft X has 1/3 the mass of Spacecraft Y. They orbit Earth at the same radius. Which of these…

A: The gravitational force exerted between two objects of mass M and m , is calculated by using the…

Q: Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down…

A: The acceleration due to gravity at depth inside the earth surface is given by the relation,

Q: A Mars orbiter is orbiting Mars at 35,000 m above the Martian surface. What is its period in…

A: Height of Mars orbiter above the Martial surface: h = 35000 m Mass of Mars: Mm = 6.42 x 1023 kg…

Q: Consider a moon orbiting planet A in a radius R with a given period T. If the planet has a mass of…

Q: A satellite of mass m is orbiting Earth in a stable circular orbit of radius R. The mass and radius…

A: Satellite speed and independent of mass of satellite.

Q: The attractive gravitational force between a spherical body of mass M and another spherical body of…

A: ω=2πf Acceleration of satellite = ω2r r = radius of revolution = RE+h Force experienced by…

Q: Show that the square of the escape speed is equal to the product of diameter of the Earth and the…

A: Escape velocity is the minimum velocity with which a body must be project vertically upward so that…

Q: Find the force of gravitational attraction from a uniform ring of mass M and radius a on a small…

Q: Find the force of gravitational attraction from a uniform disk of mass M and radius a on a small…

Q: The mass of Jupiter is 314 times that of Earth and the diameter of Jupiter is 11.35 times that of…

A: The equation for the acceleration due to gravity on earth is given by,

Q: The mean diameter of the planet Uranus is 5.11 ✕ 107 m, and the acceleration due to gravity at its…

A: Mean diameter of planet Uranus = 5.11 × 107 m Acceleration due to gravity at surface = 8.87 m/s2

Q: (III) (a) Show that if a satellite orbits very near the surface of a planet with period T, the…

A: (a) Let M denote the mass of the given satellite, and let v denote its speed of revolution. Very…

Q: Find the escape velocity that a 1500 kg satellite needs to escape from the Solar System from Earth…

Q: Assuming the earth to be a sphere of uniform mass density, how much would a body weight half way…

Q: Find the escape velocity of a 1500 kg satellite from the Solar System while on the Earth's orbit.…

Q: A 2210 kg space station orbits Earth at an altitude of 5.35 × 10° m. Find the magnitude of the force…

A: Given data : Mass of space station, ms = 2210 kg Height from the surface of…

Q: The gravitational attraction (N) between two identical spheres of mass 43 kg and radius 0.82 m in…

Q: With what orbital speed will a satellite circle Jupiter if placed at a height of 9.00 106 m above…

A: Given data: Height (h) = 9.00 × 106 m Mass of jupiter (M) = 1.90 × 1027 Radius of jupiter (R) =…

Q: An artificial satellite is in a circular orbit d 520.0 km above the surface of a planet of radius r…

A: Given data : radius of planet, r = 4.65 × 103 km = 4650000 m height of satellite, d = 520 km =…

Q: A satellite moves in a circular orbit around the earth at a speed of 3400 m/s determine. a) The…

Q: A woman whose weight is 680 N on the Earth’s surface is in a spacecraft at an altitude above the…

A: Weight, W = 680 N Weight in the spacecraft, W' = ?

Q: A newly discovered planet X has a mass of 36.7 × 1023 kg and radius 2.47 × 106 m. What is g on this…

Q: A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. If…

A: Given: acceleration due to gravity on the surface of Mars is gm. Height, h = 3 R where, R is the…

Q: How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around…

A: Write the expression to obtain the mass of the Sun.

Q: For a satellite to be in a circular orbit 890 km above the surface of the earth, (a) what orbital…

Q: Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down…

Q: If all planets had the same average density, how would the acceleration due to gravity at the…

A: Acceleration due to gravity

Q: What is the orbital speed (in km/s) of a 187 kg satellite orbiting at an altitude of 4.53 x 103 km…

A: Given data: Mass of satellite (m) = 187 kg Altitude (h) = 4.53×103 km = 4.53×106 m Mass of earth (M)…

Q: It was stated that a satellite with negative total energy is in a bound orbit, whereas one with zero…

A: Consider a satellite of mass m orbiting around it at a distance r from the planet of mass M. For the…

Q: Show that the minimum period for a satellite in orbit around a spherical planet of uniform density p…

A: The mathematical formulation of the gravitational force is given as, Here, M is the mass of the…

Q: A 2290 kg space station orbits Earth at an altitude of 4.67 x 10° m. Find the magnitude of the force…

Q: Two satellites, A having mass of 500 kgs and B having mass of 1200 kgs, are launched from earth.…

A: Given: The mass of the first satellite is 500 kg. The mass of the second satellite is 1200 kg. The…

Q: An artificial satellite is in a circular orbit 5.50×102 km from the surface of a planet of radius…

A: Given data: The distance between satellite and planet is, d= 5.50×102 km=5.50×105 m The radius of…

Q: The attractive gravitational force between two particles is increasing if: O a. the product of thier…

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

7. Show that the orbital period of a satellite close to the surface of a spherical object depends on the
mean density of the object, but not on its size. Find this period for the Earth (density 5.51 g cm
cm-3).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet
The mean diameter of the planet Mercury is 4.88106m , and the acceleration due to gravity at its surface is 3.78m/s2 . Estimate the mass of this planet.
The mean diameter of the planet Saturn is 1.2108m , and its mean mass density is 0.69g/cm3 . Find the acceleratin due to gravity at Saturn’s surface.
(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.
Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?
(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.
3. The gravitational acceleration at Earth's surface (ge) is about 10 m/s? and ge = GM/R?. What is gp at the surface of a planet with 2X Earth's mass and 3X Earth's radius?
3 3 3 23 24 There are three planets in a distant solar system. Planet P, Planet Q, and Planet R have equal volumes and radii. They differ by their masses. Planet P is the most massive. Planet R is the least massive. The picture shows the planets for comparison. Planet P 1000 Tg Which planet has the strongest gravity field at its surface? A. Planet P C. Planet R B. Planet Q D. All have equal surface gravity. Which forms of matter have gravity? A. Solids C. Gases & Liquids B. Solids & Liquids D. Gases, Liquids, & Solids Planet Q 500 Tg Planet R 100 Tg
02 2. Earth's radius is 6370 km and the moon's radius is 1738 km. The acceleration of gravity at the surface of the moon is 1.62 m/s². What is the ratio of the average density of the moon to that of Earth? 0.605
The average density of the planet Neptune is 1.67x10 kg/m The ratio of the mass of Uranus to that of Neptune is 0.840. The ratio of the radius of Uranus to that of Neptune is 1.03. Find the average density of Uran us. 11 -
1. Compute the gravitational force exerted by the earth to a 70 kg man whose elevation above the surface of the earth equals the radius of the earth. Assume Me- 5.9742x10 kg and the diameter of the earth is 12756 km.
3. Mars has a mass of 6.46 × 1023 kg and a radius of 3.39 × 10° m. a) Calculate the acceleration due to gravity on Mars. b) How much would a 65 kg person weigh on this planet?