Find an expression for the square of the orbital period. Express your answer in terms of G, M, R, and π. The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U=−G*Mm/R. What is the kinetic energy K of the satellite? Express your answer in terms of the potential energy U.

Find an expression for the square of the orbital period. Express your answer in terms of G, M, R, and π. The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U=−G*Mm/R. What is the kinetic energy K of the satellite? Express your answer in terms of the potential energy U.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 83PQ

See similar textbooks

Related questions

Q: As discussed on many different days of the semester, the number 4 x 1026 corresponds to what very…

A: Option (b) is correct. The sun's total power output is 3.8×1026 W So , the power output of sun is…

Q: Gravitational attraction force between two objects with masses m, and m2, separated by distance x,…

Q: A satellite of mass 20000 Kg orbits the earth along a path of long 3 x 108 m calculate: a) The…

A: Given- Mass of satellite, ms = 20000 kg = 2 ×104 kg Length of path l = 3 x 108 m Gravitational…

Q: Two Earth satellites, A and B, each of mass mmm = 940 kg, are launched into circular orbits around…

A: Given : m = 940 kg rA = 4500 km = 4.5 x 106 m rB = 11100 km = 1.11 x 107 m

Q: Answer no. 1 ( a&b) and no. 2 please 1. Assume that a satellite orbits Earth 225 km above its…

A: given that, Height (h) = 225km Mass of Earth (M)= 5.97 x 10^24 kg Radius of Earth (r) = 6.38 x 10^6…

Q: A natural satellite of a distant planet orbits 421,700 km from the planet's center once every 42.5…

A: Consider a satellite having mass m revolving around the planet (mass M) in a circular orbit of…

Q: Given four masses with their mass and height relative to the ground shown. Which mass has the most…

Q: Two satellites are in circular orbits around a planet Part A that has radius 9.00 x 106 m. One…

Q: An astonaut stands on the surface of the moon. If the astronaut has a mass of 86.0 kg what is the…

A: Given,

Q: The potential function for the gravitational force field due to a mass M at the origin acting on a…

Q: 1. Find the orbital speed v of a satellite in a circular orbit of radius R around a planet of mass…

A: 1)The centripetal force on satellite is equal to the gravitational force of attraction between…

Q: For the purposes of this problem, treat the Earth as a solid, uniform sphere with mass 5.97x1024 kg…

A: It is given that, M=5.97×1024 kgRe=6.37×106 mRo=1.5×1011 m

Q: If all the items in the figure have the same mass,which two items will have the same gravitational…

A: Let mass of each object A, B, C, and D = m The acceleration due to gravity = g ( for each object).…

Q: planet’s

A: When the height of the object above the ground is more, then its gravitational potential energy will…

Q: The mass of Mars is 6.42 × 10^23 kg. Its moon Phobos is 9.378 x 10^6 meters away from Mars, with a…

Q: 29. A unit for gravitational potential energy is the (1) watt (2) joule (3) newton (4) kilogram .…

A: 29) To find : The uit for gravitational potential energy

Q: A planet is observed to be in an elliptical orbit around the sun as shown below. Which of the…

A: According to Kepler's second law if any planet moves in elliptical orbit around sun having it one of…

Q: How much energy is required to move a 1250 kg object from the Earth's surface to an altitude twice…

A: Given data: Mass of object is, m=1250 kg.

Q: A satellite of mass m, originally on the surface of the Earth, is placed into Earth orbit at an…

Q: In a shuttle craft of mass m = 4500 kg, Captain Janeway orbits a planet of mass M = 9.70 x 1025 kg,…

A: Given: mass of shuttle craft m = 4500 kg Mass of planet M = 9.70*1025 kg radius of circular orbit r…

Q: Chapter 13, Problem 011 In the figure, two spheres of mass m = 9.24 kg. and a third sphere of mass M…

Q: In this problem you will measure the gravitational constant in a series of “observational…

A: Given that initial velocity vi 494 m/sec ME = 5.95×1024 kg Ri = 6.41×106 m H = 12.7 km Question…

Q: For a 100 kg satellite orbiting Earth in a circular orbit of radius 6500 km, determine the…

A: Part (a) Basic Details The kinetic energy of the satellite depends on the mass of the satellite, the…

Q: Problem 1. A planet with a mass of 7.00x10-" kg is in a circular orbit around a star with a mass of…

Q: A comet orbits the sun (mass m_S) in an elliptical orbit of semi-major axis a and eccentricity e…

Q: (f 601) N

A: Calculating the minimum velocity (escape) on the basis of kinetic energy

Q: Find an expression for the kinetic energy of a satellite of mass m in an orbit of radius r about a…

A: Consider a satellite having mass m revolving around the planet with mass M and the radius of the…

Q: (a) At what position in its elliptical orbit is the speed of a planet a maximum? O when it is…

A: Kepler's planetary law states that the areal velocity of a planet is constant that is a planet…

Q: A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Calculate the energy of the moon orbiting the Earth. (mass of the Earth = 6.02 x 10^24 kg, mass of…

Q: Kepler’s laws of planetary motion can be derived from Newton’s laws of motion and Newton’s universal…

A: There is no external force is acting on the solar system, the total mechanical energy of the…

Q: A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant…

Q: Calculate the gravitational force between two 100 kg objects located 10 m from one another. F, =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: A satellite is in orbit above a planet. Which of the following is TRUE? 1. The total energy of the…

A: The answer is below

Q: B. At what distance above the earth's surface will your weight decrease to half of what it is at the…

A: Radius of Earth, r = 6370 × 103 m Gravitational constant, G = 6.67 × 10-11 Nm2/kg2 Acceleration due…

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: he figure, a square of edge length 19.0 cm is formed by four spheres of masses m1 = 5.20 g, m2 =…

A: GivenEdge length of square, a=19 cm=19×10-2 mm1=5.20 g=5.2×10-3 kgm2=2.9 g=2.9×10-3 kgm3=1.5…

Q: An earth-like planet with a mass of 6.00×1024 kg has a space station of mass 4.60×104 kg orbiting it…

A: M = 6x1024 kg m = 4.6x104 kg r = 5x105 km G = 6.7x10-11 Nm2/kg

Q: A space station has a mass of 5.00x 10 kg and orbit at radius of 6.38× 10m from the center of Earth.…

A: Mass of space station (M) = 5 * 105 kg Radius of orbit of space station = 6.38 * 106 m Mass of earth…

Q: A satellite with a mass of 1000 kg is placed in Earth orbit at an orbit of 500 km above the surface.…

A: Given data The mass is m=1000 kg The distance above the surface is, h=500 km (b) The satellite’s…

Q: A spacecraft of mass 1.00 × 10^3 kg orbits the sun (mass 1.99 * 1030 kg) in a circular orbit of…

A: Given: The mass (m) of the spacecraft is 103 Kg. The mass (M) of the sun is 1.99×1030 Kg.…

Q: A spacecraft is on a journey between 2 planets. The masses of the Planet A and Planet B are…

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

Find an expression for the square of the orbital period.

Express your answer in terms of G, M, R, and π.

The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by

U=−G*Mm/R.

What is the kinetic energy K of the satellite?

Express your answer in terms of the potential energy U.

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

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

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

What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?
(a) What is the change in energy of a 1000-kg payload taken from rest at the surface of Earth and placed at rest on the surface of the Moon? (b) What would be the answer if the payload were taken from the Moon’s surface to Earth? Is this a reasonable calculation of the energy needed to move a payload back and forth?
(a) Using the data in the previous problem for the asteroid Vesta which has a diameter of 520 km and mass of 2.671020kg , what would be the orbital period for a space probe in a circular orbit of 10.0 km from its surface? (b) Why is this calculation marginally useful at best?
For a 100 kg satellite orbiting Earth in a circular orbit of radius 6500 km, determine the following: Part A its kinetic energy, K Enter your answer in scientific notation in the following format: The coefficient, followed by the capital letter E, followed by the exponent. For example, if your answer is 5.0\times10^8 \space J5.0×108 J, enter 5.0E8 J Part B its potential energy, U (U = 0 at infinity) Enter your answer in scientific notation in the following format: The coefficient, followed by the capital letter E, followed by the exponent. For example, if your answer is 5.0\times10^8 \space J5.0×108 J, enter 5.0E8 J
A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. First, find an expression for the gravitational potential energy PE in terms of G, M, m, and R. a)Calculate the value of PE in joules. b)Enter an expression for the total energy E of the satellite in terms of m and v. c)Calculate the value of the total energy E in joules.
The gravitational force on a point mass m due to a point mass M is a gradient field with GMm potential U(r) = - where G is the gravitational constant and r = √√x² + y² + z² is the 1 r distance between the masses. Answer parts a through c. What is a vector t that is always tangent to this shape? O A. (-yz, -xz,2xy) OB. (x,y,z) OC. (-y,z,-x) O D. (xy.yz,2xz)
How much work is required to lift a 500-kg satellite to an altitude of 3⋅10^6 m above the surface of the Earth? The gravitational force is F=GMm/r^2, where M is the mass of the Earth, m is the mass of the satellite, and r is the distance between the satellite and the Earth's center. The radius of the Earth is 6.4⋅10^6 m, its mass is 6⋅10^24 kg, and in these units the gravitational constant, G, is 6.67⋅10^−11. Work= (include units)
calculate the energy required to send a 1 kg object from the surface of Earth to the satellite located 42.16*10^6m from the center of the Earth. Assume the location from which the object is being launched is 6.37*10^6m from the center. a. Use the object's weight at the surface of the earth (g=9.8) to find Newton's proportional constant k for this object. b. Write a definite integral that calculates the energy required to send the object to orbit, then use the Fundamental theorem of calculus to calculate the energy. c. Write t he formula for a Reimann sum that is guaranteed to estimate the energy required to send the object to orbit, accurate with 10^5 J. d. calculate the fraction of the object's total distance traveled at which half of the total required energy is expended.
A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. a)Enter an expression for the kinetic energy KE of the satellite in terms of m and v. Calculate the value of KE in joules. b)Enter an expression for the magnitude of the gravitational force F in terms of M, R, m and the gravitational constant G. c)Enter an expression for the centripetal acceleration of the satellite ac in terms of the speed of the satellite, v, and R.
A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.01 x 10* m/s. The mass of the planet is M = 6.02 x 1024 kg. The mass of the satellite is m= 3.2 × 103 kg. Enter an expression for the kinetic energy KE of the satellite in terms of m and v. Calculate the value of KE in joules. Enter an expression for the magnitude of the gravitational force F in terms of M, R, m and the gravitational constant G. Enter an expression for the centripetal acceleration of the satellite a, in terms of the speed of the satellite, v, and R. Enter an expression for the radius R in terms of G, M and v. Calculate the value of R in meters. Enter an expression for the gravitational potential energy PE in terms of G, M, m, and R. Calculate the value of PE in joules. Enter an expression for the total energy E of the satellite in terms of m and v. Calculate the value of the total energy E in joules.
Part A Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.1×104 m/s when at a distance of 2.6x1011 m from the center of the sun, what is its speed when at a distance of 4.0×1010 m. Express your answer in meters per second. Πνα ΑΣΦ m/s
Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. Part A Find the gravitational force of one star on the other. Express your answer in terms of G, M, R. Πν ΑΣφ ? F = Part B Find the orbital speed of each star. Express your answer in terms of G, M, R. να ΑΣΦ7 ? Part C