The maximum distance from the Earth to the Sun (at aphelion) is 1.521 × 1011 m, and the distance of closest approach (at perihelion) is 1.471 × 1011 m. The Earth’s orbital speed at perihelion is 3.027 × 104 m/s. Determine (a) the Earth’s orbital speed at aphelion and the kinetic and potential energies of the Earth–Sun system (b) at perihelion and (c) at aphelion. (d) Is the total energy of the system constant? Explain. Ignore the effect of the Moon and other planets.

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10…

A: (a) orbital period of the star T=2πr3GM=2π6.0×104 ly39.461×1015 m1 ly36.67×10-11…

Q: A spacecraft of mass 250 kg is in a circular orbit around the Earth at an altitude equal to the…

A:

Q: A 750 kg spacecraft has total energy -0.55 TJ and is in circular orbit around the Sun. Part A Find…

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Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 180 km above…

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Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 180 km above…

A: As you have asked only solution of the part (c) so that I have solved only part (c). The answer of…

Q: If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity, its…

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Q: A satellite of mass 190 kg is placed into Earth orbit at a height of 750 km above the surface.…

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Q: When a falling meteoroid is at a distance above the Earth's surface of 2.85 times the Earth's…

A:

Q: How much energy is required to move a l250 kg object from the Earth's surface to an altitude twice…

A: (given) Mass (m) of moving object =1250 kg    Mass of Earth (M E ) =  5.9742 × 1024 kg    Radius of…

Q: As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly…

A: The amount of the work done needed to carry a unit mass from infinity to a desired point is called…

Q: Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from…

A: Given that---- Mass of ball = 1024 kg Mass of planet = 41.5 x 1015 kg Radius of planet = 7.1 x 106…

Q: A star has a mass of 1.87 x 1030 kg and is moving in a circular orbit about the center of its…

A: mass of star (m) = 1.87×1030 kg radius of orbit (R) = 2.3×104 light years = 2.3×104×9.5×1015 m =…

Q: A 500-kg communications satellite is in a circular geosynchronous orbit and completes one revolution…

A: We have Given here, Mass of Satellite = 500 kg, Time to complete one revolution about the earth = 23…

Q: A satellite of mass m = 3.94e + 3 kg is in circular orbit around the Earth, and the radius of this…

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Q: When a falling meteoroid is at a distance above the Earth's surface of 2.3 times the Earth's radius,…

A: Given: Meteoroid is at a distance of 2.3 times of that of the Earth's radius.

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

A: Given data: The mass of the satellite, m=20000 kg. The radius of the orbit, r=3×108 m. The value of…

Q: (Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from…

A: The expression for the acceleration due to gravity on the surface of the planet is g=GMR2 Use the…

Q: It iš lóčáted at the planets surface. How far from the surface is there a point where the magnitude…

A: Part (a) Basic Details The gravitational force on the apple depends on the gravitational constant,…

Q: A merry-go-round is a playground ride that consists of a large disk mounted to that it can freely…

A: Given: Radius of marry go round, R = 1.3 metersMass of marry go round, M = 251 kgMass of small boy,…

Q: A uniform horizontal disc has a point mass of 70 kg placed on its edge. The system rotates about a…

A: point mass = 70 kg original frequency = 12 HzFinal frequency = 30 Hz

Q: You find yourself stranded on Phobos, a moon of Mars, has a radius of 11.1 x 10' m and a mass of…

A: We need to calculate at what speed should the ball be released in order to put it in an orbit of…

Q: A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from…

A: F=GmM/R2 ac =  v2/R. v= √(GM/R) v=4578.5 m/s

Q: An average-sized asteroid located 5.0x107 km from the centre of the Earth with mass 2.0x1013 kg is…

A: Given data: Distance of asteroid from the center of Earth, r=5×107km=5×1010m Mass of asteroid,…

Q: In March 1999 the Mars Global Surveyor (GS) entered its final orbit about Mars, sending data back to…

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Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10…

A: mass of milky way (m) = 8×1011 solar masses = 8×1011×2×1030kg = 16×1041 kg distance (d) = 5.6×104…

Q: Can you help me on p. 7.39

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Q: A meteoroid is heading directly to the Earth. The speed of the meteoroid is 2000 m/sec when it is at…

A: Given Data:  Speed of Meteoroid Sm=2000 msec Distance between Meteoroid and Earth is (d)=3.84×108 m…

Q: A communications satellite is launched into circular orbit around the Earth, at an altitude h. The…

A: a) Write the equation of Kepler’s third law.

Q: The orbit of Earth around the Sun is almost circular: The closest and farthest distances are 1.47 x…

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Q: When a falling meteoroid is at a distance above the Earth's surface of 3.10 times the Earth's…

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Q: Derive an equation for the orbital period T of the spacecraft in terms of m, ME, R, and physical…

A: Let the mass of the spacecraft = m   Let the mass of earth = Me   Let the radius of orbit of…

Q: A satellite with mass 850 kg is placed in its orbit with the orbital radius of 4.5 x 107 m from the…

A: Gravitational Potential Energy is negative at the surface of Earth, because work is completed by the…

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

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Q: A small astronomical object falls toward the Mars. It starts from rest with respect to the Mars when…

A: H = 5220 km R = 3390 KmM = 6.39 * 1023 Kg

Q: Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that…

A: According to the Kepler’s third law, T2=4π2GMa3

Q: merry-go-round is a playground ride that consists of a large disk mounted to that it can freely…

A: Given that:Radius of the disk, R=1.3 mMass of the disk, M=251 kgMass of boy, m=42 kgSpeed of boy,…

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: Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from…

A:

Q: You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630…

A: height of spaceship above the surface of a planet (h) = 630 km radius of planet (R) = 4.48×106 m…

Q: In hydrogen atom the electron rotates around the nucleus by a constant speed 2.5 x 10° m/s in a…

A: Given:speed of the electron, v = 2.5 x 106 m/sradius of the circular radius, r = 5.29 x 10-11m

Q: A "kiloton of TNT" is an energy of 4.184 x 1012 J. How much mass would an object need to have to…

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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.