In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work ? applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 975 kg and 259 km. Earth's mass and radius are 5.98×1024 kg and 6370 km.

Q: Two Earth satellites, A and B, each of mass m = 980 kg , are launched into circular orbits around…

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Q: How much work is required to lift a 1000-kg satellite to an altitude of 3⋅10^6 m above the surface…

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Q: A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What…

A: The gravitational potential energy(U) for a system of two masses m1 and m2 separated by a distance…

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: gravitational potential energy function U(r) is shown for a planet with mass M and radius R. a) If a…

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Q: A meteor falls toward Earth’s surface. Given that the acceleration due to gravity is 9.8 m/s2, what…

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Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 195 km above…

A: Solution: Given data: Mass of the satellite, m = 175 kg, Height of the orbit, h = 195 km =1.95×105 m…

Q: A satellite from the Glonass navigation system weighs 7,350 N on the surface of Earth. How much work…

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Q: Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's…

A: Given:- Satellite A is to orbit at an altitude of 5730 km. satellite B is to orbit at an altitude of…

Q: What is the total mechanical energy of the ISS assuming that it's a perfect circular orbit at an…

A: Given,  Mass of ISS, Height of ISS above earth surface,

Q: How much energy Δ? would be required to move the Moon from its present orbit around Earth to a…

A: Given: The radius of the Moon's orbit is 3.84x108 m.

Q: 1. If you are going to launch a 10,000 kg spacecraft from Earth, (a) how much kinetic energy it must…

A: Answer - Given data              Mass of earth =5.98×1024 kg              Radius of earth =6.37×106…

Q: An asteroid starts at rest infinitely far from Earth. The asteroid has a mass of 1.00×10ª kg.…

A: The work done by the Moon's gravitational field can be evaluated through the change in potential…

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: Compute the work W against the earth’s gravitational field required to move a satellite of mass m =…

A: Mass of satellite (m)=1000 kg Initial altitude of orbit (r1)=4000 km Final altitude of orbit…

Q: A 4500 kg spacecraft is in a circular orbit 1500 km above the surtace of Mars (my = 6.42 x 1023 kg.…

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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: How much work is required to move a 1550 kg satellite from a circular orbit with an altitude of 105…

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Q: An object of mass m placed at a height h from the ground has a gravitational potential energy PE_1.…

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Q: An asteroid starts at rest infinitely far from Earth. The asteroid has a mass of 2.00×104 kg.…

A: The change in the gravitational energy of the asteroid can be determined as follows.…

Q: An asteroid starts at rest infinitely far from Earth. The asteroid has a mass of 1.00x104 kg.…

A: 1)Change in gravitational potential energy = - GMm/R  = -6.67 * 10-11 * 6 * 1024 * 104/(6378000) = -…

Q: A “treetop satellite” moves in a circular orbit just above the surface of a planet, assumed to offer…

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

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Q: A spacecraft moves around Earth in a circular orbit with a constant radius. How much work is done by…

A: The work done is given by  W = F x s x cos A  where, F is the force, s is the displacement and A is…

Q: (f 601) N

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

Q: A 1750 kg weather satellite moves in a circular orbit with a gravitational potential energy of 1.69x…

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Q: An object of mass m placed at a height h from the ground has a gravitational potential energy PE_1.…

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Q: An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial…

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Q: A satellite of mass  243kg orbits the Earth at a constant speed in a circular orbit. The work done…

A: Given : Mass of a satellite (m) = 243 kg

Q: Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no…

A: The Gravitational Force is a Conservative Force, therefore the total energy E will be conserved. We…

Q: A 1950 kg weather satellite moves in a circular orbit with a gravitational potential energy of 1.69…

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Q: A satellite is held in orbit by a 2 000-N gravitational force. Each time the satellite completes an…

A: Given Data:- Gravitational force on the satellite is F=2000 N Circumference of the orbit is d=80000…

Q: In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a…

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Q: A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of…

A: Given: Closest distance of comet from sun, r1 = 4.9×1010 m with speed, v1 = 9.3×104 m/s Farthest…

Q: An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at…

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Q: One of your summer lunar space camp activities is to launch a 1010 kg rocket from the surface of the…

A: Given: The mass of the rocket is 1010 kg. The altitude is 209 km. The mass of the moon is 7.36×1022…

Q: A 1 kg satellite is to be placed at 3.55e7 meters above the earth's surface. What is the difference…

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Q: A 1500 kg satellite is in a stable orbit at an altitude of 4.0 × 10 5 m above Earth's surface. What…

A: SOlution: Given that m =1500 kg h= 4.0 × 10 5 m Mearth = 5.97x1024 kg rearth = 6.4x106 m

Q: satelite is in geostationary orbit. How much energy is required to move it to a circular orbit where…

A: Time period of geostationary satellite = 1 day = 24 hours  Time period in second case = 8 days…

Q: As it orbits Earth, the 11,000-kg Hubble Space Telescope travels at a speed of 7,900 m/s and is…

A: Given: Mass of Hubble space Telescope M = 11000 kg. Speed of telescope v = 7900 m/s Height from…

Q: Calculate the work done by the force of gravity when a satellite moves in an orbit of radius 40,000…

A: Work done by the force of gravity is given by,  Work done =F×S cosθF = forceS = displacementθ =…

Q: A satellite has a mass of 94 kg and is located at 2.04  106 m above the surface of Earth. (a) What…

A: Given:  mass of satellite, m = 94 kg  height, h = 2.04 x 106 m mass of earth, M = 5.9 x 1024 kg…

Q: A Satellite in an elliptical orbit is moving from position A, where its Kinetic energy is 15 MJ and…

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Q: There are required 44.76 kJ of gravitational work to elevate a mass 76.22 m in the earth's…

A: Work required,  Height,  Local gravitational field,  Initial potential energy,

Q: a. Planet Alpha has a mass of 2.34 x 1025 kg and a radius of 5.67 × 107 m. What is the gravitational…

A: Given data: Mass of the planet Alpha m=2.34×1025 kg Radius r =5.67×107 m

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.