2GM ľp 2GM rA IA + rp ľp IA + rp ľA VP Гр- Р

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 tunnel is drilled from the surface of a planet straight down to its antipodal point on the other…

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Q: In a faraway galaxy, a meteoroid is moving along a straight line that will pass a planet at a…

A: Given:Let,Mass of the meteoroid =mpSpeed when far away=vDistance,ri=5RpPlant's…

Q: The energy to place a satellite into orbit consists of the work against gravity and addition kinetic…

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Q: A planet is discovered orbiting a distant star. The mass of the planet is 40 times the mass of the…

A: The equation for the escape speed is given by, ve=2GMR Here, G is the universal gravitation…

Q: Find the speed (in m/s) needed to escape from the solar system starting from the surface of Uranus.…

A: We know that:Mass of Sun, MS=1.98×1030 kgMass of Uranus, Mu=8.68×1025 kgDistance between sun and…

Q: In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational…

A: Gravity pulls an object towards it. It is a central force which brings 2 bodies towards each other.…

Q: At apoapsis (furthest point from the star), the

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Q: Suppose that a planet were discovered between the Sun and Mercury, with a circular orbit of radius…

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Q: A comet of mass me is in an elliptical orbit around the sun (mass Mo), which is located at one focus…

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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: Show that the areal velocity for a circular orbit of radius r about a mass M is ΔA/Δt =1/2 √GMr .…

A: Let,  A = the area swept by planet ,while moving in a circular orbit.         T= Time period of the…

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: What is the gravitational acceleration close to the surface of a planet with a mass of 4M and radius…

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Q: Very far from earth (at R=∞), a spacecraft has run out of fuel and its kinetic energy is zero. If…

A: Solution:Explanation:Mechanical energy includes both kinetic energy (energy due to motion) and…

Q: A satellite (above the equator of the Earth) has a perigeum height of 150 km, and the ratio between…

A: Given, Height of the satellite from the earth surface=150 Km hp=rp-r=150 Km

Q: private space agency places a satelite of mass 58 kg into orbit about the earth.  The orbital…

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Q: 9. In a general curvilinear track, the particle's acceleration can neither be tangential nor normal…

A: in this question we discuss  about the velocity and acceleration .

Q: A private space agency places a satelite of mass 30 kg into orbit about the earth. The orbital…

A: mass of satellite, M=30 kg, Altitude (h) = 230 km

Q: The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of…

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Q: A satellite of earth has a speed of 5900 m/s. Find: a) the radius of the orbit b) the period of…

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Q: The star Sirus A has a mass of 2.06 MO and a radius of 1.71 RO, where M0 is the mass of the Sun…

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Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011…

A: Given: M= 8 x 1011 solar mass r=6 x 104 light years T= 6 x 107 years

Q: In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational…

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Q: For an elliptic Earth orbit find the ratio of the time required to travel from a point on the lower…

A: Given: The value of ν for lower latus parameter is -π3. The value of ν for upper latus parameter is…

Q: A satelite of mass m orbits in an elipse a planet of mass M. When the satellite's orbit is closest…

A: This is a question from astrophysics and motion under the central force. The fig given below shows…

Q: An object of mass mm is launched from a planet of mass MM and radius RR.  a) Derive and enter an…

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Q: As mentioned in class, the methods used to determine the electric field can also be used to…

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Q: (a) What is the escape speed on a spherical asteroid whose radius is 624 km and whose gravitational…

A: Given: The radius of the asteroid is 624 km. The acceleration due to gravity on the surface of the…

Q: A satellite orbiting above the equator of the earth is geosynchronous if the period is T = 24 hours…

A: Kepler's third law states that the square of the period is proportional to the cube of the…

Q: (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an…

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Q: A satellite orbiting above the equator of the earth is geosynchronous if the period is T = 24 hours…

A: Given values:- Time period,(T)=24 Hr=24 x 3600 sec=86400 sec ----(1) Distance from the center of the…

Q: Consider an object that is in an elliptical orbit with semimajor axis a = 7.9×106 m about a planet…

A: Relation b/w the apogee ( furthest ) and perigee (closest) point with Semimajor axis(a) are as:…

Q: you know about kinetic energy and energy conservation, show that the expression for the escape…

A: To find expression for escape velocity we just have to use energy conservation Initially we have…

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: A satellite describes a circular orbit at an altitude of 19 110 km above the surface of the earth.…

A: Part (a) Given: The altitude of the satellite is h=19110 km. The radius of earth is R=6370 km. The…

Q: A satellite has a mass of 5850 kg and is in a circular orbit 4.10 × 105 m above the surface of a…

A: Satelite mass (m) = 5850kgOrbital radius (r) = 4.10 x 103 m +4.15 x 106mGravitational constant (G) =…

Q: Assume a new planet discovered has a mass (1/81) that of Earth and a radius (1/4) that of Earth.…

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Q: A satellite (above the equator of the earth) has a perigeum height of 150 km. (a) The ratio between…

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Q: (a) Calculate how much work is required to launch a spacecraft of mass m from the surface of the…

A: a)Ui=-GMEmREUf=-GMEm2REW=Uf-Ui=GMEm2RE work is required to launch a spacecraft of mass m from the…

Q: What is the escape speed from a planet of mass M = 3.1 x 1023 kg and radius R = 2.6 x 106 m? Write…

A: Given data:  Mass of planet (M) = 3.1×1023 kg Radius (R) = 2.6×106 m Universal Gravitational…

Q: On the ground level, the weight of a satellite is W N. The satellite is launched and stays in an…

A: On surface of the earth gravity is g = GMR2 , where R is radius of earth , G is gravitational…

Q: (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an…

A: given,  Vi = 5.96x104 m/s from conservation of energy, the initial total energy of the object at the…

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.