An asteroid has a mass of m = 2.6 x 106 kg and is approaching Earth. When the asteroid is exactly 3 radii away from the Earth's centre,  it's speed relative to the Earth's centre is u = 8.7 x 103 ms-1. The asteroid then falls to the Earth's surface, but remains intact without dissipating any energy as it passes through the Earth's atmosphere. If the rotation of the asteroid and the Earth is ignored, what is the kinetic energy of the asteroid just before it hits the ground?  The Earth has mass ME = 5.98 x 1024 kg and a radius of 6.38 x 106 m. To find the relevant potential energies, you must use G = 6.67 x 10-11 N m2 kg-2

Q: 2. A satellite of mass m is in an elliptical orbit around the Earth, which has mass Me and radius…

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Q: This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.78…

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Q: The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass…

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Q: Part A Find the speed se of the spacecraft when it crashes into the earth.

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Q: We have a non-rotating space station in the shape of a long thin uniform rod of mass 2.60 x 10^6 kg…

A: Since the system has no external torque, the angular momentum of the system will be conserved.…

Q: how fast will the station be spinning?

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Q: 2.0 x103 kg satellite is in a circular orbit around the earth (m = 5.98 x 1024 kg). The satellite…

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Q: In a 2-body system, a space craft is in a circular orbit at a fixed radius B (450*10^8) around a…

A: The total energy of a circular orbit in a 2-body system can be calculated using the equation: E = -G…

Q: A star has a mass of 2.94 x 1030 kg and is moving in a circular orbit about the center of its…

A: Given :    mass of star, M  = 2.94*1030 kg    Radius of orbit, R = 3.6*104 light year…

Q: Pulsars. When a star with a mass at least ten times that of the Sun explodes outward in a supernova,…

A: Given that:a) Time of separation of the pulses: t=1.3373 secb) Fastest angular speed, ωmax=716…

Q: A satellite of mass m is in an elliptical orbit around the Earth, which has mass ME and radius RE.…

A: a) The gravitational potential of the satellite at a point r from the center of the earth is…

Q: A planet orbits a small star in a circular orbit. The planet orbits at a speed of 1000 m/s in a…

A: Solution:-

Q: A satellite is in elliptical orbit with a period of 8.00 * 10^4 s about a planet of mass 7.00 * 1024…

A: The radius of the perihelion is,

Q: Gm,m2 F, 2GM 2nr GM r2 , dc = V 3= T R2 , Vesc = R Gm,m2 Gm,m2 КЕ — E = KE +U, , Ecircular G = 6.674…

A: Given data: The orbital distance between the Earth and the Sun is, rE=1.5×1011 m. The orbital…

Q: shape of a long thin uniform rod of mass 9.03 x 10^6 kg and length 1153 meters. Small probes of mass…

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Q: A planet is in an elliptical orbit around a distant star. At periastron (the point of closest…

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Q: In the figure, two satellites, A and B, both of mass m = 36.8 kg, move in the same circular orbit of…

A: using conservation of momentum and  orbital velocity concept.

Q: This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.07…

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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: This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 4.23…

A: Given that: The mass of the uniform rod is M=4.23×106 kg The length is L=660 m The mass of prob is…

Q: On an asteroid like Bennu, where NASA just landed a probe on October 20, a pressurized nitrogen…

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Q: s time we have a non-rotating space station in the shape of a long thin uniform rod of mass 1.20 x…

A: GivenMass of rod, M=1.2×106 kgLength of rod, L=1428 mFor probesMass of small probe, m=6066 kgSpeed…

Q: Consider an infinitesimally thin circular disk of radius R and mass M centered at the origin sitting…

A: (b) Consider a small element on the disk. The mass element be calculated as,…

Q: This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 8.92…

A: The mass of the rod: M=8.92×106 kg The length of the rod: L=867 m The mass of the probe: m=7618 kg…

Q: AU is a unit of distance. If the orbital speed of Earth at aphelion is v, what is the orbital speed…

A: Angular momentum of earth about sun is conserved which means that at any point in the path of earth…

Q: We have a non-rotating space station in the shape of a long thin uniform rod of mass 6.38 x 10^6 kg…

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Q: An uncrewed mission to the nearest star, Proxima Centauri, is launched from the Earth's surface as a…

A: Given data The initial speed of the spacecraft is given as u = 43.1 km/s.   Let us consider the…

Q: This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 6.65…

A: Write the expression for the moment of inertia of the rod and substitute the corresponding values.…

Q: Three collinear masses are separated by the distances shown. How much work does it take to pull…

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Q: In the figure, two satellites, A and B, both of mass m = 49.1 kg, move in the same circular orbit of…

A: Given data: The mass of the two satellites are m=49.1 kg The radius is r=7410 km The mass of the…

Q: A spaceship with m = 1.00 ✕ 104 kg is in a circular orbit around the Earth, h = 800 km above its…

A: Given: Mass of spaceship, m = 1 X104 kg Height of spaceship = 800 km Apogee , d = 3 X 104 km Mass of…

Q: A space capsule of mass 505 kg is at rest 8.00 x 10 m from the center of the Earth. When it has…

A: We know that the potential energy is given as  P.E = mgh  where m is the mass and g is 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.