(a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at the Earth’s orbit? (b) Voyager 1 achieved a maximum speed of 125 000 km/h on its way to photograph Jupiter. Beyond what distance from the Sun is this speed sufficient to escapethe solar system?

Q: Ex. 20 : A satellite is moving round a planet in a circular orbit with a velocity of 8 km/s, at a…

A:

Q: A research team has discovered that a moon is circling a planet of our solar system: The moon orbits…

A: The time period of the planet is given as, T = 7 hrs (or) T = 25,200 s The orbital distance is given…

Q: (a) Calculate the work (in MJ) necessary to bring a 104 kg object to a height of 991 km above the…

A: Given that: The mass of an object is m=104 kg The earth's mass is M=5.97×1024 kg The height is h=991…

Q: A space probe is about to launch with the objective to explore the planets Mars and Jupiter. To use…

A: Below you find the orbital period and the semi major axis of the three planets:   orbital period…

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: d face to the blasting rockets, to the fuel gauge, and back to his worried expression as the engines…

A: The hero may have used the idea of conservation of momentum to achieve his aim (going back to his…

Q: If the gravitational force between two objects of mass M and m, separated by a distancer, has…

A:

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: 6. NASA is expected to send a 2600-kg satellite 450 km above the earth's surface. (a) What is its…

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Q: What will be the escape velocity from the surface of the moon if it is 11.2 km/s at the surface of…

A: The minimum velocity required by anyone or any thing to resist the gravitational pull of the planet…

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

A:

Q: What minimum energy is required to take a stationary 3.5 ×103 kg satellite from the surface of the…

A:

Q: A comet goes around the Sun in an elliptical orbit. At its farthest point, 440 million miles from…

A:

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: tellite travels with constant speed vin a circular orbit 320 km above the earth's surface. Calculate…

A:

Q: A satellite is given a boost of 595 MJ of energy to move it from its initial orbit at an altitude of…

A:

Q: : Find kinetic energy, potential energy, total energy and binding energy of an artificial satellite…

A: To find-a Kinetic energy (KE)=?(b) Potential energy PE=?(c) Total energy (TE)=?d Binding energy…

Q: The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free…

A:

Q: A spacecraft with a mass of 5000kg is in circular orbit 2000km above the surface of mars. How much…

A: Answer

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) State Newton's law of gravitation in word form. (b) Use the law to show that that the escape…

A:

Q: A satellite of mass 200 kg is launched from a site on the Equator into an orbit at 200 km above…

A: Solution: m = 200 kg h = 200 km

Q: (a) What is the escape speed on a spherical asteroid whose radius is 103 km and whose gravitational…

A:

Q: Show that the radius r of the orbit of a moon of a given planet can be determined from the radius R…

A: Given values,  Radius of Jupiter = R = 71492 km Time required to complete one full rotation = 3.551…

Q: A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it…

A: Let h represent the bullet's climb in height.  Gravitational acceleration changes with height as…

Q: A spacecraft departing from a 200 km LEO has a total AV of 10 km/s. Determine the following: a) The…

A:

Q: A minimum-energy orbit to an outer planet consists ofputting a spacecraft on an elliptical…

A: (a)Let the departure planet is Earth and positioned at perihelion and the arrival planet is Mars and…

Q: Assume that an enough large asteroid (m = 30,000 kg) coming from the deep space (out of our galaxy…

A:

Q: Show that the values vA and vP of the speed of an earth satellite at the apogee A and the perigee P…

A: Let M is the mass of earth, and m is the mass of satellite. According to principle of conservation…

Q: Determine the minimum velocity(m/s)  necessary to orbit freely about a planet or moon at an altitude…

A: The minimum velocity required to orbit freely is,

Q: Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 44.4 km/s, and v,…

A:

Q: Find the escape velocity ve for an object of mass m that is initially at a distance R from the…

A: Escape velocity is minimum velocity to overcome the gravitational potential energy.Kinetic energy of…

Q: Find the saving in energy if a satellite of mass 1000 kg is launched from an aeroplane at a height…

A:

Q: (a) What is the escape speed on a spherical asteroid whose radius is 685 km and whose gravitational…

A: This problem can be solved using basic formula related to gravitation

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

A:

Q: A space probe is in orbit around Mars at an altitude of 1200 km. To move to a higher orbit, small…

A: Assuming a circular orbit of the satellite, the speed of the satellite at height h above Martian…

Q: Find the escape velocity ve for an object of mass m that is initially at a distance R from the…

A: Write the expression for the kinetic energy. KE=12mve2   Write the expression for the binding…

Q: A spacecraft is launched from Cape Canaveral to a 28.3 400 km. We want to reach the ISS, which orbit…

A: On an orbital inclination of 51.6 degrees, the station travels from west to east. Depending on the…

Q: If you took the Earth and reduced its radius to one fourth its current size, what would the escape…

A:

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.