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 x 10¬11 N· m²/kg? 2r Problem 1: Let's assume the Earth and Jupiter orbit the Sun in circular orbits. The distance between the Earth and the Sun is rE = 1.5 x 1011 m and the orbital period of the Earth around the Sun is TE = 1 year. The distance between Jupiter and the Sun is rj = 7.8 x 1011 m. Calculate TJ, the orbital period of Jupiter around the Sun, in years. 1 year = 3.154 × 107 sec.

Q: 3. The Earth moves in an almost perfectly uniform circular orbit with the Sun at its center, 1.5 ×…

A: Radius of the orbit is given to be R=1.5*108km=1.5*1011m, Mass of the sun is around M=2*1030kg and…

Q: Different situation now. You re out in space, on a rotating wheel-shaped space station of radius 542…

A:

Q: The earth's radius is 6.37×106m6.37×106m; it rotates once every 24 hours. What is the speed of a…

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Q: NASA scientists propose using rotating cylindrical craft to mimic gravity while in a weightless…

A:

Q: L. St In B Scientists want to place a 4100 kg satellite in orbit around Mars. They plan to have the…

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Q: 1. The Soyuz are a Russian spacecraft used to take astronauts to the International Space Station…

A:

Q: There is a CD-rom that's spinning a CD at 2,000 rpm. There is a bit of dirt, weighing 0.220 g,…

A:

Q: Part 3: Dependence of the centripetal force, F on radius, r for a constant rotating mass, m m = 1.5…

A: Why does the period T change? Explain:

Q: The code Orbit (Appendix J) can be used to generate orbital positions, given the mass of the central…

A: Required : Plots of the orbits.

Q: The Sputnik 1 satellite orbited Earth (mass = 5.98 x 1024 kg) in a circle of %3D radius 6.96 x 106…

A: Given value--- mass of earth M = 5.98 × 1024 kg . radius of circle r = 6.96 × 106 m. We have to…

Q: Scientists want to place a 4100 kg satellite in orbit around Mars. They plan to have the satellite…

A: If a particle moves in a circle of radius r with velocity v, the acceleration is given by v2r…

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: Consider a planet that is a uniform sphere of radius R that has a narrow radial tunnel extending…

A:

Q: A planet has a mass of 5.98 x 10²4 kg. It has an average orbital speed of 2.978 x 104 m/s as it…

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

A:

Q: One dimension. In the figure, two point particles are fixed on an x axis separated by distance d.…

A:

Q: can you help me with this problem:

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Q: QUESTION 12 A meteoroid is traveling straight toward the moon at 2,000 m/s when it is at an altitude…

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Q: I) If the force in H) is due to the gravitational pull of the sun, use the values you've calculated…

A: The force acting on earth while it is in orbit is given to be 3.84 x 1022 N Let F=3.84×1022 N The…

Q: The centers of two 25.0 kg spheres are separated by 5.00 m. The magnitude of the gravitational force…

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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: a. A ferris wheel starts from rest and accelerates at 0.036 rad/s² to get up to its operating speed…

A: Given data:  Initial angular velocity (ω0) = 0 rad/s Angular acceleration (α) = 0.036 rad/s2 Final…

Q: A disk spins at 3.0rev/s speeds up to 15rev/s at a steady rate over a time of 24.0 seconds. Through…

A: Given data: Initial angular velocity (ω0) = 3.0 rev/s Final angular velocity (ω) = 15 rev/s Time (t)…

Q: A disk with velocity v= 10m/s, mass m=4 kg, and radius r=.3 m. Find the total kinetic energy.

A: The total kinetic energy is the sum of the translation kinetic energy and rotational kinetic energy.…

Q: One model for a certain planet has a core of radius Rand mass M surrounded by an outer shell of…

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Q: In a distant solar system, a planet of mass 5.0 x 1024 kg orbits a sun of mass 3.0 x 1000 kg at a…

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Q: Wo satellit Ces are in circular orbits around a 3.0 kg, orbital radius 7 x 10" m, and orbital spe…

A: Given: 7. To find the mass of HD 68988 and express the answer in sun's mass as,

Q: A uniform distribution of dust in the solar system adds to the gravitational attraction of the Sun…

A: Given that, A uniform distribution of dust in the solar system adds to the gravitational attraction…

Q: A disk with velocity v= 10m/s, mass m=5 kg, and radius r=2 m. Find the total kinetic energy.

A: We know that for a disc: Inertia(I) is as below. value of the rotational kinetic energy is: value…

Q: m has a mass = 2.4 x1030 kg, and is spinning to make one revolution in 60 years (i.e. Earth years,…

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.