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A planet of mass m orbits a star of mass M in an elliptical orbit with semi major axis a. The distance of closest approach to the star is a / 4 . Assuming the ratio of the plant's speed at perigee (when a planet is closest to the star) to the planet's speed at apogee (when the planet is furthest away from the star) is
Problem 1 Planetary Orbits Consider the two-body problem for a planet-star system. The planet, of mass m, is initially in a circular orbit of radius r and angular speed w about the star, of mass M. (i) What is the gravitational potential energy of the system, U? What is the kinetic energy of the planet, K? What is the total energy of the system, E = K +U? (ii) The star suddenly loses half of its mass, M + M/2....
Planet M has a mass if 4.86x10^24 kg and it orbits 1.09x10^8 km from a star with a period of 225 days. What is the angular momentum if the olant around its star? Answe in kg m^2/sec
Let a satellite orbits a planet of mass M at circular orbit of radius R. Find the orbital period T. Express your answer in terms of G, M, R, and π If the mass of the planet is 5.98 x 1024 kg, calculate the ratio of T2 to R3.
9. (5 Pts.) A star with a radius R, 109 m is rotating with initial angular velocity w 108 rad/s. The star collapses in on itself until it becomes a neutron star with the same mass, and a final radius Ry 10t m. Modeling the star as a uniform solid sphere, what is the final angular velocity of the star? (Hint: angular momentum is conserved)
A solid disk of mass m = 9.2 kg and radius R = 0.2 m is rotating with a constant angular velocity of w = 38 rad/s. A thin rectangular rod with mass m2 = 3.7 kg and length L = 2R = 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? kg-m2/s Submit...
1. A moon of mass \(m\) orbits around a non-rotating planet of mass \(M\) with orbital angular velocity \(\Omega\). The moon also rotates about its own axis with angular velocity \(\omega\). The axis of rotation of the moon is perpendicular to the plane of the orbit. Let \(I\) be the moment of inertia of the moon about its own axis. You can assume \(m<<M\)so that the center ofmass of the system is at the center of the planet.(a) What is...
A system of two bodies consisting of a rod of mass m and length L, and a disk of mass M and radius R, moves in the x-y plane. The disk rotates about the axis attached to the rod at a distance b from its axis of rotation. The absolute angular velocity of the rod is 2, and the angular velocity of the disk relative to the rod is @. Determine the ratio E/Ho of the kinetic energy E of...
Planet X has a mass of 4.86 x 102 kg and it orbits 1.09 x 108 km from a star with a period of 225 days. What is the angular momentum of the planet around its star? Answer in units of kg m²/sec. Due to its large distance from its star, you can treat the planet as a point mass in its circular motion around the star. O 1.86 x 1040 O 1.61 x 1039 O 2.93 x 1039 O...
A new extrasolar planet (outside our solar system) has been discovered. This planet orbits a star of mass 1.03×1031 kg with a period of 6.52 years . It is also known that the planet has an eccentricity of 0.694. Part A Part complete What is the semi-major axis of the planet's orbit? View Available Hint(s) Semi−majoraxis= 9.03×1011 m SubmitPrevious Answers Correct Part B What is the average velocity of the planet in its orbit Part C What is the distance of closest approach to its...