Imagine a moon revolving around a planet. If gravitational effects from the moon slow down the...
Imagine a moon revolving around a planet. If gravitational effects from the moon slow down the planet's rotation about its own axis, will the orbital radius of the moon increase or decrease in order to conserve the total angular momentum of the planet-moon system? (This is the case with the orbital radius of the moon)
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Imagine a moon revolving around a planet. If gravitational
effects from the moon slow down the...
3. Imagine a moon revolving around a planet. If gravitational effects from the moon slow down...
3. Imagine a moon revolving around a planet. If gravitational effects from the moon slow down the planet's rotation about its own axis, will the orbital radius of the moon increase or decrease in order to conserve the total angular momentum of the planet-moon system? (This is the case with the orbital radius
A moon of mass m orbits around a non-rotating planet of mass M with orbital angular velocity . The moon also rotates about its own axis with angular velocity .
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...
The tidal forces between the Earth and the Moon slowed down the Moon’s rotation about its own axis until the rotation period became equal to the Moon’s orbital period around the Earth as we observe today.
The tidal forces between the Earth and the Moon slowed down the Moon's rotation about its own axis until the rotation period became equal to the Moon's orbital period around the Earth as we observe today. The same effect is also slowing down the Earth's rotation about its own axis and increasing the separation \(D\) between the Moon and the Earth at a rate of \(\Delta D / \Delta t=3.8 \mathrm{~cm}\) per year. In this problem, you can ignore the...
Problem 1 Planetary Orbits Consider the two-body problem for a planet-star system. The planet, of mass...
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....
points A newly discovered planet is in a circular orbit around a distant star with an...
points A newly discovered planet is in a circular orbit around a distant star with an orbital period of 400 Earth days. The planet also rotates on its axis, making one full rotation every 4.00 Earth days. The radius of the planet is rp = 7.00 × 106 m and the radius of the planet's orbit about the star is r 7.00×1011 m. My Notes Ask Your Tea Determine the ratio of the radial acceleration, due to the rotation of...
Question 7 (0.5 points) What causes the Moon to move about 12° across the sky from...
Question 7 (0.5 points) What causes the Moon to move about 12° across the sky from one night to the next (at the same time of night, of course)? O Because the Earth is turning on its axis. O Because the Moon is moving in its orbit. The Sun has also moved 15° across the sky and gravitationally pulls the Moon with it. The celestial sphere the Moon is attached to has moved 15°. O It is an optical illusion....
1.) So we know that the planet Jupiter and its big Galilean moons are sometimes termed...
1.) So we know that the planet Jupiter and its big Galilean moons are sometimes termed as a ‘mini-solar system’ because Jupiter is composed of mainly hydrogen and helium like stars and the Galilean moons seem like planets revolving around it. The total angular momentum of a system is contributed by the sum of orbital and rotational angular momenta of the central body and the bodies orbiting around it. Note: For parts a and also b you can go ahead...
Cart mr 6- A planet of mass m and radius r orbits a star at a...
Cart mr 6- A planet of mass m and radius r orbits a star at a distance R (between their centres) with an angular velocity Wort = 2 rad/s. The planet also rotates around its own axis with an angular velocity of spin = 10 rad/s. The mass of the star is M-1000m. The moment of Star -R 00 inertia of a solid sphere is I = 2 mr 2- Calculate the total angular momentum L of the planet in...
Today, the Moon’s orbit around Earth has a semi-major axis of a=384,400 km and an orbital...
Today, the Moon’s orbit around
Earth has a semi-major axis of a=384,400 km and an orbital period
of 27.32166 days.
a. The Moon slowly moves outward due to tidal braking of the
Earth’s rotation, and at some future date the Moon will have an
orbital period of 47 days. Compute the semi-major axis of the
Moon’s orbit at this future date (express your answer in
kilometers).
semi-major axis = 5.5*10^5 km
b. Today, the Moon has an angular diameter of...
All the planets we know of rotate, some fast and some slow. Is there any limit...
All the planets we know of rotate, some fast and some slow. Is there any limit on how fast they can rotate, or could it in principle be any speed? In this problem we will answer that question! Suppose (to keep it simple) that a particular planet is spherical and has a uniform mass density ρ. Consider a rock resting on the surface of that planet, at the equator. (a) Draw a free-body diagram of that rock, and write down...
3. Imagine a moon revolving around a planet. If gravitational effects from the moon slow down the planet's rotation about its own axis, will the orbital radius of the moon increase or decrease in order to conserve the total angular momentum of the planet-moon system? (This is the case with the orbital radius
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....
points A newly discovered planet is in a circular orbit around a distant star with an orbital period of 400 Earth days. The planet also rotates on its axis, making one full rotation every 4.00 Earth days. The radius of the planet is rp = 7.00 × 106 m and the radius of the planet's orbit about the star is r 7.00×1011 m. My Notes Ask Your Tea Determine the ratio of the radial acceleration, due to the rotation of...
Question 7 (0.5 points) What causes the Moon to move about 12° across the sky from one night to the next (at the same time of night, of course)? O Because the Earth is turning on its axis. O Because the Moon is moving in its orbit. The Sun has also moved 15° across the sky and gravitationally pulls the Moon with it. The celestial sphere the Moon is attached to has moved 15°. O It is an optical illusion....
Cart mr 6- A planet of mass m and radius r orbits a star at a distance R (between their centres) with an angular velocity Wort = 2 rad/s. The planet also rotates around its own axis with an angular velocity of spin = 10 rad/s. The mass of the star is M-1000m. The moment of Star -R 00 inertia of a solid sphere is I = 2 mr 2- Calculate the total angular momentum L of the planet in...
Today, the Moon’s orbit around
Earth has a semi-major axis of a=384,400 km and an orbital period
of 27.32166 days.
a. The Moon slowly moves outward due to tidal braking of the
Earth’s rotation, and at some future date the Moon will have an
orbital period of 47 days. Compute the semi-major axis of the
Moon’s orbit at this future date (express your answer in
kilometers).
semi-major axis = 5.5*10^5 km
b. Today, the Moon has an angular diameter of...
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