Planet Earth revolves around the Sun in an almost circular orbit (hint: how long does it take for this revolution to happen?). The (average) radius of this orbit is called A.U., Astronomical Unit, and it is equal to 1.5 108 km. Earth also rotates about its axis (hint: how long does it take for this rotation to happen?). Considering the Earth as a sphere, with a mass of 6.0 1024 kg and radius 6.4 106 m, a) what is the magnitude of Earth's orbital angular momentum with respect to the Sun? [ Select ] kg m 5-1 b) what is the magnitude of its spinning angular momentum? [Select ] kg m2 5-1

Answers

Answer 1
Answer:

Answer:

The orbital angular momentum of the Earth is equal to the product of the mass of the Earth (6.0x 10^24 kg) and its orbital velocity (29.7 km/s) multiplied by its distance from the Sun (1.5x 10^8 km), which results in a magnitude of 3.6x 10^40 kg m^2/s.

The spinning angular momentum of the Earth is equal to the product of its mass (6.0x 10^24 kg) and its angular velocity (7.3x 10^-5 radians/s) multiplied by the square of its radius (6.4x 10^6 m), which results in a magnitude of 3.8x 10^37 kg m^2/s.

Answer 2
Answer:

Final answer:

a) The magnitude of Earth's orbital angular momentum with respect to the Sun is [ Select ] kg m^2/s. b) The magnitude of its spinning angular momentum is [Select ] kg m^2/s.

Explanation:

To calculate the magnitude of Earth's orbital angular momentum with respect to the Sun, we need to use the formula:

Angular Momentum = Moment of Inertia * Angular Velocity

For Earth's orbital angular momentum, the moment of inertia can be calculated using the formula for a sphere:

Moment of Inertia = (2/5) * mass * radius^2

Substituting the given values:

Moment of Inertia = (2/5) * 6.0 x 10^24 kg * (6.4 x 10^6 m)^2

Next, we need to calculate the angular velocity. The time taken for Earth to complete one revolution around the Sun is known as the orbital period. The orbital period of Earth is approximately 365.25 days or 31,557,600 seconds.

Angular Velocity = 2π / Orbital Period

Substituting the values:

Angular Velocity = 2π / 31,557,600 s

Now, we can calculate the orbital angular momentum:

Orbital Angular Momentum = Moment of Inertia * Angular Velocity

For the spinning angular momentum, we can use the same formula:

Spinning Angular Momentum = Moment of Inertia * Angular Velocity

However, the moment of inertia for spinning angular momentum is different. It depends on the mass distribution of Earth and its axis of rotation. Since Earth is considered a sphere, the moment of inertia for spinning angular momentum can be calculated using the formula mentioned earlier.

Substituting the given values:

Moment of Inertia = (2/5) * 6.0 x 10^24 kg * (6.4 x 10^6 m)^2

Finally, we can calculate the spinning angular momentum:

Spinning Angular Momentum = Moment of Inertia * Angular Velocity

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Answers

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