Final answer:
The momentum of Earth is 1.74 × 10^29 kg. m/s, its kinetic energy is 2.6754 × 10^33 J, and its gravitational potential energy is considered to be zero. The angular momentum of Earth is approximately 2.66 × 10^40 kg. m²/s.
Step-by-step explanation:
a. What is its momentum?
To find the momentum of Earth, we can use the formula:
momentum = mass x velocity
Given that the mass of Earth is 6.00 × 10^27 g and its velocity is 2.90 × 10^4 m/s, we can convert the mass to kg by dividing it by 1000:
mass = 6.00 × 10^27 g / 1000 = 6.00 × 10^24 kg
Now we can substitute the values into the formula:
momentum = 6.00 × 10^24 kg x 2.90 × 10^4 m/s
Simplifying the calculation, we get:
momentum = 1.74 × 10^29 kg. m/s
Therefore, the momentum of Earth is 1.74 × 10^29 kg. m/s.
b. What is its kinetic energy?
To find the kinetic energy of Earth, we can use the formula:
kinetic energy = 0.5 x mass x velocity^2
Using the mass and velocity given for Earth, we can substitute the values into the formula:
kinetic energy = 0.5 x 6.00 × 10^24 kg x (2.90 × 10^4 m/s)^2
Performing the calculation, we find:
kinetic energy = 2.6754 × 10^33 J
Therefore, the kinetic energy of Earth is 2.6754 × 10^33 J.
c. What is its gravitational potential energy?
The gravitational potential energy of an object is given by the formula:
gravitational potential energy = mass x acceleration due to gravity x height
Given that the mass of Earth is 6.00 × 10^24 kg and the acceleration due to gravity on Earth is approximately 9.8 m/s^2, we can calculate the gravitational potential energy using the formula:
gravitational potential energy = 6.00 × 10^24 kg x 9.8 m/s^2 x height
However, the height of Earth is infinite since it extends into space. Therefore, the gravitational potential energy of Earth is considered to be zero.
d. What is its angular momentum?
The angular momentum of an object is given by the formula:
angular momentum = moment of inertia x angular velocity
For Earth, the moment of inertia is typically defined as its mass multiplied by the square of its radius. The angular velocity of Earth is the rate at which it rotates on its axis, which is approximately 7.2921159 × 10^-5 radians per second.
Using the mass and radius of Earth given in the question, we can calculate the moment of inertia:
moment of inertia = mass x radius^2 = 6.00 × 10^24 kg x (6.4 × 10^6 m)^2
Substituting the values into the formula, we have:
angular momentum = (6.00 × 10^24 kg x (6.4 × 10^6 m)^2) x (7.2921159 × 10^-5 rad/s)
Simplifying the calculation, we find:
angular momentum ≈ 2.66 × 10^40 kg. m²/s
Therefore, the angular momentum of Earth is approximately 2.66 × 10^40 kg. m²/s.