What is the potential energy of the Earth, considered as an object orbiting the Sun? Compare your result with the kinetic energy of the Earth in its orbit. Given Earth mass = 6.34×1024kg , Sun mass =1.934×1030kg, and distance from the Earth to the Sun =1.434×108km.
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To calculate the potential energy of an object orbiting the Sun, we need to use the gravitational potential energy formula:
Potential Energy = -G * (mass of object) * (mass of Sun) / (distance between object and Sun)
Where:
G is the gravitational constant (G ≈ 6.67430 × 10^-11 N(m/kg)^2),
mass of object is the mass of the Earth (6.34 × 10^24 kg),
mass of Sun is the mass of the Sun (1.934 × 10^30 kg),
and distance between object and Sun is the distance from the Earth to the Sun (1.434 × 10^8 km) converted to meters (1 km = 1000 m).
First, let's convert the distance from kilometers to meters:
1.434 × 10^8 km * 1000 m/km = 1.434 × 10^11 m
Now, we can calculate the gravitational potential energy:
Potential Energy = -6.67430 × 10^-11 N(m/kg)^2 * (6.34 × 10^24 kg) * (1.934 × 10^30 kg) / (1.434 × 10^11 m)
Calculating this expression will give us the potential energy of the Earth in its orbit around the Sun.
To compare this result with the kinetic energy of the Earth in its orbit, we need to use the formula for kinetic energy:
Kinetic Energy = (1/2) * (mass of object) * (velocity)^2
The velocity of the Earth in its orbit can be calculated using the equation:
velocity = √(G * (mass of Sun) / (distance between object and Sun))
Using the same values for the mass of the Sun and distance between the Earth and the Sun as before, we can calculate the velocity.
Once we have the velocity, we can substitute it into the kinetic energy formula along with the mass of the Earth. This will give us the kinetic energy of the Earth in its orbit around the Sun.
Comparing the calculated potential energy and kinetic energy will allow us to determine how they relate to each other.