An 884 kg satellite in orbit around a planet has a gravitational potential energy of -5.44*10^10 J.
The orbital radius of the satellite is 8.52*10^6 m and its speed is 7.84*10^3 m/s.
A) What is the mass of the planet?
B) What is the kinetic energy of the satellite?
C) What is the total energy of the satellite.
Thank you.
To solve these questions, we can use the formulas for gravitational potential energy, kinetic energy, and total energy.
The formula for gravitational potential energy is given by:
PE = -G * (mass of the satellite) * (mass of the planet) / (radius)
where G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2).
The formula for kinetic energy is given by:
KE = 1/2 * (mass of the satellite) * (velocity)^2
And the total energy is the sum of potential energy and kinetic energy:
Total Energy = PE + KE
Now, let's solve each part of the question.
A) What is the mass of the planet?
Rearranging the gravitational potential energy formula, we can solve for the mass of the planet (M):
PE = -G * (mass of the satellite) * (mass of the planet) / (radius)
Rearranging the equation gives us:
mass of the planet = - (PE * radius) / (G * mass of the satellite)
Substituting the given values:
mass of the planet = - (-5.44 x 10^10 J * 8.52 x 10^6 m) / (6.67 x 10^-11 N m^2/kg^2 * 884 kg)
Simplifying the equation will give us the mass of the planet.
B) What is the kinetic energy of the satellite?
We can use the formula for kinetic energy:
KE = 1/2 * (mass of the satellite) * (velocity)^2
Substituting the given values, we can calculate the kinetic energy.
C) What is the total energy of the satellite?
The total energy is the sum of potential energy (PE) and kinetic energy (KE):
Total Energy = PE + KE
Substituting the given values, we can calculate the total energy of the satellite.
By following these steps, you should be able to find the answers to all three parts of the question.