Final answer:
The mechanical energy of a satellite orbiting the Earth is calculated by summing the gravitational potential energy and kinetic energy. This requires knowing the mass of the Earth and satellite, the gravitational constant, and the orbital radius of the satellite.
Step-by-step explanation:
The question seeks to find the mechanical energy of a satellite with a mass of 2072 kg, orbiting the Earth at an altitude of 410 km. The mechanical energy in a circular orbit is the sum of the kinetic and potential energy, which can be calculated using the gravitational constant, the mass of the Earth, the mass of the satellite, and the distance from the center of the Earth to the satellite.
Calculation Steps
Calculate the radius of the satellite's orbit by adding the Earth's radius to the altitude of the satellite's orbit.
Utilize the formula for gravitational potential energy (U) = -GMm/r, where G is the gravitational constant, M is the Earth's mass, m is the satellite's mass, and r is the radius of the orbit.
For kinetic energy (K), use the formula K = GMm/(2r) in a circular orbit.
The total mechanical energy (E) is given by E = K + U, which simplifies to E = -GMm/(2r) for a circular orbit.
Important Concepts
Understanding gravitational potential energy and kinetic energy in the context of celestial mechanics is foundational in calculating the mechanical energy of orbiting bodies. The concept of an inertial frame of reference in relation to the centripetal acceleration experienced by orbiting objects is also important.