The gravitational potential energy of a satellite can be calculated by the formula -G * (m1 * m2) / r, where 'r' is the distance from the center of Earth to the satellite. The satellite in question is 1000 kg in mass and orbits at a distance of two Earth radii from the center of Earth. The total energy, which is the sum of kinetic and potential energy, determines if the satellite is in a bound orbit.
Gravitational Potential Energy of a Satellite
When we talk about the gravitational potential energy (GPE) of a satellite in circular orbit, it is given by the formula U = -G * (m1 * m2) / r, where G is the universal gravitational constant, m1 and m2 are the masses of the Earth and the satellite, respectively, and r is the distance from the center of the Earth to the satellite. In this case, the satellite's mass is 1000 kg and the orbit's radius is double the Earth's radius, so the satellite is far away from Earth's surface by a distance equal to the Earth's radius.
The satellite's kinetic and potential energy can be calculated using relevant formulas: kinetic energy (KE) is given by KE = 0.5 * m * v^2, where v is the orbital velocity, and potential energy (U), as mentioned before.
The total energy (E) is the sum of kinetic and potential energy, E = KE + U, which indicates whether the orbit is bound or unbound. A satellite with negative total energy is in a bound orbit. This information can be used to assess whether a satellite is gravitationally bound to Earth.