Answer :
To move the satellite into a circular orbit with an altitude of 193 km, approximately 1.88 x 10⁷ Joules of energy must be added to the system.
In order to calculate the energy required to move the satellite into the new orbit, we can use the principle of conservation of energy, specifically the gravitational potential energy of the satellite. The change in potential energy ΔPE is given by the formula:
ΔPE = G (mM/r₂) - G (mM/r₁)
Where:
G = Gravitational constant (6.674 × 10⁻¹¹ N m²/kg²)
m = Mass of the Earth (5.972 × 10²⁴kg)
M = Mass of the satellite (1.006 kg)
r₂ = Final orbit radius (Earth's radius + new altitude)
r₁ = Initial orbit radius (Earth's radius + initial altitude)
By substituting the given values into the formula, we find the change in potential energy to be approximately 1.88 x 10⁷ Joules.
This energy must be added to the system to increase the satellite's potential energy, enabling it to move into the higher orbit. This calculation assumes an idealized scenario without considering factors such as atmospheric drag or the satellite's velocity.
The energy required to move a 1.006-kg satellite from an orbit of 110 km to 193 km involves increasing both the gravitational potential and kinetic energy. Calculations must factor in Earth's mass, radius, and the gravitational constant, along with the new orbital parameters.
To calculate the energy required to move a satellite into a higher orbit, we need to understand the principles of orbital mechanics and energy conservation in gravitational fields. This involves both kinetic and potential energy changes as the satellite moves from one circular orbit to another.
The total mechanical energy of a satellite in orbit is the sum of its kinetic energy (due to its motion) and its gravitational potential energy (due to its position in Earth's gravitational field). When moving a satellite to a higher orbit, you must add energy to the system to account for the increase in gravitational potential energy and any changes in kinetic energy.
To calculate the specific energy change, we use the conservation of mechanical energy and Kepler's third law, which relates the orbital period to the radius of the orbit. In this process, work done or energy provided to transition a satellite from one orbit to another can be considered as coming from the chemical potential energy stored in the rocket's fuel.
For the given problem, assuming the satellite mass is 1.006 kg and the change in altitude is from 110 km to 193 km above Earth's surface, we will need additional information such as Earth's mass and radius as well as gravitational constant to make precise calculations. As the altitude increase also changes the potential and kinetic energy, both need to be factored in to determine the total energy required for the new orbit.
