Question

a space transportation vehicle releases a 586 kg communications satellite while in an orbit 280 km above the surface of the earth. a rocket engine on the satellite boosts it into a geosynchronous orbit. how much energy does the engine have to provide? solution conceptualize notice that the height of 280 km is much lower than that for a geosynchronous satellite, 35,800 km. therefore, energy must be expended correct: your answer is correct. to raise the satellite to this much higher position.

Answer 1

The rocket engine needs to provide approximately 202,310,464,000 J of energy to boost the communications satellite into geosynchronous orbit.

The amount of energy the rocket engine needs to provide to boost the communications satellite into geosynchronous orbit can be calculated using the principle of conservation of energy. In this case, the energy required is equal to the change in potential energy.

To determine the change in potential energy, we first find the difference in height between the satellite's initial orbit and the geosynchronous orbit. The height difference is 35,800 km - 280 km = 35,520 km.

Next, we calculate the change in potential energy using the formula: ∆PE = mgh, where m is the mass of the satellite, g is the acceleration due to gravity, and h is the change in height. Plugging in the values: ∆PE = (586 kg)(9.8 m/s²)(35,520,000 m) = 202,310,464,000 J or 2.02 x 10¹¹ J. Therefore, the engine needs to provide approximately 202,310,464,000 J of energy.