To increase the acceleration on the new station due to Earth's gravity, you decide
either to place it 1.2RE from Earth or 1.3RE from Earth. How would you determine
the best location? Support your answer with math reasoning.
Does this location prevent the new station from being in free-fall? Explain

Respuesta :

Positioning the space station to a position of [tex]1.2\cdot R_{E}[/tex] from Earth represents a higher free-fall acceleration.

Determination of the best position of a space station with respect to Earth

According to Newton's law of gravitation, the gravitational force ([tex]F[/tex]), in newtons, is inversely proportional to the square of the distance between the center of the Earth and the space station ([tex]R[/tex]), in meters. In addition, the gravitational force is directly proportional to the free-fall acceleration ([tex]g[/tex]), in meters per square second, experimented by the space station.

[tex]g \propto \frac{1}{R_{E}^{2}} [/tex] (1)

Thus, positioning the space station to a position of [tex]1.2\cdot R_{E}[/tex] from Earth represents a higher free-fall acceleration. [tex]\blacksquare[/tex]

To learn more on Newton's law of gravitation, we kindly invite to check this verified question: https://brainly.com/question/9373839