The international space station is maintained in a nearly circular orbit with a mean altitude of 330 km and a maximum of 410 km. An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is

Question

The international space station is maintained in a nearly circular orbit with a mean altitude of 330 km and a maximum of 410 km. An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is (A) zero (B) nearly zero and directed towards the earth (C) nearly g and directed along the line of travel of the station (D) nearly g and directed towards the earth

Tardigrade Admin · Accepted Answer

At height h, acceleration due to gravity is gh=(G M/(R+h)2) For h < < R, gh ≈ (G M/R2)=g Direction is towards centre of earth.

Q. The international space station is maintained in a nearly circular orbit with a mean altitude of $330 km$ and a maximum of $410 km$ . An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is

zero

nearly zero and directed towards the earth

nearly $g$ and directed along the line of travel of the station

nearly g and directed towards the earth

At height $h$ , acceleration due to gravity is
$g_{h} = \frac{GM}{( R + h ) ^{2}}$
For $h << R,$
$g_{h} \approx \frac{GM}{R ^{2}} = g$
Direction is towards centre of earth.

Q. The international space station is maintained in a nearly circular orbit with a mean altitude of 330km and a maximum of 410km. An astronaut is floating in the space station's cabin. The acceleration of astronaut as measured from the earth is