An astronaut is floating happily outside her spaceship, which is orbiting the earth at a distance above the earths surface equal to 1 earth radius. The astronauts weight is An astronaut is floating happily outside her spaceship, which is orbiting the earth at a distance above the earths surface equal to 1 earth radius.

The astronauts weight is:

a. one-fourth her normal weight on earth

b. equal to her normal weight on earth

c. half her normal weight on earth

d. zero

The astronaut's weight will be one-forth of her normal weight on earth.

Explanation:

From Newton's law of gravitation, we can write the acceleration due to gravity (g) on Earth's surface is given by

where 'G' is gravitational constant, '' is Earth's mass and 'R' is Earth's radius.

As shown in the figure, if the astronaut is at a height 'h' from earth's surface and if '' be the value of the acceleration due to gravity at that height, then

Taking the ratio of both the equations, and as given h = R.

So,

where 'm' is the mass of the astronaut.

So the weight of the astronaut will be one-forth her normal weight on earth.

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