A) The mass is an intrinsic property of an object: it means it depends only on the properties of the object, so it does not depend on the location of the object. Therefore, Gary's mass at 300 km above Earth's surface is equal to his mass at the Earth's surface.
b) The weight of an object is given by
where
m is the mass
is the gravitational acceleration at the location of the object, with G being the gravitational constant, M the mass of the planet and r the distance of the object from the center of the planet.
At the Earth's surface,
, so Gary's weight is
(1)
where m is Gary's mass.
Then, we must calculate the value of g at 300 km above Earth's surface. the Earth's radius is
So the distance of Gary from the Earth's center is
The Earth's mass is
, so the gravitational acceleration is
Therefore, Gary's weight at 300 km above Earth's surface is
(2)
If we compare (1) and (2), we find that Gary's weight has changed by
So, Gary's weight at 300 km above Earth's surface is 91% of his weight at the surface.
b) The weight of an object is given by
where
m is the mass
At the Earth's surface,
where m is Gary's mass.
Then, we must calculate the value of g at 300 km above Earth's surface. the Earth's radius is
So the distance of Gary from the Earth's center is
The Earth's mass is
Therefore, Gary's weight at 300 km above Earth's surface is
If we compare (1) and (2), we find that Gary's weight has changed by
So, Gary's weight at 300 km above Earth's surface is 91% of his weight at the surface.