Calculate Earth's gravitational force on the ISS astronauts while orbiting at an altitude of 401.5 km above Earth’s surface.

F = m g

g = gsurface * Rearth^2/R^2

=
9.81 * Rearth^2/(Rearth+401500)^2

88.1%

To calculate the Earth's gravitational force on the ISS astronauts, we need to use the formula for gravitational force. The formula is given as:

F = (G * (m1 * m2)) / r^2

Where:
F is the gravitational force (in newtons)
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 is the mass of one object (Earth, in this case, approximately 5.972 × 10^24 kg)
m2 is the mass of the other object (the mass of the astronauts, which we can assume to be 1000 kg)
r is the distance between the centers of the two objects (the distance between the center of the Earth and the ISS, which is the altitude above the Earth's surface plus the Earth's radius)

First, let's convert the altitude of 401.5 km to meters:
401.5 km = 401.5 × 1000 = 401,500 meters.

Next, we need to add the Earth's radius which is approximately 6,371,000 meters:
r = 401,500 + 6,371,000 = 6,772,500 meters.

Now, we can substitute the given values into the formula to calculate the gravitational force:

F = (6.67430 × 10^-11 * (5.972 × 10^24 * 1000)) / (6,772,500)^2

F = 3.7103 × 10^6 newtons

Thus, the Earth's gravitational force on the ISS astronauts while orbiting at an altitude of 401.5 km above Earth's surface is approximately 3.7103 × 10^6 newtons.