Answer:
The gravitational field strength at an altitude of 300 km above the surface of the earth can be calculated using the formula:
g = GM/(r+h)^2
where g is the gravitational field strength, G is the gravitational constant, M is the mass of the earth, r is the radius of the earth, h is the altitude above the surface of the earth.
Using the values:
G = 6.67 x 10^-11 N(m/kg)^2
M = 5.97 x 10^24 kg
r = 6.38 x 10^6 m
h = 3 x 10^5 m
we can calculate:
g = (6.67 x 10^-11) x (5.97 x 10^24)/((6.38 x 10^6 + 3 x 10^5)^2)
g = 8.62 m/s^2
This means that the gravitational field strength at an altitude of 300 km above the surface of the earth is about 8.62 m/s^2.
To calculate the weight of the astronaut at this altitude, we can use the formula:
F = mg
where F is the force of gravity (weight), m is the mass of the astronaut, and g is the gravitational field strength at this altitude.
Using the value: m = 70 kg, and g = 8.62 m/s^2, we get:
F = 70 x 8.62
F = 603.4 N
Therefore, the weight of the astronaut at an altitude of 300 km above the surface of the earth is about 603.4 N.