The mass of the Earth=Mg=5.97x10^24 kg. The radius of the Earth=RE= 6.38 x10^6 m.
A) What is the weight of the 75 kg person?
B) Determine the acceleration due to gravity aboard a space shuttle at an altitude of 400km.
A) To calculate the weight of a person, we can use the formula:
Weight = mass x acceleration due to gravity
Given that the mass of the Earth, M, is 5.97x10^24 kg and the radius of the Earth, R_E, is 6.38x10^6 m, we can determine the acceleration due to gravity using the following formula:
Acceleration due to gravity = (G x M) / (R_E)^2
Where G is the gravitational constant, approximately 6.67x10^-11 N(m/kg)^2.
So, we can substitute the values into the equation:
Weight = mass x acceleration due to gravity
Weight = 75 kg x ((6.67x10^-11 N(m/kg)^2 x 5.97x10^24 kg) / (6.38x10^6 m)^2)
Simplifying this equation will give us the weight of the person in Newtons.
B) To determine the acceleration due to gravity aboard a space shuttle at an altitude of 400 km, we need to consider the change in distance from the center of the Earth to the location of the space shuttle. The radius of the Earth, R_E, is 6.38x10^6 m and the altitude of the space shuttle, h, is 400 km, which is equivalent to 400,000 m.
The new distance from the center of the Earth becomes (R_E + h). Thus, we can use the following formula to calculate the acceleration due to gravity:
Acceleration due to gravity = (G x M) / (R_E + h)^2
Substituting the given values into the formula will give us the acceleration due to gravity aboard the space shuttle.