The radius of earth is 6.37x10^6 m. If a spacecraft on the surface of the earth

Question

The radius of earth is 6.37x10^6 m. If a spacecraft on the surface of the earth weighs 7.20x10^3 N, what would the weight of the spacecraft be at: A) 6.37x10^6 m above the surface of earth?
B) 1.28x10^4 km above the surface of the earth?
C) the mass of Mars is 6.42x10^23 kg and its radius is 3.38x10^6 m. what is the weight of a 70.0kg student on this planet?

D) how far in km from the surface of the earth does a rocket have to travel so that the astronaut's weight is one-third of what it would be on earth? The radius of earth is 6.37x10^6 m. If a spacecraft on the surface of the earth weighs 7.20x10^3 N, what would the weight of the spacecraft be at: A) 6.37x10^6 m above the surface of earth?
B) 1.28x10^4 km above the surface of the earth?
C) the mass of Mars is 6.42x10^23 kg and its radius is 3.38x10^6 m. what is the weight of a 70.0kg student on this planet?

D) how far in km from the surface of the earth does a rocket have to travel so that the astronaut's weight is one-third of what it would be on earth? The radius of earth is 6.37x10^6 m. If a spacecraft on the surface of the earth weighs 7.20x10^3 N, what would the weight of the spacecraft be at: A) 6.37x10^6 m above the surface of earth?
B) 1.28x10^4 km above the surface of the earth?
C) the mass of Mars is 6.42x10^23 kg and its radius is 3.38x10^6 m. what is the weight of a 70.0kg student on this planet?

D) how far in km from the surface of the earth does a rocket have to travel so that the astronaut's weight is one-third of what it would be on earth? A) 6.37x10^6 m above the surface of earth?
B) 1.28x10^4 km above the surface of the earth?
C) the mass of Mars is 6.42x10^23 kg and its radius is 3.38x10^6 m. what is the weight of a 70.0kg student on this planet?

D) how far in km from the surface of the earth does a rocket have to travel so that the astronaut's weight is one-third of what it would be on earth?

Explanation / Answer

a.)

g' =g* R^2/(R+h)^2

g' is acceleration due to gravity at height h

g' =   9.81 * (6.37x10^6)^2 / (6.37x10^6 +6.37x10^6)^2 = 2.45 m/s^2

weight at height h = mg' = 7.20x10^3*0.245 = 17658 N

b.)

g' =g* R^2/(R+h)^2

g' is acceleration due to gravity at height h

g' =   9.81 * (6.37x10^6)^2 / (6.37x10^6 +1.28x10^7)^2 = 1.07 m/s^2

weight at height h = mg' = 7.20x10^3*0.1104 = 795 N

c.) g = Gm/r^2

g = 6.67*10^-11 * 6.42* 10^23 / (3.38*10^6)^2 = 3.748 m/s^2

weight of 70 kg body on mars = mg = 70*3.748 =262.37 N

d.) weight become 1/3 that means g become g/3

g' =g* R^2/(R+h)^2

1/3 = (6.37x10^6)^2 / ( 6.37x10^6 + h )^2

h = 4.66*10^6 m

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