Any help is greatly appreciated, even if its only one question. Thank you!
1. Many people mistakenly believe that the astronauts that orbit Earth are "above gravity." Calculate g for space shuttle territory 160 km above Earth's surface. Assume Earth's mass is 6.0 1024 kg, and its radius is 6.38 106 m (6380 km). Your answer is what percentage of 9.8 m/s 2?
2. If you stood atop a ladder that was so tall that you were one and a half times as far from Earth's center, how would your weight compare with its present value?
Wnew / Wcurrent =
3. By what factor would your weight change if Earth's diameter were halved and its mass were quadrupled?
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Verified answer
Gravitational attraction in newtons
F = G m₁m₂/r²
G = 6.674e-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers
earth GM = 3.987e14
earth radius 6,371 km = 6.37e6 meters
w = mg
substituting
g = MG/r² = (3.987e14) / (6.37e6 + 160000)² = 9.35 m/s²
or 95% of g at the surface
others are similar
Use this formula to solve your problems:
EARTH
g = G x M(earth) / d^2
where g = Acceleration of gravity
G = universal gravitational constant 6.67259e-11
M = mass earth 5.98e24 kg
d = distance to center 6.38e6 meters