On February 20, 1962, John Glenn became the first American to orbit Earth. If John Glenn weighed 640 N on Earth’s surface, a) how much would he have weighed if his Mercury spacecraft had (hypothetically) remained at twice the distance from the center of Earth? b) Why is it said that an astronaut is never truly “weightless?”
since F is proportional to 1/r^2,
twice the radius is 1/4 the force
not zero force
a) To calculate John Glenn's weight if his Mercury spacecraft had remained at twice the distance from the center of the Earth, we need to understand the relationship between gravitational force and distance.
The gravitational force between two objects is given by the equation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the universal gravitational constant (approximately 6.674 × 10^(-11) N·m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, we assume that John Glenn's mass remains the same. The mass of the Earth also remains constant.
Since John Glenn is twice as far from the center of the Earth, the distance, r, would be doubled. Therefore, the gravitational force would be reduced by a factor of (1/2)^2 or 1/4.
So, to find John Glenn's weight at twice the distance, we can multiply his weight on Earth by 1/4:
Weight at twice the distance = 640 N * (1/4) = 160 N
Therefore, if John Glenn's Mercury spacecraft had hypothetically remained at twice the distance from the center of the Earth, he would have weighed 160 N.
b) It is said that an astronaut is never truly "weightless" because they are still subject to the gravitational pull of celestial bodies.
When an astronaut is in space, like aboard the International Space Station (ISS) or during spacewalks, they appear to be weightless because they are in constant free-fall around the Earth. The force of gravity still acts on them, but their spacecraft or the space station is also falling towards the Earth at the same rate, creating the sensation of weightlessness.
In other words, the astronaut and the spacecraft are in a state of continuous free-fall towards the Earth, maintaining a constant distance and speed, resulting in a perceived absence of weight. However, this does not mean that gravity is no longer acting on them.
So, even though an astronaut may experience weightlessness in space, they are still subject to the force of gravity and are not truly without mass or weight.