Compare an astronauts weight in orbit with the astronauts weight on Earth, assuming the mass of the astronaut doesn't change.
The weight is same but their is less gravity in space so the astronauts would float.
To compare an astronaut's weight in orbit with their weight on Earth, we need to understand the concept of weight and its relation to mass and gravity.
Weight is the force with which an object is pulled towards the center of the Earth (or any other celestial body). It is measured in units of force, such as pounds or Newtons. Weight is influenced by two factors: mass and gravity.
Mass is the amount of matter present in an object and is usually measured in kilograms. It represents the intrinsic property of an object and remains constant regardless of the gravitational field it's in.
Gravity is the force that attracts objects with mass towards each other. The force of gravity between two objects is dependent on their masses and the distance between them. The strength of gravity decreases as the distance between two objects increases.
An astronaut's weight on Earth is determined by the force of gravity pulling them towards the Earth's center. The average acceleration due to gravity on Earth's surface is approximately 9.8 meters per second squared (9.8 m/s^2).
In orbit, such as in the International Space Station (ISS), astronauts experience microgravity or freefall. In this state, they are still influenced by Earth's gravity, but they are constantly falling around the Earth, resulting in a sensation of weightlessness. The force they feel in this situation is called apparent weight.
The apparent weight in orbit is much less than the weight on Earth because the astronaut and the spacecraft are in freefall together. Therefore, the normal force (which determines apparent weight) is reduced or canceled out by the absence of contact forces. This results in the sensation of weightlessness.
So, to directly answer the question, an astronaut's weight in orbit (which is equivalent to their apparent weight) would be significantly less than their weight on Earth because there is less normal force acting upon them. However, since mass remains constant, their mass in orbit and on Earth would be the same.
To calculate the exact weight change, we need to apply the equation:
Weight = mass x acceleration due to gravity
On Earth, we assume a standard acceleration due to gravity of 9.8 m/s^2.
For example, let's say an astronaut has a mass of 80 kilograms:
Weight on Earth = 80 kg x 9.8 m/s^2 = 784 Newtons (or approximately 176 pounds-force)
In orbit, the acceleration due to gravity is low, but not zero. For the sake of comparison, let's assume it is approximately 90% less than on Earth:
Weight in Orbit = 80 kg x (9.8 m/s^2 x 0.1) = 78.4 Newtons (or approximately 17.6 pounds-force)
Therefore, the astronaut's weight on Earth, assuming the mass doesn't change, is approximately 784 Newtons (176 pounds), while their weight in orbit would be approximately 78.4 Newtons (17.6 pounds).