The weight of an astronaut, in an artificial satellite revolving around the earth, is

The correct option is Zero.

To understand why the weight of an astronaut in an artificial satellite revolving around the Earth is zero, we must look at the physics of circular orbital motion and gravity.

1. Gravitational Force and Centripetal Acceleration:
When a satellite revolves around the Earth in a stable circular orbit, it is in a state of continuous free fall toward the Earth. The gravitational force exerted by the Earth on the satellite (and everything inside it, including the astronaut) provides the necessary centripetal force to keep it in orbit. This can be expressed as:
$F_g=\frac{G·M·m}{r^2}=m·a$
where $G$ is the gravitational constant, $M$ is the mass of the Earth, $m$ is the mass of the astronaut/satellite, $r$ is the distance from the center of the Earth, and $a$ is the acceleration of the satellite. Thus, the acceleration due to gravity at that orbit is:
$\mathrm{g\text{'}}=\frac{G·M}{r^2}$

2. Apparent Weight and the Normal Contact Force:
The "weight" we feel on Earth (apparent weight) is actually the normal force (contact force) exerted on us by the surface supporting us (like the floor). Inside the satellite, both the astronaut and the satellite itself are accelerating toward the Earth at the exact same rate:
$a=\mathrm{g\text{'}}$
Because both the astronaut and the satellite are falling together with the same acceleration, there is no relative motion or tendency to push against each other. The surface of the satellite does not exert any upward normal reaction force ($R$) on the astronaut.

Mathematically, the equation of motion for the astronaut of mass $m$ inside the satellite is:
$m·\mathrm{g\text{'}}-R=m·a$
Since the acceleration $a$ is equal to the gravitational acceleration $\mathrm{g\text{'}}$ at that height:
$m·\mathrm{g\text{'}}-R=m·\mathrm{g\text{'}}$
Subtracting $m·\mathrm{g\text{'}}$ from both sides gives:
$R=0$

Since the reaction force $R$ is zero, the astronaut experiences a state of weightlessness. Therefore, the apparent weight of the astronaut inside the revolving satellite is zero.