An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth's surface the radius of the earth is R while its mass is M the gravitational pull `F_(G)` on the astronaut is

Options

A. Zero since astronaut feels weightless
B. `0 lt F_G lt (GMm)/R^2`
C. `(GMm)/((R+h)^2) lt F_G lt (GMm)/R^2`
D. `F_G=(GMm)/((R+h)^2)`

Explanation

To find the gravitational pull \( F_G \) on the astronaut working on a satellite orbiting the Earth, we can follow these steps:

### Step 1: Understand the scenario
The astronaut of mass \( m \) is in a satellite at a distance \( h \) above the Earth's surface. The radius of the Earth is \( R \), and the mass of the Earth is \( M \).

### Step 2: Determine the distance from the center of the Earth
The total distance \( r \) from the center of the Earth to the astronaut is given by:
\[ r = R + h \]

### Step 3: Use the formula for gravitational force
The gravitational force \( F_G \) acting on the astronaut can be calculated using Newton's law of gravitation:
\[ F_G = \frac{G \cdot M \cdot m}{r^2} \]
where \( G \) is the universal gravitational constant.

### Step 4: Substitute the expression for \( r \)
Substituting \( r = R + h \) into the gravitational force equation, we get:
\[ F_G = \frac{G \cdot M \cdot m}{(R + h)^2} \]

### Step 5: Conclusion
Thus, the gravitational pull \( F_G \) on the astronaut is:
\[ F_G = \frac{G \cdot M \cdot m}{(R + h)^2} \]

### Final Answer
Among the given options, the correct one is:
\[ F_G = \frac{G \cdot M \cdot m}{(R + h)^2} \]