If a satellite is orbiting the earth very close to its surface, then the orbital velocity mainly depends on

Options

A. Mass of satellite
B. Mass of earth
C. Radius of earth
D. Orbital radius

Answer

To solve the question "If a satellite is orbiting the earth very close to its surface, then the orbital velocity mainly depends on," we can follow these steps:

### Step 1: Understand the formula for orbital velocity
The orbital velocity \( v \) of a satellite can be expressed using the formula:
\[ v = \sqrt{\frac{GM}{r}} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( r \) is the distance from the center of the Earth to the satellite.

### Step 2: Simplify for a satellite close to the Earth's surface
When a satellite is orbiting very close to the Earth's surface, the radius \( r \) is approximately equal to the radius of the Earth \( R \). Thus, we can rewrite the formula as:
\[ v = \sqrt{\frac{GM}{R}} \]

### Step 3: Relate gravitational acceleration to orbital velocity
We also know that the gravitational acceleration \( g \) at the surface of the Earth is given by:
\[ g = \frac{GM}{R^2} \]
From this, we can express \( GM \) as:
\[ GM = gR^2 \]

### Step 4: Substitute \( GM \) back into the orbital velocity formula
Substituting \( GM \) into the orbital velocity formula gives:
\[ v = \sqrt{\frac{gR^2}{R}} = \sqrt{gR} \]

### Step 5: Conclusion about the dependence of orbital velocity
From the final expression \( v = \sqrt{gR} \), we can conclude that the orbital velocity mainly depends on:
- The gravitational acceleration \( g \),
- The radius \( R \) of the Earth.

Since the question asks for the main dependence, we can say that the orbital velocity mainly depends on the radius \( R \) of the Earth when the satellite is very close to the surface.

### Final Answer
Thus, the correct option is that the orbital velocity mainly depends on the radius of the Earth.

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