If a satellite is orbiting in space having air and no energy is being supplied, then the path of that satellite would be

Options

A. circular
B. spiral of increases radius
C. spiral of decreasing radius
D. elliptical

Answer

To solve the problem of a satellite orbiting in space with air and no energy being supplied, we can analyze the situation step by step:

### Step 1: Understand the Environment
The question states that the satellite is orbiting in space where air is present. This implies that there is a medium (air) that can exert frictional forces on the satellite.

**Hint:** Consider how the presence of air affects the motion of the satellite.

### Step 2: Analyze the Effect of Air Resistance
In the presence of air, the satellite experiences drag or air resistance. This resistance opposes the motion of the satellite and causes it to lose energy over time.

**Hint:** Think about how air resistance impacts the velocity of an object moving through it.

### Step 3: Consider the Orbital Velocity
The orbital velocity of a satellite is given by the formula:
\[ v = \sqrt{\frac{GM}{r}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the distance from the center of the Earth to the satellite.

Since the satellite is losing energy due to air resistance, its orbital velocity will decrease.

**Hint:** Recall how changes in velocity affect the radius of the orbit.

### Step 4: Relate Orbital Velocity to Radius
As the satellite's orbital velocity decreases, the radius of its orbit must also decrease. This is because a lower velocity means that the satellite cannot maintain its current orbit and will spiral inward.

**Hint:** Consider the relationship between velocity and the radius of an orbit.

### Step 5: Determine the Path of the Satellite
With the decrease in velocity and radius, the path of the satellite will not be circular anymore. Instead, it will follow a spiral path as it moves closer to the Earth.

**Hint:** Visualize how a spiral path looks compared to a circular path.

### Conclusion
The path of the satellite, due to the presence of air and the absence of energy supply, will be a spiral path of decreasing radius.

**Final Answer:** The path of the satellite would be a spiral of decreasing radius.