The geostationary orbit of the earth is at a distance of about 36000 km from the earth's surface. Find the weight of a 120 kg equipment placed in a geostationary satellite. The radius of the earth is 6400 km.

Explanation

To find the weight of a 120 kg equipment placed in a geostationary satellite, we can follow these steps:

### Step 1: Understand the Problem
We need to find the weight of the equipment in a geostationary orbit, which is located 36,000 km above the Earth's surface. The radius of the Earth is given as 6400 km.

### Step 2: Calculate the Total Distance from the Center of the Earth
The total distance \( d \) from the center of the Earth to the satellite can be calculated as:
\[ d = R + h \]
where:
- \( R \) is the radius of the Earth (6400 km),
- \( h \) is the height of the geostationary orbit (36,000 km).

Converting these distances to meters:
- \( R = 6400 \times 10^3 \) m,
- \( h = 36,000 \times 10^3 \) m.

Now, calculate \( d \):
\[ d = 6400 \times 10^3 + 36,000 \times 10^3 = 36,640,000 \text{ m} \]

### Step 3: Use the Gravitational Force Formula
The weight \( W \) of the equipment in the satellite can be calculated using the formula for gravitational force:
\[ W = \frac{G \cdot M \cdot m}{d^2} \]
where:
- \( G \) is the gravitational constant \( (6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2) \),
- \( M \) is the mass of the Earth \( (5.972 \times 10^{24} \, \text{kg}) \),
- \( m \) is the mass of the equipment (120 kg),
- \( d \) is the distance from the center of the Earth (calculated in Step 2).

### Step 4: Substitute the Values
Now substitute the values into the formula:
\[ W = \frac{(6.674 \times 10^{-11}) \cdot (5.972 \times 10^{24}) \cdot (120)}{(36,640,000)^2} \]

### Step 5: Calculate the Weight
Calculating the numerator:
\[ 6.674 \times 10^{-11} \cdot 5.972 \times 10^{24} \cdot 120 \approx 4.78 \times 10^{16} \]
Calculating the denominator:
\[ (36,640,000)^2 \approx 1.34 \times 10^{15} \]
Now, calculate \( W \):
\[ W \approx \frac{4.78 \times 10^{16}}{1.34 \times 10^{15}} \approx 35.6 \text{ N} \]

### Step 6: Conclusion
The weight of the 120 kg equipment placed in a geostationary satellite is approximately **35.6 N**.

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