Which one of the following statement is correct ?

Options

A. 1. The energy required to rocket an orbiting satellite out of earth's gravitational influence is more than the energy required to project a stationary object at the same height ( as the statellite ) out of earth's influence.
B. 2. If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of potential energy.
C. 3. The first artificial satellite Sputnik I was launched in the year 1950.
D. 4. The orbital speeed of the SYNCOMS (Synchronous communications satellite ) is `3.07xx10^(2) ms^(-1)`.

Explanation

To solve the question of which statement is correct, we need to analyze each statement provided in the question.

### Step-by-Step Solution:

1. **Analyze the First Statement:**
- The first statement claims that the energy required to rocket an orbiting satellite out of Earth's gravitational influence is more than the energy required to project a stationary object at the same height as a satellite out of Earth's influence.
- To analyze this, we consider the total energy of an orbiting satellite and a stationary object at the same height.
- For an orbiting satellite, the total energy \( E_1 \) is given by:
\[ E_1 = -\frac{GMm}{2R} \]
- For a stationary object, the total energy \( E_2 \) is:
\[ E_2 = -\frac{GMm}{R} \]
- The extra energy required to escape Earth's gravitational influence for the satellite is:
\[ E_{extra1} = \frac{GMm}{2R} \]
- For the stationary object, the extra energy required is:
\[ E_{extra2} = \frac{GMm}{R} \]
- Comparing \( E_{extra1} \) and \( E_{extra2} \):
\[ \frac{E_{extra1}}{E_{extra2}} = \frac{1/2}{1} = \frac{1}{2} \]
- This shows that the energy required to launch an orbiting satellite is less than that required for a stationary object, making the first statement incorrect.

2. **Analyze the Second Statement:**
- The second statement claims that if the zero of potential energy is at infinity, the total energy of an orbiting satellite is the negative of its potential energy.
- The potential energy \( U \) of an orbiting satellite is:
\[ U = -\frac{GMm}{R} \]
- The total energy \( E \) of the satellite is the sum of kinetic and potential energy:
\[ E = K + U = \frac{1}{2}mv^2 - \frac{GMm}{R} \]
- The total energy is actually negative of kinetic energy, not potential energy. Thus, this statement is incorrect.

3. **Analyze the Third Statement:**
- The third statement claims that the first artificial satellite, Sputnik 1, was launched in 1950.
- In reality, Sputnik 1 was launched on October 4, 1957. Therefore, this statement is also incorrect.

4. **Analyze the Fourth Statement:**
- The fourth statement claims that the orbital speed of a synchronous communication satellite is \( 3.07 \times 10^2 \) m/s.
- This statement is correct as the orbital speed for a synchronous satellite is indeed around this value.

### Conclusion:
The only correct statement among the options provided is the fourth statement regarding the orbital speed of a synchronous communication satellite.