There have been suggestions that the value of the gravitational constant `G` becomes smaller when considered over very large time period (in billions of years) in the future. If the happens for our earth.

Options

A. nothing will change
B. we will become hotter after billions of years
C. we will be going around but not strictly in closed orbits
D. after sufficiently long time we will leave the solar system

Explanation

To analyze the implications of a decreasing gravitational constant \( G \) over a long time period, we can break down the problem step by step:

### Step 1: Understanding the Gravitational Force
The gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by Newton's law of gravitation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
Here, \( G \) is the gravitational constant.

### Step 2: Analyzing the Effect of a Decreasing \( G \)
If \( G \) decreases over time, then the gravitational force \( F \) will also decrease since \( F \) is directly proportional to \( G \):
\[ F \propto G \]
This means that as \( G \) decreases, the force of attraction between the Earth and other celestial bodies will also decrease.

### Step 3: Implications on Orbital Motion
According to the inverse square law, if the gravitational force \( F \) decreases, the distance \( r \) between the masses must increase to maintain the relationship:
\[ F \propto \frac{1}{r^2} \]
If \( F \) decreases, then \( r \) must increase, indicating that the orbits of celestial bodies will become larger over time.

### Step 4: Long-term Effects on Earth's Orbit
As the gravitational force weakens, the Earth will not be able to maintain its current stable orbit. Instead, it will start to drift away from the Sun. This means:
- The Earth will not remain in a closed orbit.
- Over billions of years, the Earth may eventually leave the solar system.

### Step 5: Conclusion
In conclusion, if the gravitational constant \( G \) decreases over a long time period, it will lead to:
- A decrease in gravitational force.
- An increase in the distance between Earth and the Sun.
- The potential for Earth to leave its orbit and possibly the solar system.

### Summary of Key Points:
- \( G \) decreasing leads to a decrease in gravitational force.
- This results in an increase in the distance \( r \).
- Earth may not remain in a stable orbit and could drift away from the Sun.