Question
If the mass of a planet is cut in half, how would the force of gravity between that planet and the Sun change?(1 point)
Responses
The force of gravity would not change
The force of gravity would not change
The force of gravity would double
The force of gravity would double
The force of gravity would increase four times
The force of gravity would increase four times
The force of gravity would decrease
Responses
The force of gravity would not change
The force of gravity would not change
The force of gravity would double
The force of gravity would double
The force of gravity would increase four times
The force of gravity would increase four times
The force of gravity would decrease
Answers
GPT-4o mini
The force of gravity between two objects is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) is equal to the product of the masses of the two objects (in this case, the planet and the Sun) divided by the square of the distance between their centers:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where \( G \) is the gravitational constant, \( m_1 \) is the mass of the planet, \( m_2 \) is the mass of the Sun, and \( r \) is the distance between them.
If the mass of the planet is cut in half, the new force of gravity would be:
\[ F' = G \frac{(m_1/2) m_2}{r^2} = \frac{1}{2} \left( G \frac{m_1 m_2}{r^2} \right) = \frac{1}{2} F \]
This means the force of gravity would decrease.
So the correct response is:
**The force of gravity would decrease.**
\[ F = G \frac{m_1 m_2}{r^2} \]
Where \( G \) is the gravitational constant, \( m_1 \) is the mass of the planet, \( m_2 \) is the mass of the Sun, and \( r \) is the distance between them.
If the mass of the planet is cut in half, the new force of gravity would be:
\[ F' = G \frac{(m_1/2) m_2}{r^2} = \frac{1}{2} \left( G \frac{m_1 m_2}{r^2} \right) = \frac{1}{2} F \]
This means the force of gravity would decrease.
So the correct response is:
**The force of gravity would decrease.**