Answer :
To calculate the gravitational force that Earth exerts on the asteroid, we can use the formula for gravitational force:
\[ F = \dfrac{{G \times m_1 \times m_2}}{{r^2}} \]
Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)),
- \( m_1 \) is the mass of the Earth (\( 5.972 \times 10^{24} \, \text{kg} \)),
- \( m_2 \) is the mass of the asteroid (15,750 kg),
- \( r \) is the distance between the Earth's center and the asteroid.
Given:
- \( r = 65,800 \, \text{km} = 65,800,000 \, \text{m} \)
Now, we can plug in the values into the formula and calculate the gravitational force.
\[ F = \dfrac{{G \times m_1 \times m_2}}{{r^2}} \]
Where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\( 6.67430 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)),
- \( m_1 \) is the mass of the Earth (\( 5.972 \times 10^{24} \, \text{kg} \)),
- \( m_2 \) is the mass of the asteroid (15,750 kg),
- \( r \) is the distance between the Earth's center and the asteroid.
Given:
- \( r = 65,800 \, \text{km} = 65,800,000 \, \text{m} \)
Now, we can plug in the values into the formula and calculate the gravitational force.
