Respuesta :
Explanation:
To calculate the weight of the Voyager 2 probe at its closest approach to Neptune, you can use the gravitational force formula:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant (\(6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2\)),
- \( m_1 \) and \( m_2 \) are the masses of the two objects (probe and Neptune),
- \( r \) is the separation distance between the centers of the two masses.
The weight (\( W \)) of the probe is related to the gravitational force by \( W = m \cdot g \), where \( g \) is the acceleration due to gravity.
Let's denote:
- \( m \) as the mass of the Voyager 2 probe (722 kg),
- \( r \) as the separation distance (altitude) between the probe and Neptune (29,240,000 m + Neptune's radius).
Now, calculate \( r \) and use the formulas to find the weight of the Voyager 2 probe at that moment. Make sure to convert all units to meters and kilograms for consistency.
\[ r = 29,240,000 \, \text{m} + 24,900,000 \, \text{m} \]
\[ r^2 = r \cdot r \]
\[ F = \frac{G \cdot m_{\text{probe}} \cdot m_{\text{Neptune}}}{r^2} \]
\[ W = m_{\text{probe}} \cdot g \]
Plug in the values and calculate the result. Note: \( g \) is the acceleration due to gravity on Neptune, which can be calculated using the same formula \( g = \frac{G \cdot m_{\text{Neptune}}}{r_{\text{Neptune}}^2} \).
