To determine the gravitational force you would experience on the surface of Mercury, we need to use Newton's law of gravitation.
The formula for calculating the gravitational force [tex]\( F_{\text{gravity}} \)[/tex] is:
[tex]\[ F_{\text{gravity}} = \frac{G \cdot m_1 \cdot m_2}{r^2} \][/tex]
Where:
- [tex]\( G \)[/tex] is the gravitational constant, [tex]\( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex]
- [tex]\( m_1 \)[/tex] is the mass of the object (your mass), [tex]\( 68.05 \, \text{kg} \)[/tex]
- [tex]\( m_2 \)[/tex] is the mass of Mercury, [tex]\( 3.30 \times 10^{23} \, \text{kg} \)[/tex]
- [tex]\( r \)[/tex] is the radius of Mercury, [tex]\( 2.44 \times 10^6 \, \text{m} \)[/tex]
Let's put these values into the formula step-by-step:
1. Identify the values:
- [tex]\( G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2 \)[/tex]
- [tex]\( m_1 = 68.05 \, \text{kg} \)[/tex]
- [tex]\( m_2 = 3.30 \times 10^{23} \, \text{kg} \)[/tex]
- [tex]\( r = 2.44 \times 10^6 \, \text{m} \)[/tex]
2. Calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = (2.44 \times 10^6 \, \text{m})^2 = 5.9536 \times 10^{12} \, \text{m}^2 \][/tex]
3. Plug the values into the formula:
[tex]\[ F_{\text{gravity}} = \frac{(6.67 \times 10^{-11}) \cdot (68.05) \cdot (3.30 \times 10^{23})}{5.9536 \times 10^{12}} \][/tex]
4. Calculate the numerator:
[tex]\[ 6.67 \times 10^{-11} \cdot 68.05 \cdot 3.30 \times 10^{23} = 1.4982835 \times 10^{14} \][/tex]
5. Calculate the force:
[tex]\[ F_{\text{gravity}} = \frac{1.4982835 \times 10^{14}}{5.9536 \times 10^{12}} = 251.58703137597416 \, \text{N} \][/tex]
Thus, the gravitational force you would experience on the surface of Mercury is approximately [tex]\( 251.59 \, \text{N} \)[/tex].
