m=4,87•10^24 d=6052км g-?
To find the gravitational acceleration \( g \) at the surface of a planet, you can use the formula:
\[ g = \frac{G \cdot m}{r^2} \]
where:
- \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \),
- \( m \) is the mass of the planet,
- \( r \) is the radius of the planet.
In your case:
- Given mass (\( m \)) = \( 4.87 \times 10^{24} \, \text{kg} \)
- Given diameter (\( d \)) = \( 6052 \, \text{km} \)
First, convert the diameter to meters to find the radius:
\[ d = 6052 \, \text{km} = 6052000 \, \text{m} \]
Therefore, the radius (\( r \)) is:
\[ r = \frac{d}{2} = \frac{6052000 \, \text{m}}{2} = 3026000 \, \text{m} \]
Now we can substitute \( m \) and \( r \) into the formula for \( g \):
\[ g = \frac{(6.674 \times 10^{-11}) \cdot (4.87 \times 10^{24})}{(3026000)^2} \]
Calculating this step-by-step:
- Calculate \( r^2 \):
\[ r^2 = (3026000)^2 = 9156763600000 \, \text{m}^2 \]
- Now, calculate \( G \cdot m \):
\[ G \cdot m = (6.674 \times 10^{-11}) \cdot (4.87 \times 10^{24}) \approx 3.2532998 \times 10^{14} \, \text{N} \cdot \text{m}^2/\text{kg} \]
- Now substitute these values back into the \( g \) formula:
\[ g = \frac{3.2532998 \times 10^{14}}{9156763600000} \approx 35.43 \, \text{m/s}^2 \]
So, the gravitational acceleration \( g \) at the surface of the planet is approximately \( 35.43 \, \text{m/s}^2 \).
