An object rests on the surface of planet y. Its mass is unknown. Find the acceleration due to gravity near the surface of planet y. Answer in m/s/s.
G=6.673x10^-23
radius of planet y=2439700m
mass of planet y=3.302x10^23kg
radius of planet x=71492000m
mass of planet x=1.89x10^27kg
To find the acceleration due to gravity near the surface of planet y, we can use the formula:
\[ g = \frac{{G \cdot M}}{{r^2}} \]
where:
- g is the acceleration due to gravity,
- G is the gravitational constant (6.673x10^-11 N m^2/kg^2),
- M is the mass of planet y (3.302x10^23 kg),
- r is the radius of planet y (2439700 m).
First, we need to calculate the value of \( G \cdot M \):
\[ G \cdot M = (6.673x10^-11 \, \text{N m}^2/\text{kg}^2) \times (3.302x10^23 \, \text{kg}) \]
Multiply the numbers:
\[ G \cdot M \approx 2.203x10^{13} \, \text{N m}^2 \]
Next, we need to calculate \( r^2 \):
\[ r^2 = (2439700 \, \text{m})^2 \]
Square the number:
\[ r^2 \approx 5.9599x10^12 \, \text{m}^2 \]
Now, substitute the values into the formula:
\[ g = \frac{{2.203x10^{13} \, \text{N m}^2}}{{5.9599x10^12 \, \text{m}^2}} \]
Divide the numbers:
\[ g \approx 3.6934 \, \text{m/s}^2 \]
Therefore, the acceleration due to gravity near the surface of planet y is approximately 3.6934 m/s^2.