We are given the following information:

• Mass of the planet $M = 1.9 \times 10^{27} \, \text{kg}$
• Radius of the planet $r = 7.1 \times 10^{7} \, \text{m}$
• Gravitational constant $G = 6.673 \times 10^{-11} \, \text{N} \cdot \text{m}^2 \cdot \text{kg}^{-2}$

To find the acceleration due to gravity $g$, we use the formula:

$g = \frac{GM}{r^2}$

Substituting the given values into the equation:

$g = \frac{(6.673 \times 10^{-11}) \times (1.9 \times 10^{27})}{(7.1 \times 10^7)^2}$

Now, let's calculate this.The acceleration due to gravity on the planet is approximately $25.2 \, \text{m/s}^2$.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How does the acceleration due to gravity change with the radius of a planet?
2. What is the effect of doubling the planet's mass on the gravitational acceleration?
3. How would the gravitational acceleration on this planet compare to Earth’s $9.81 \, \text{m/s}^2$?
4. What is the gravitational force on a 10 kg object on this planet?
5. How does gravitational constant $G$ affect celestial motions?

Tip: Gravitational acceleration on a planet depends directly on its mass and inversely on the square of its radius.