Find the acceleration due to gravity on a planet with mass 1.9 cross times 10 to the power of 27 kg and radius 7.1 cross times 10 to the power of 7 m.

Information you might need:

F equals fraction numerator G M m over denominator r squared end fraction gives the magnitude of the gravitational force on an object of mass m on a planet of mass M and radius r, where G is Newton’s universal gravitational constant.

F equals m g gives the magnitude of the gravitational force on an object of mass m on a planet with acceleration due to gravity g.

G equals space 6.673 cross times 10 to the power of negative 11 end exponent space straight N space straight m squared space kg to the power of negative 2 end exponent

You do not need to include units with your answer; just give the numerical answer to an appropriate number of significant figures.

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.

Find the acceleration due to gravity on a planet with mass 1.9 × 10^27 kg and radius 7.1 × 10^7 m.

Learn how to calculate the acceleration due to gravity on a planet with mass 1.9 × 10^27 kg and radius 7.1 × 10^7 m using Newton's Law of Universal Gravitation and the formula g = GM/r^2. This detailed step-by-step solution explains gravitational force concepts, key formulas, and is suitable for Grades 9-12.

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