A planet has a mass of `2.4xx10^(26)` kg with a diameter of `3xx10^(8)` m. What will be the acceleration due to gravity on that planet ?

Explanation

To find the acceleration due to gravity on the planet, we can use the formula:

\[ g = \frac{GM}{R^2} \]

where:
- \( g \) is the acceleration due to gravity,
- \( G \) is the universal gravitational constant, approximately \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
- \( M \) is the mass of the planet,
- \( R \) is the radius of the planet.

### Step 1: Identify the mass and diameter of the planet
- Mass \( M = 2.4 \times 10^{26} \, \text{kg} \)
- Diameter \( D = 3 \times 10^{8} \, \text{m} \)

### Step 2: Calculate the radius of the planet
The radius \( R \) is half of the diameter:
\[ R = \frac{D}{2} = \frac{3 \times 10^{8}}{2} = 1.5 \times 10^{8} \, \text{m} \]

### Step 3: Substitute the values into the formula for \( g \)
Now, we can substitute the values into the formula for acceleration due to gravity:
\[ g = \frac{GM}{R^2} \]
Substituting the known values:
\[ g = \frac{(6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2)(2.4 \times 10^{26} \, \text{kg})}{(1.5 \times 10^{8} \, \text{m})^2} \]

### Step 4: Calculate \( R^2 \)
First, calculate \( R^2 \):
\[ R^2 = (1.5 \times 10^{8})^2 = 2.25 \times 10^{16} \, \text{m}^2 \]

### Step 5: Substitute \( R^2 \) back into the equation for \( g \)
Now substitute \( R^2 \) back into the equation:
\[ g = \frac{(6.67 \times 10^{-11})(2.4 \times 10^{26})}{2.25 \times 10^{16}} \]

### Step 6: Calculate the numerator
Calculate the numerator:
\[ 6.67 \times 10^{-11} \times 2.4 \times 10^{26} = 1.6008 \times 10^{16} \]

### Step 7: Divide the numerator by \( R^2 \)
Now divide the result by \( R^2 \):
\[ g = \frac{1.6008 \times 10^{16}}{2.25 \times 10^{16}} \approx 0.711 \, \text{m/s}^2 \]

### Final Result
The acceleration due to gravity on that planet is approximately:
\[ g \approx 0.711 \, \text{m/s}^2 \]