Question

The mass of the Earth is 80 times that of the Moon while the radius of the Earth is four times that of the Moon. The surface gravity of the Earth is______times that of the Moon? (In integer)

Answer 1

Correct Answer: 5

To find the ratio of the surface gravity of the Earth to that of the Moon, we must use the formula for gravitational acceleration: \( g = \frac{G \cdot M}{R^2} \), where \( M \) is the mass and \( R \) is the radius of the celestial body.

Step 1: Define the variables for Earth and Moon:

• Mass of Earth \( M_e = 80M_m \) (where \( M_m \) is the mass of the Moon)
• Radius of Earth \( R_e = 4R_m \) (where \( R_m \) is the radius of the Moon)

Step 2: Calculate \( g \) for Earth and Moon:

• Earth’s surface gravity: \( g_e = \frac{G \cdot M_e}{R_e^2} = \frac{G \cdot 80M_m}{(4R_m)^2} = \frac{80G \cdot M_m}{16R_m^2} = \frac{5G \cdot M_m}{R_m^2} \)
• Moon’s surface gravity: \( g_m = \frac{G \cdot M_m}{R_m^2} \)

Step 3: Determine the ratio of \( g_e \) to \( g_m \):

• \(\frac{g_e}{g_m} = \frac{\frac{5G \cdot M_m}{R_m^2}}{\frac{G \cdot M_m}{R_m^2}} = 5\)

The surface gravity of the Earth is 5 times that of the Moon.