Final answer:
To calculate the mass of Venus, use Newton's universal law of gravitation and solve for Venus's mass with the given surface gravity and radius. The mass of Venus is found to be approximately 4.867 × 10²4; kg.
Step-by-step explanation:
The student's question concerns the calculation of the mass of Venus using its radius and surface gravity. The formula that relates these variables is Newton's universal law of gravitation:
F = G * (m1 * m2) / r²
Where F is the force due to gravity (weight), G is the gravitational constant (6.674 × 10&supmin;11 N m² kg&supmin;2), m1 and m2 are the masses of the two bodies, and r is the distance between the centers of the two bodies (in this case, the radius of Venus). The surface gravity, g, is the acceleration due to gravity at Venus's surface and is equivalent to the force per unit mass (F/m2):
g = G * m1 / r²
By rearranging this formula to solve for m1 (the mass of Venus), we get:
m1 = g * r² / G
Substituting the given values, we find:
m1 = 8.87 m/s² * (6.05 × 10&sup6; m)² / 6.674 × 10&supmin;11 N m² kg&supmin;2
m1 = (8.87 × (6.05 × 10&sup6;)²) / 6.674 × 10&supmin;11
m1 ≈ 4.867 × 10²4; kg
This result shows that the mass of Venus is approximately 4.867 × 10²4; kilograms.