Final answer:
To calculate the mass of an Earth-sized planet with a gravitational strength of 6.5 m/s².
We use Newton's Law of Universal Gravitation and rearrange the formula. Substituting the value for Earth's radius and the gravitational constant into the equation, we can solve for the planet's mass.
Step-by-step explanation:
To calculate the mass of a planet with a given gravity strength, we need to use Newton's Law of Universal Gravitation and rearrange the formula to solve for mass (M).
The formula is given by gravitational force (F) = G * (m1 * m2) / r²,.
Where:
G is the gravitational constant
m1 and m2 are the masses of the two objects
r is the distance between their centers.
For the surface gravity of a planet, we compare the gravitational force exerted on an object (m2) at the planet's surface to its weight on Earth.
As we are given the surface gravity (g = 6.5 m/s²) and we assume an Earth-sized planet, we can take the radius of Earth (r) as approximately 6.371 x 10⁶ m.
The weight of an object (m2) would equal its mass multiplied by the surface gravity (W = m2 * g).
The gravitational force is also equal to the weight of the object. Therefore, we can express the gravitational force as F = G * (M * m2) / r² = m2 * g.
If we cancel out m2 and rearrange the equation to solve for M, we get M = g * r² / G. Substituting the known values, we have M = 6.5 * (6.371 x 10⁶ m)² / (6.67 x 10⁻¹¹ N.m²/kg²).
By performing this calculation, we can find the mass of the planet in question.
Keep in mind that this is a theoretical calculation and actual planetary mass would depend on various factors, including density and composition, which are not factored into this simple gravitational model.