A 2.5 kg mass weighs 23.75 N on the surface
of a planet similar to Earth. The radius of this planet is roughly 7.7 × 10^6 m.
Calculate the mass of of this planet. The value of the universal gravitational constant is 6.67259 × 10^−11N · m2/kg2.
Answer in units of kg
g' om the planet is Wt/mass = 9.5 m/s^2
On earth, it is 9.8 m/s^2
M'/R'^2 = (95/98) Me/Re^2
Knowing the earth radius, Re and mass Me, you can calculate M'
You could also get M' from
F = G M' m/R'^2
To solve this problem, we can use the formula for gravitational force:
F = (G * M * m) / r^2
Where:
F is the gravitational force
G is the universal gravitational constant
M is the mass of the planet
m is the mass of the object
r is the distance between the center of the planet and the object
In this case, we know the mass of the object (m), the gravitational force (F), and the radius of the planet (r). We need to find the mass of the planet (M).
First, we rearrange the formula to solve for M:
M = (F * r^2) / (G * m)
Substituting the given values into the formula:
M = (23.75 N * (7.7 × 10^6 m)^2) / ((6.67259 × 10^−11 N · m2/kg2) * 2.5 kg)
Calculating this expression:
M = 6.97 × 10^24 kg
Therefore, the mass of the planet is approximately 6.97 × 10^24 kg.