Given Information:
circumference of planet = C = 25.7 km
height of release = h = 1.43 m
time = t = 30 s
Required Information:
Mass of planet = M = ?
Answer:
Mass of planet = M = 7.963×10¹⁴ kg
Explanation:
The mass of the planet can be found using Newton's law of gravitation,
g = GM/R²
M = gR²/G
Where g is the gravitational acceleration at the planet, R is the radius of the planet and G is the gravitational constant.
G = 6.6743×10⁻¹¹ m³/kg⋅s²
First we need to find R and g
The relation between circumference and radius is given by
C = 2πR
Where R is the radius of planet
25.7 = 2πR
R = 25.7/2π
R = 4.09 km
From the equations of motion we have,
h = ut + ½gt²
Where u is the initial speed which is zero, t is the time and h is the height of release.
Re-arrange the above equation for g
h = ½gt²
g = 2h/t²
g = (2*1.43)/(30)²
g = 0.003177 m/s²
Finally, the mass of the planet is
M = gR²/G
M = 0.003177*(4.09×10³)²/6.6743×10⁻¹¹
M = 7.963×10¹⁴ kg
Therefore, the mass of the given planet is 7.963×10¹⁴ kg
