Answer:
M = 5.882 10²³ kg
Explanation:
Let's use Newton's second law to analyze the satellite orbit around Mars.
F = m a
force is universal attraction and acceleration is centripetal
a = v²/ R
the modulus of velocity in a circular orbit is constant
v= d/T
the distance of the cicule is
d =2pi R
a = 2pi R/T
we substitute
- G m M / R² = m ( )
G M =
M =
the distance R is the distance from the center of the planet Mars to the center of the satellite Deimos
R = 23460 km = 2.3460 10⁷ m
the period of the orbit is
T = 1,263 days = 1,263 day (24 h / 1 day) (3600s / h)
T = 1.0912 10⁵ s
let's calculate
M =
M = 509.73418 10²¹ /8.66640 10⁻¹
M = 58.817 10²² kg
M = 5.882 10²³ kg