Phobos obits Mars at a distance of 9376 km from the center of the planet and has a period of 0.3 189 days. Assume Phobos’s orbit is circular. Calculate the mass of Mars. (Hints: Use the circular orbit velocity formula in Reasoning with Numbers 4-1; make sure to convert relevant quantities to units of meters, kilograms. and seconds.)
To calculate:
The mass of Mars based on the distance and orbit angle of Phobos
Answer to Problem 5P
The mass of Mars =
Explanation of Solution
Given Information:
Radius of orbit = 9376 Km
Period of Orbit = 0.3189 Days
Formula Used:
Circular orbit velocity =
Also, VS=distance/time
Calculation:
Assume Phobos (Moons) orbit to be circular.
First convert the quantities into proper units
Now,
Circular Velocity =
Where, G = Gravitational Constant =
r = Radius of Planet. (m)
m= Mass of Planet (Kg)
Rewriting in terms of m
∴ m =
For finding circular velocity that is distance covered per unit time.
∴ VS =Distance/time
Distance between but circumference of orbit.
∴
∴ Moon must cover 5.9 x 107 m distance in 27552.96 sec
∴ its circular velocity must be,
∴ put all the Values in mass of Mars formula,
=
=
Conclusion:
Mass of Mars is
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