PHYSICS HIGH SCHOOL

Deimos completes one (circular) orbit of Mars in 1.26 days. The distance from Mars to Deimos is 2.35×107m. What is the centripetal acceleration of Deimos?

Answers

Answer 1

Answer:

Answer:

The centripetal acceleration of Deimos is $0.077m/s^(2)$ .

Explanation:

The centripetal acceleration is defined as:

$a = (v^(2))/(r)$ (1)

Where v is the velocity of Deimos and r is the orbital distance.

Notice that is necessary to determine the velocity first.

The speed of the Deimos can be found by means of the Universal law of gravity:

$F = G(M \cdot m)/(r^(2))$ (2)

Then, replacing Newton's second law in equation 2 it is gotten:

$m\cdot a = G(M \cdot m)/(r^(2))$ (3)

However, a is the centripetal acceleration since Deimos almost describes a circular motion around Mars:

$a = (v^(2))/(r)$ (4)

Replacing equation 4 in equation 3 it is gotten:

$m(v^(2))/(r) = G(M \cdot m)/(r^(2))$

$m \cdot v^(2) = G (M \cdot m)/(r^(2))r$

$m \cdot v^(2) = G (M \cdot m)/(r)$

$v^(2) = G (M \cdot m)/(rm)$

$v^(2) = G (M)/(r)$

$v = \sqrt{(G M)/(r)}$ (5)

Where v is the orbital speed, G is the gravitational constant, M is the mass of Mars, and r is the orbital radius.

$v = \sqrt{((6.67x10^(-11)N.m^(2)/kg^(2))(6.39x10^(23)kg))/(2.35x10^(7)m)}$

$v = 1346m/s$

Finally, equation 4 can be used:

$a = ((1346m/s)^(2))/(2.35x10^(7)m)$

$a = 0.077m/s^(2)$

Hence, the centripetal acceleration of Deimos is $0.077m/s^(2)$ .

Answer 2

Answer:

Final answer:

The centripetal acceleration of Deimos, one of Mars' moon, can be calculated using its orbital period and distance from Mars. Convert the time units to seconds and use the formulas for velocity and centripetal acceleration to get an answer of approximately 7.84x10^-5 m/s^2.

Explanation:

To find the centripetal acceleration of Deimos, we can use the formula for centripetal acceleration, which is a =v^2/r , where v is the velocity and r is the radius (distance from Mars to Deimos). The velocity can be found using the formula v = 2πr/T, where T is the period (time for one complete orbit).

First, convert the days into seconds because the SI unit of time in physics is second. So, 1.26 days = 1.26 * 24 * 60 * 60 = 108864 seconds.

Then, calculate the velocity: v = 2 * π * 2.35x10^7m / 108864s = 1.36 km/s.

Finally, substitute v and r into the centripetal acceleration formula: a = (1.36x10^3m/s)^2 / 2.35x10^7m = 7.84x10^-5 m/s^2.

The centripetal acceleration of Deimos is approximately 7.84x10^-5 m/s^2.

Learn more about Centripetal Acceleration here:

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