Calculating Period of Rotation for Mars-Bound Weight at 3.8 m/s2

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In summary, the astronauts need to rotate their spacecraft with a period of 1.2*10^2 seconds to simulate an acceleration due to gravity of 3.8 m/s^2 on their journey to Mars. This can be achieved by equating the force produced by the spacecraft's rotation to the required acceleration.
  • #1
HKfish
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Homework Statement


As a spacecraft of diameter 2.8km approaches Mars, the astronauts want to experience what their Mars-bound weight will be. What should the period of rotation be to simulate an acceleration due to gravity of magnitude 3.8 m/s2 ?

Mass of Mars = 6.37*1023
Radius of Mars = 3.40*106

Homework Equations


(1) Fg = (GMm)/r2

(2) ac = (mv2)/r

(3) T = (2∏r)/v

The Attempt at a Solution



Fg = ac
(GMm)/r2 = (mv2)/r

Solving for v
v = √((GM)/r)

Sub v into eqn. (3)
T = (2∏r)*(√(r)/√(GM))
T = (2∏r(3/2))/√(GM)

And that's as far as i got cause I'm not sure what to do with the given information... The answer is 1.2*102s.
 
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  • #2
You don't need to do anything with G or those mass figures. They already gave you the acceleration required. So the force produced will be F=ma=m*(3.8m/s^2). Equate that to mv^2/r.
 

FAQ: Calculating Period of Rotation for Mars-Bound Weight at 3.8 m/s2

1. What is the equation for calculating the period of rotation for a Mars-bound weight at 3.8 m/s2?

The equation for calculating the period of rotation for a Mars-bound weight at 3.8 m/s2 is T = 2π√(r/g), where T is the period of rotation, r is the distance from the center of Mars, and g is the acceleration due to gravity on Mars (3.8 m/s2).

2. How do you determine the distance from the center of Mars for the calculation?

The distance from the center of Mars can be determined by using the radius of Mars, which is approximately 3,389.5 kilometers.

3. Is the period of rotation the same for all objects on Mars?

No, the period of rotation will vary depending on the distance from the center of Mars and the mass of the object. Objects with a larger distance from the center or a larger mass will have a longer period of rotation.

4. Can this equation be used for other celestial bodies?

Yes, this equation can be used for other celestial bodies as long as the appropriate values for distance from the center and acceleration due to gravity are used.

5. How accurate is this calculation?

This calculation is accurate for a simplified scenario where the acceleration due to gravity on Mars is constant and there are no other external forces acting on the object. In reality, there may be variations in the acceleration due to gravity and other factors that can affect the period of rotation.

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