A spacecraft is in orbit close to the moon's surface. The centripetal acceleration is 1.6 m/s^2. If the radius of the moon is about 1.7 x 10^6 m, determine:
a)the orbital speed
b)the period of the orbit
v^2/r=1.6 m/s^2
find v
then, period
v=distance/period
period=2PI*r/v
To determine the orbital speed of the spacecraft, we can use the formula for centripetal acceleration:
a = v^2 / r
where:
- a is the centripetal acceleration
- v is the orbital speed
- r is the radius of the orbit
Given that the centripetal acceleration is 1.6 m/s^2 and the radius of the moon is 1.7 x 10^6 m, we can rearrange the formula to solve for the orbital speed.
a) Solving for the orbital speed (v):
v^2 = a * r
v = sqrt(a * r)
Plugging in the values:
v = sqrt(1.6 m/s^2 * 1.7 x 10^6 m)
Calculating this equation will give us the orbital speed in m/s.
b) The period of the orbit can be found using the formula:
T = 2π * r / v
where:
- T is the period of the orbit
- π is a mathematical constant approximately equal to 3.14159
Plugging in the values, including the calculated orbital speed, will give us the period of the orbit in seconds.