Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. the moon has a diameter of 3500 km , and the free-fall acceleration at the surface is 1.60 m/s^2.how much time in minutes does it take for the spacecraft to complete one orbit?

Explanation:

The acceleration due gravity (free-fall acceleration) of a body is given by the following formula:

  (1)

Where:

is the gravitational constant

the mass of the body (the moon in this case)

is the distance from the center of mass of the body to its surface. Assuming the moon is a sphere with a diameter , its radius is

If the value of is given: we can find the mass of the moon with equation (1):

  (2)

  (3)

  (4)

Now, according to the 3rd Kepler's Law, there is a relation between the orbital period of a body (the spacecraft in this case) orbiting a greater body (the moon) in space with the size of its orbit.

   (5)

Substituting the known values and the calculated mass of the moon in (6), we can find the period of the orbit of the spacecraft around the moon:

   (6)

  (7)

Finally:

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find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2