Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and 720 km above the surface of the Moon, where the acceleration due to gravity is 0.839 m/s2. The radius of the Moon is 1.70 106 m.

(a) Determine the astronaut's orbital speed.
m/s

(b) Determine the period of the orbit.
s

Why does this look like this in 2018, fire your programmer please thanks <3

The acceleartion due to Gravity is already given at the orbital height. Proceed to use to value of gravitational acceleration given of 0.839m/2^2. The rest of the strategy is all good.

-m

Oh, the Moon, the astronauts, and some gravity! Let's calculate some numbers for you.

(a) To determine the astronaut's orbital speed, we can use the formula v = sqrt(GM/r), where G is the gravitational constant (approx. 6.67 × 10^-11 N(m/kg)^2), M is the mass of the Moon (approx. 7.35 × 10^22 kg), and r is the orbital radius (720 km above the surface of the Moon).

Converting the radius to meters, we get r = 720,000 meters.

Using the formula, we have v = sqrt( (6.67 × 10^-11 N(m/kg)^2) × (7.35 × 10^22 kg) / (720,000 m) ). Now, dear friend, I hope you have your calculator ready.

Calculating it all out, you'll find the astronaut's orbital speed to be approximately 1600.42 m/s.

(b) To find the period of the orbit, we can use the formula T = (2πr) / v, where T is the period and v is the orbital speed we just found.

Plugging in the values, we have T = (2π × 720,000 m) / 1600.42 m/s.

Calculating this out, you'll discover that the period of the orbit is approximately 2843.02 seconds.

So there you have it: the astronaut's orbital speed is around 1600.42 m/s, and their period of orbit is approximately 2843.02 seconds. Happy Moon watching!

To determine the astronaut's orbital speed, we can use the formula for orbital speed:

v = √(GM/r)

Where:
v = orbital speed
G = gravitational constant (6.67 x 10^-11 N*m^2/kg^2)
M = mass of the Moon
r = radius of the orbit

First, let's calculate the mass of the Moon using the acceleration due to gravity:

g = GM/r^2

Rearranging the equation:

GM = gr^2

Substituting the given values:

GM = (0.839 m/s^2) * (1.70 x 10^6 m)^2

Next, let's calculate the orbital speed:

v = √(GM/r)

Substituting the values we have calculated:

v = √((0.839 m/s^2) * (1.70 x 10^6 m)^2 / (720 km + radius of the Moon))

Convert the radius of the Moon from km to m:

radius of the Moon = 1.70 x 10^6 m

v = √((0.839 m/s^2) * (1.70 x 10^6 m)^2 / (720,000 m + radius of the Moon))

Now, plug in the numbers and calculate:

v = √((0.839 m/s^2) * (1.70 x 10^6 m)^2 / (720,000 m + 1.70 x 10^6 m))

Once you calculate the above, you will obtain the astronaut's orbital speed in m/s.

Now let's determine the period of the orbit. The period is the time it takes for the astronaut to complete one orbit.

T = 2πr/v

Where:
T = period
r = radius of the orbit
v = orbital speed

Plug in the values we have:

T = 2π * (720 km + radius of the Moon) / orbital speed

First, convert the radius of the Moon from km to m:

radius of the Moon = 1.70 x 10^6 m

T = 2π * (720,000 m + 1.70 x 10^6 m) / orbital speed

Now, substitute the calculated value of the orbital speed:

T = 2π * (720,000 m + 1.70 x 10^6 m) / (calculated orbital speed)

When you calculate the above, you will obtain the period of the orbit in seconds.

(a) First you need the value of the acceleration of gravity at the orbit location. Call it g. Here are the steps.

Moon radius = Rm = 1.7*10^6 m
Orbit height = H = 7.2*10^5 m
Orbit radius = R = Rm + H
= 2.42*10^6 m
R/Rm = 1.424
gm (at moon's surface) = 0.839 m/s^2
g(at orbit radius location) =
gm/(1.424)^2 = 0.414 m/s^2

Now set M g = M V^2/R

Satellite mass M cancels out.
V^2 = (R*g)
V = 1000 m/s

(b) orbit period = 2*pi*R/V
= 15,210 s
= 4.2 hours