## Part 2 of 3

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Gravity, Energy, and Velocities

We can use some simple equations and calculations we learned in class to examine the physics of an object in orbit (we will mostly stick to the satellite mentioned in Part 1).

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Gravitational Acceleration

We know that the acceleration due to gravity on Earth is . Let's take a look at Kerbal Space Program and see how it compares (assuming we are on the surface).

: mass of body in orbit; : acceleration due to gravity; : universal gravitational constant; : radius of planet(from center of mass M)

; ;

While we're at it, we can do the same for the Mun (KSP's version of the Moon, it is pronounced the same way).

; ;

It turns out that

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Orbital Mechanical Energy

We can find the total energy in a spacecraft using some simple equations we've already learned.

is the orbital velocity and is given by the equation  with  being the gravitational parameter of the parent body ().

If we don't want to solve for  we can remove it using the equation for the net force of of circular motion (). In this case we are assuming the orbit of the craft is completely circular and  from the parent body is the only acting force.

We can now substitute this final value into the  equation.

: total energy of the orbit (J); : gravitational potential energy (J); : kinetic energy (J); :universal gravitational constant (); : mass of parent body (kg); : mass of orbiting body (kg); : radius of orbit (m); : orbital speed (

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We can see how the equations apply to our satellite in Part 1 (assuming that the fuel mass lost is negligible).

For the 100 km orbit ():

The final answers are negative and the craft is in a stable orbit. If the total energy was , the craft would be on a hyperbolic trajectory and would overpower the parent planet's gravitational pull.

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We can also find the orbital velocity of the craft at the different altitudes.

At 100 km:

At 200 km:

 Altitude (including 600 km radius) km (m/s) 100 2245.13 200 2100.13 300 1980.02 400 1878.41 500 1791.00 600 1714.75 700 1647.48 800 1587.55 9000 153.72 1,000 1485.02
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