We are exploring an unknown planet in an unknown solar system. The plane is called Planet X, and it has a moon orbiting it. Both the orbits of the planet and its moon are very close to circular.

The following quantities are known:

• Period of the moon's orbit around the planet ()
• Period of the planet's rotation ()
• Period of the planet's revolution around its sun (
• Radius of the planet ()
• Radius of the planet's orbit around its sun ()
• Radius of the moon's orbit around the planet

Your primary goal is to determine three parameters that you can't directly measure from your spaceship:

• Mass of Planet X ()
• Mass of Planet X's sun ()
• The gravitational acceleration "g" at the surface of Planet X

MODEL

• The orbits are assumed to be circular.

SOLVE:

Now you are ready to solve for

• Mass of Planet X ()
• Mass of Planet X's sun ()
• The gravitational acceleration "g" at the surface of Planet X

Using the six quantities you measured that are listed above (the three periods and the three distances). Show your work.

1. Mass of Planet X's sun (). First, decide on which two objects' interaction to study to find this mass.

1. Mass of Planet X (). First, decide on which two objects' interaction to study to find this mass.

1. The gravitational acceleration "g" at the surface of Planet X. (neglect the rotation)