SOLVE: Now you are ready to figure out the three quantities you were charged with calculating. For each one, show how you determined it give your final expression in terms of the six quantities you measured (the three periods and the three distan ces). 3. Mass of Planet X's sun (Mgun). First, decide on which two objects' interaction to studyto find this mass. 4. Mass of Plan et X (Mg). First, decide on which two objects' interaction to study to find this mass. 5. The gravitational acceleration "g" at the surface of Plan et X. (neglect the rotation)
SOLVE: Now you are ready to figure out the three quantities you were charged with calculating. For each one, show how you determined it give your final expression in terms of the six quantities you measured (the three periods and the three distan ces). 3. Mass of Planet X's sun (Mgun). First, decide on which two objects' interaction to studyto find this mass. 4. Mass of Plan et X (Mg). First, decide on which two objects' interaction to study to find this mass. 5. The gravitational acceleration "g" at the surface of Plan et X. (neglect the rotation)
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Transcribed Image Text:SOLVE:
Now you are ready to figure out the three quantities you were charged with calculating. For each one,
show how you determined it give your final expression in terms of the six quantities you measured (the
three periods and the three distan ces).
3. Mass of Plan et X's sun (Mun). First, decide on which two objects' interaction to studyto find this
mass.
4. Mass of Plan et X (Mx). First, decide on which two objects' interaction to study to find this mass.
5. The gravitation al acceleration "g" at the surface of Plan et X. (neglect the rotation)
Transcribed Image Text:Newton's Law of gravitation
GMm
FM on m = Fm on M
=
with G = 6.67 × 10-11 N m? /kg?
As R. Blake, theintrepid captain of the space ship Liberator, you are approaching a solar system on the
outer edge of known space (known to your species, at least). You are looking for planets for possible
colonization and you are most interested in one of the planets (you've named it Planet X), which happens
to have a moon orbiting it. Both the orbits of the plan et and its moon are very close to circular.
As you approach the solar system, you are able to determine these quantities from visual observations:
Period of the moon's orbit around the planet (Tmoon)
Period of the planet's rotation (Trotate)
Period of the planet's revolution around its sun (T,revolve)
Radius of the planet (Rptanet)
Radius of the plan et's orbit around its sun (Rorbit)
Radius of the moon's orbit around the planet (Rmoon)
While you do not observe long en ough to see a full revolution of the planet or even the moon, you are
able to obser ve enough to extrapolate to a full period.
Your primary goal is to determine three parameters that you can't dir ectly measure from your spaceship:
Mass of Plan et X (Mx)
Mass of Planet X's sun (Mgun)
The gravitation al acceleration "g" at the surface of Plan et X
MODEL
The orbits are assumed to be circular.
VISUALIZE
1. What is the speed and acceleration of Planet X as it revolves (counter -
dockwise) around its sun? (Express your answer in terms of the
quantities you have already determined, the three periods and three
sun
distances, as needed.) Draw the velocity vector and acceleration vector
of Planet X on the diagram to the right.
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