Download Determining Planet Masses: Circular Orbits and Centripetal Force and more Exams Earth, Atmospheric, and Planetary Sciences in PDF only on Docsity!
How do we Determine the Mass of a Planet?
Activity I: How do objects move in a circular orbit? In this experiment we will verify how objects such as planets move in a circular orbit. The apparatus consists of a long string threaded through a short tube, one end connected to a rubber stopper and the other end to a hanging mass. Procedure:
- Attach a hanging mass at the end of the string.
- Mark a spot on the string about 1 inch below the tube.
- Twirl the stopper above your head so that the mark does not move up or down.
- Change the speed at which you rotate the rubber stopper so that the mark moves up and down? hanging mass (M) rubber stopper (m)
What happens to the mark when you speed up the stopper? _________________________
What happens to the mark when you slow down the stopper? ________________________
Why does the hanging mass not fall down? ________________________________________
- If the hanging mass is not moving up or down the weight of the hanging mass ( Fg ) is equal to the centripetal force ( Fc ).
- If you spin the stopper too fast the centripetal force will be greater than the weight of the hanging mass and the hanging mass will move up.
- If you spin too slowly is smaller centripetal force and the mass slides down. Fc Fg
Activity II. Repeat the experiment Procedure:
- Measure the mass of the mass hanging at the end of the string.
- Calculate the weight of the hanging mass. The weight is equal to the mass times the acceleration from gravity. Fg = Mg
- Measure the distance between the tube and rubber stopper ( r ).
- Mark a spot on the string about 1 inch below the tube.
- Twirl the stopper above your head so that the mark does not move up or down.
- Record the time it takes for the stopper to go around once. It might be easier if you measure the time it takes the stopper to go around 10 times (T 10 ) and divide by 10.
- Calculate the velocity. T r time dis ce velocity
tan 2 π
- Calculate the centripetal force r mv Fc 2 =
- Repeat with a different hanging mass.
Activity III. On the graph below plot mass of the hanging mass (M) versus r/T 2 (on the x-axis) What pattern do you see when you made your graph? ______________________________ _____________________________________________________________________________ M (kg) r/T^2
Activity IV. The Mass of a planet The mass of the planets in our solar system is given in the table below. The mass of Earth is 598 x 10^22 kg, which is 5,980,000,000,000,000,000,000,000 kg (598 with 22 zeros after that). Planet Mass (kg) Mercury 330 x 10 22 Venus 488 x 10 22 Earth 598 x 10 22 Mars 642 x 10 21 Jupiter 190 x 10 25 Saturn 568 x 10^24 Uranus 868 x 10 23 Neptune 103 x 10^24 Pluto 129 x 10^21 How do we know the mass of the planets? Is there a scale large enough to hold a planet?
If the gravitational attraction is the centripetal force ( r M v r
M M
G
2 2 2 (^1 2) = ) then we can get the mass of the center body by measuring the distance between the bodies and the time for the satellite to make a complete orbit. 2 2 3 1
T
r G
M
If we plot M 1 and (^2) 3 T r then we should get a straight line with a slope equal to G
Or you can determine the mass of a planet by multiplying (^2) 3 T r by (^79). 3
2
G
M (kg) R^3 /T^2 (m^3 /d^2 )
Using the time it takes for the given satellites to revolve around the planet and the distance between the satellite and the planet, determine the mass of the following planets. Jupiter Satellite Distance from Jupiter (m) Days for 1 revolution (d)
R
3 /T 2 Mass of Jupiter (kg) Io 422 x 10^6 1. Europa 671 x 10^6 3. Callisto 189 x 10 7
Mars Satellite Distance from Mars (m) Days for 1 revolution (d)
R
3 /T 2 Mass of Mars (kg) Phobos 940 x 10^4 0. Deimos 235 x 10 5
Earth Satellite Distance from Earth (m) Days for 1 revolution (d)
R
3 /T 2 Mass of Earth (kg) Moon 384 x 10^6 27. How do the values you obtained for the mass compare to the values in the table?________ _____________________________________________________________________________
