**Use the Basic Data Table above for challenges 1-3.**

1. Determine the gravitational force that attracts the Earth to the sun.

2. Determine the gravitational force that attracts the sun to the Earth. Explain its relationship to your answer in question 1.

3. Determine the gravitational force that attracts Jupiter to the sun.

4. Determine the speed needed for the space shuttle to orbit the Earth 400,000 meters above its surface.

**Use the Basic Data Table above for challenges 5 & 6.**

5. Calculate the following ratios of the planet's mean radius of orbit (R) to the planet's period of revolution (T).

6. Which ratio remains relatively constant?

7. State Kepler's three Laws.

8. With which of Kepler's three laws is your answer to challenge 6 consistent?

9. Derive Kepler's third law using universal gravitation and the centripetal force equation.

10. Physicists say that the total momentum of the Earth-sun system is zero as viewed from a point at rest with respect to our solar system. Explain how this is possible.

11. Using the Basic Data Table above, determine the velocity with which the Earth is hurling around the sun.

12. Again using the Basic Data Table above, determine the velocity with which the sun would need to move to provide the total system with zero momentum.

13. Determine the velocity with which the sun would have to move to provide the sun-Jupiter system with zero momentum.

14. Determine the position of the center of mass of the sun-Jupiter system with respect to the center of the Sun.

15. Does this point lie within the sun's Radius? Explain what your answer means.

16. Does your answer to challenge 15 agree with your answer to challenge 13? Explain.

17. Determine the observed frequency of a 400 Hz horn if the source of the horn's sound moved

- (a) toward you with a velocity of 45 m/s.
- (b) away from you with a velocity of 45 m/s.

18. Does light also experience a Doppler shift? Explain including the terms "blueshift" and "redshift".

**The following graphs and data (below star pictures) represent
data collected for what scientists claim to be evidence of a planet
existing around a star entitled Rho in the constellation Corona
Borealis as shown below. Use this data to determine the answers to
challenges 19-27.**

- Harvard University The Constellation Corona Borealis page, Available at http://cannon.sfsu.edu/~williams/planetsearch/rhocrb/rhoCrB_harvard.html

**The following represents data set up by Sylvain G.
Korzenn (skorzennik@cfa.harvard.edu). Use the data and graph shown
below to answer challenges 19-27.**

- Harvard University A Planet Orbiting the Star rho Coronae Borealis Available at http://cannon.sfsu.edu/~williams/planetsearch/rhocrb/rhoCrB_harvard.html

Precise Doppler measurements of the star rho Coronae Borealis have been made during the past year by Robert W. Noyes, Saurabh Jha, Sylvain G. Korzennik, Martin Krockenberger, Peter Nisenson, Timothy Brown, Edward Kennelly, and Scott Horner using the "Advanced Fiber Optic Echelle" spectrometer. Rho Coronae Borealis (link to picture) is a solar-type star (G0V), and is probably at least as old as the sun, judging from its weak chromospheric activity. The Doppler periodicity for rho Cor Bor is very convincing, having an amplitude of 67 meters/sec.

The research team concluded that the period is 39.6 days, the minimum mass is 1.1 Jupiter masses, the orbit has small eccentricity, and the orbital radius is 0.23 AU. You will be comparing your results below to these.

**The physical parameters of the star rhoCrB (from the
scientific literature) are: **

- R.A.: 16:01:03.39
- Dec.: +33:18:51.5 (2000.0)
- Vis Mag.: 5.40
- aka: HD 143761, HR 5968
- Spectral Type: G0V or G2V
- T(eff): 5760, 5783, 5868 K
- Parallax: 60 +/- 6 mas
- Distance: 16.7 +/- 1.7 pc, or 54.5 +/- 5.5 ly
- Luminosity: 1.61 L(sun)
- Age: 10 Gyr
- Mass: 1.0 M(sun)
- P(rotation): 20 d
- log(g): 4.11, 4.19, 4.23

**More on the Planetary Companion to rhoCrB**

**The orbital parameters (based on the AFOE's
observations) are: **

- Period: 39.645 +/- 0.088 days
- K1: 67.4 +/- 2.2 m/s
- e: 0.028 +/- 0.040
- omega: 210 +/- 74 degrees (longitude of periastron)
- T: 2,450,413.7 +/- 8.2 (time of periastron, HJD)
- a1 sin(i): (36.75 +/- 0.92) x 1E+6 m
- f1(m): (1.258 +/- 0.093) x 1E-9 M(Sun)
- m2 sin(i): 1.13 M(Jup)
- T(transit): 2,450,559.37 +/- 0.54 (HJD)

19. Determine CorBr period of rotation.

20. Determine the planet's period of rotation.

21. Determine the radius of the planet's orbit.

22. Determine the velocity of the planet in its orbit.

23. Determine the velocity of the sun it its orbit.

24. Using the fact that the planet and sun have a total momentum of zero, determine the mass of the planet.

25. Using the radius of the planet, the mass of the sun and the mass of the planet, determine the center of mass of the sun-planet system.

26. Use the radius of the sun's orbit and its period to determine the velocity of the sun as it orbits. Does this value agree with your answer in challenge 21?

27. Are any of your answers significantly different than the answers found by the research group? Explain any significant differences.

Glenbrook South's Physics Page

Author: Brian K. Wegley, Glenbrook South High School, Glenview, IL Multimedia Handbook of Engaged Learning Projects sponsored by Fermi National Accelerator Laboratory Education Office and Friends of Fermilab. Funded by the North Central Regional Technology in Education Consortium based at the North Central Regional Educational Laboratory (NCREL). Created: July 9, 1997

http://www-ed.fnal.gov/help/97/et/etbaschl.html