Suppose we have made a model of the Solar system scaled down in the ratio `eta` but of materials of the same mean density as the actual materials of the planets and the Sun. How will the orbital periods of revolution of planetary models change in this case?

Read the following text and answer the following questions on the basis of the same: Spectrum Analysis and Astronomy Each element in the periodic table can appear in gaseous form and produce its own spectrum unique to that element. Hydrogen will not look like Helium, which wil not look like carbon which will not look like iron....and soon. Astrophysists can identify what kinds of materials are present in stars from the analysis of star's spectra. This type of study is called astronomical spectroscopy. The science of spectroscopy is quite sophisticated. From spectrum lines analysis astrophysists can determine not only the element, but the temperature and density of that element in the star. The spectral line also can tell us about any magnetic field of the star. The width of the line can tell us how fast the material is moving. We can learn about winds in stars from this. The shifting of spectral liens shift back and forth indicates that the star may be orbiting another star. The following table shows a rough guide for the relationship between the temperature of a star and the electromagnetic spectrum. If the spectrum of a star is red or blue shifted, then it can be used to infer its velocity along the line of sight. Edwin Hubble observed that more distant galaxies tended to have more red shifted spectra. This establishes the theory of expansion of the universe. Which nature of spectrum establishes the theory of the expanding universe?

Read the following text and answer the following questions on the basis of the same: Spectrum Analysis and Astronomy Each element in the periodic table can appear in gaseous form and produce its own spectrum unique to that element. Hydrogen will not look like Helium, which wil not look like carbon which will not look like iron....and soon. Astrophysists can identify what kinds of materials are present in stars from the analysis of star's spectra. This type of study is called astronomical spectroscopy. The science of spectroscopy is quite sophisticated. From spectrum lines analysis astrophysists can determine not only the element, but the temperature and density of that element in the star. The spectral line also can tell us about any magnetic field of the star. The width of the line can tell us how fast the material is moving. We can learn about winds in stars from this. The shifting of spectral liens shift back and forth indicates that the star may be orbiting another star. The following table shows a rough guide for the relationship between the temperature of a star and the electromagnetic spectrum. If the spectrum of a star is red or blue shifted, then it can be used to infer its velocity along the line of sight. Edwin Hubble observed that more distant galaxies tended to have more red shifted spectra. This establishes the theory of expansion of the universe. The lines in a star's spectrum is found to shift back and forth. What conclusion may be drawn from this observation?

Astronomers observe two separate solar systems each consisting of a planet orbiting a sun. The two orbits are circular and have the same radius R . It is determined that the planets have angular momenta of the same magnitude L about their suns, and that the orbital periods are in the ratio of three to one, i.e. T_(1)=3T_(2) . The ratio m_(1)//m_(2) of the masses of the two planets is

Astronomers observe two separate solar systems each consisting of a planet orbiting a sun. The two orbits are circular and have the same radius R . It is determined that the planets have angular momenta of the same magnitude L about their suns, and that the orbital periods are in the ratio of three to one, i.e. T_(1)=3T_(2) . The ratio m_(1)//m_(2) of the masses of the two planets is