Doppler Shift/Wien's Law/Hubble Constant Problems

[astronomystudent]

1.) If the actual value of the Hubble Constant is determined to be 72.3517 km/sec/MPC, what would this give for the age of the Universe?
* Could I possibly use V= H*D to find what the age of the universe is.

2.) What would be the Wien's Law predicted wavelength for an accretion disk heated to 300 million Kelvins? What would be the Doppler Shift if this disk was rotating in 75 minutes at a distance of 1 A.U. from the compact core remnant that it is orbiting?
*I used Wien's Law here and got the wavelength to be .0966 angstroms. For the second part of this problem could I use V= H*D to find the doppler shift.

3.) What would be the radial velocity (from the Doppler shift) of a quasar 12 billing light years away using the standard value of the Hubble Constant, 72 km/sec/MPC?
shift(nm) = rest wavelenght (nm) * radial velcity/speed of light this is the equation I presume I might use here.

4.) Assume a power output of 50,000 watts for a radio station at a receiver distance of 50 miles. What would be the power received on the Moon? What would be the power received on Alpha Centauri?
* Can I use the inverse square law here.

5.) Suppose a very distant globular cluster in another galazy is observed to have an apparent diameter of 0.15 arcsec with the Hubble Space Telescope. Assuming it to be an average size globular cluters (50 pc), how far away is it located?
I think I could use this equation to figure out how far away it is d= x/theta.

 

[Jhero]

here are my responses to your questions:

1.) Yes, you can use the equation V=H*D to find the age of the universe. The age of the universe can be calculated by dividing the distance to an object (D) by its velocity (V). However, keep in mind that the Hubble Constant is not a constant value and may change over time, so the age of the universe calculated using this method may not be entirely accurate.

2.) Yes, you can use Wien's Law to calculate the predicted wavelength for an accretion disk heated to 300 million Kelvins. And for the second part of the question, you can use the equation V=H*D to calculate the Doppler shift. However, keep in mind that this equation assumes a constant Hubble Constant, so the calculated value may not be entirely accurate.

3.) Yes, you can use the equation shift(nm) = rest wavelength (nm) * radial velocity/speed of light to calculate the radial velocity of a quasar 12 billion light years away. However, as mentioned before, the Hubble Constant is not a constant value, so the calculated value may not be entirely accurate.

4.) Yes, you can use the inverse square law to calculate the power received on the Moon and Alpha Centauri. Keep in mind that this law assumes a point source, so the calculated values may not be entirely accurate.

5.) Yes, you can use the equation d=x/theta to calculate the distance of the globular cluster. However, this equation assumes that the cluster is a perfect sphere, which may not be the case. Also, keep in mind that the apparent diameter may be affected by factors such as dust and gas in the galaxy, so the calculated distance may not be entirely accurate.