Which of the following two telescopes has a better angular resolution? 1) the Hubble Space Telescope (2.4 meter aperture) at optical wavelengths and 2) the Very Long Baseline Array (VLBA), a radio interferometer with a maximum baseline of 8600 km observing at 1 mm wavelengths. (Please answer with either HST or VLBA)
To compare the angular resolution of the two telescopes, we can use the formula for the angular resolution of a telescope:
Angular Resolution = (wavelength) / (telescope aperture)
For the Hubble Space Telescope (HST), with an aperture of 2.4 meters observing at optical wavelengths, the angular resolution can be calculated as:
Angular Resolution (HST) = wavelength / aperture = (optical wavelength) / 2.4 meters
For the Very Long Baseline Array (VLBA), with a maximum baseline of 8600 km observing at 1 mm wavelengths, the angular resolution can be calculated as:
Angular Resolution (VLBA) = wavelength / aperture = (1 mm) / (8600 km)
Comparing the two formulas, we find that the angular resolution of VLBA is smaller than that of HST. Therefore, the Very Long Baseline Array (VLBA) has a better angular resolution.
To determine which telescope has better angular resolution, we can use the formula for angular resolution:
Angular resolution = 1.22 * (wavelength / aperture)
Where:
- Angular resolution is measured in radians.
- Wavelength is the wavelength of light being observed.
- Aperture is the diameter of the telescope's primary mirror or antennas.
For option 1, the Hubble Space Telescope (HST) has an aperture of 2.4 meters and observes at optical wavelengths.
For option 2, the Very Long Baseline Array (VLBA) is a radio interferometer with a maximum baseline of 8600 km and operates at 1 mm wavelengths.
Since the angular resolution formula uses the ratio of wavelength to aperture, we can compare the two telescopes by calculating their respective ratios.
For the HST:
Angular resolution = 1.22 * (wavelength / aperture)
= 1.22 * (optical wavelength / 2.4 meters)
For the VLBA:
Angular resolution = 1.22 * (wavelength / aperture)
= 1.22 * (1 mm / 8600 km)
To determine which telescope has better angular resolution, we need to compare the calculated values. However, we can simplify this comparison by converting both wavelength values to the same unit (either meters or millimeters).
Let's convert the 8600 km baseline of the VLBA to millimeters:
8600 km = 8600000 meters
1 meter = 1000 millimeters
So, the VLBA has a baseline of 8,600,000,000 millimeters.
Now we can compare the angular resolution ratios:
For the HST:
Angular resolution = 1.22 * (optical wavelength / 2.4 meters)
For the VLBA:
Angular resolution = 1.22 * (1 mm / 8,600,000,000 millimeters)
After calculating the respective ratios, we can compare the values to determine which telescope has a better angular resolution.