# Solar/Sidereal day/SpiralArm/Orbital Speed With Radio Telescope

• ~Sam~
In summary, the data from the radio telescope on Earth can be used to calculate the length of a solar day and a sidereal day, locate and determine the velocity of spiral arms, and calculate the orbital speed of the Earth. The key features of the data include the thick white bands representing the Sun, the S-shape of the hydrogen observations, and the broad diffuse white object in the center representing the galactic plane. The orbital speed of the Earth can be determined by analyzing the sinusoidal function in the data and comparing it to the known frequency of hydrogen.
~Sam~

## Homework Statement

Hello, I have 48-hour data from a radio telescope on Earth, and my goal is to answer these four questions:

1) Calculate the length of a solar day.
2) Calculate the length of a sidereal day
3) Explain how to locate a spiral arm on one of your plots and how to determine
its velocity, and then find the velocities of all spiral arms present.
4) Calculate the orbital speed of the Earth

I was given a picture and massive data tables(which I plotted into graphs) The first three correlates with the picture, and the last is an intensity of hydrogen vs time:

The picture data set given is actually three dimensional, with frequency in MHz on the x-axis, time in modified julian date (MJD) on the y-axis, and power in arbitrary units on the z-axis (represented by the greyscale). Taking a look at the pcture, which represents two days of observing. Some of the key features of this image.

Thick White Bands
The telescope is set at an appropriate angle such that the Sun transits through the beam twice in a 48-hour period. The Sun is the most radio-loud object in the sky, and when it passes through the telescope’s beam it appears as an extremely bright object at all frequencies in the data set, resulting in the large white bands you see.

S-shape of the Hydrogen Observations
With the exception of the hydrogen detected from the spiral arms, all other detections of hydrogen are from the local region of space. This material has the same rotation velocity about the galactic centre as the Earth. The result would be a Doppler shift of zero except for the fact that the Earth is orbiting the Sun. This orbital speed causes a Doppler shift in the frequency of the hydrogen, and, as the Earth’s daily rotation about its own axis carries the antenna beam around the sky, we see the orbital speed as the sinusoidal function present in the data.

Broad Diffuse White Object in the Centre of the Data
In addition to the Sun, the galactic plane also passes through the telescope’s beam. The galaxy is not a disk of evenly distributed hydrogen rotating around a centre, but rather a series of spiral arms. Along any given line of sight, arms at different distances will have different radial velocities as seen from the Sun, so the hydrogen emission from the different arms is Doppler shifted by different amounts and shows up at different frequencies. This creates an emission feature, with the hydrogen distributed over a large frequency range (e.g. seen at ≈ 54459.25 MJD). The Doppler shifts can be explicitly seen in the centerspectrum graph.

## Homework Equations

There will be several, unfortunately I don't know yet

## The Attempt at a Solution

My main issue here is interpreting the information, I know the Sun is the most radio loud, but how do I figure length of solar day from the data? Can I do that with an intensity of hydrogen and time graph? I know length of a sidereal day means relative to the stars, but how go by figuring that out? I'm not even sure how to do the last two..Any clues would be appreciated.

Last edited:

Hi there,

Thank you for sharing your data and questions with us. Based on the information provided, here are some suggestions on how you could approach each of the four questions:

1) To calculate the length of a solar day, you could use the data from the first graph, which shows the intensity of hydrogen vs time. The thick white bands in the graph represent the Sun transiting through the beam twice in a 48-hour period. By looking at the time stamps of when the Sun is at its highest intensity (brightest white band), you can determine the length of a solar day.

2) The length of a sidereal day refers to the time it takes for the Earth to rotate once on its axis relative to the stars. This can be calculated by looking at the data from the second graph, which shows the intensity of hydrogen vs frequency. The sinusoidal function in the data is caused by the Earth's orbital speed around the Sun. By measuring the frequency at which the sinusoidal function repeats itself, you can determine the length of a sidereal day.

3) To locate a spiral arm on one of your plots, you could use the data from the third graph, which shows the intensity of hydrogen vs frequency for a specific time stamp. Look for a broad, diffuse white object in the center of the data, which represents the galactic plane passing through the telescope's beam. To determine the velocity of the spiral arm, you can use the Doppler shift of the hydrogen emission from different arms at different distances. By comparing the frequency of the emission to the known frequency of hydrogen, you can calculate the velocity of each spiral arm present.

4) The orbital speed of the Earth can be calculated using the data from the second graph, which shows the intensity of hydrogen vs frequency. As mentioned before, the sinusoidal function in the data is caused by the Earth's orbital speed around the Sun. By measuring the frequency at which the sinusoidal function repeats itself, you can determine the orbital speed of the Earth.

I hope this helps and gives you some ideas on how to approach each question. Good luck with your analysis!

## 1. What is a solar day?

A solar day is the amount of time it takes for the Earth to complete one full rotation on its axis, which is equivalent to 24 hours. This is the basis for our standard measurement of time.

## 2. What is a sidereal day?

A sidereal day is the amount of time it takes for the Earth to complete one full rotation relative to the stars. Unlike the solar day, which is based on the position of the sun, the sidereal day is based on the Earth's position in relation to the stars in the sky.

## 3. What is the spiral arm of a galaxy?

A spiral arm is a long, curving structure that extends from the center of a spiral galaxy. These arms are made up of stars, gas, and dust that are pulled together by gravity and rotate around the galactic center.

## 4. How is orbital speed measured with a radio telescope?

Orbital speed can be measured with a radio telescope by observing the Doppler shift of radio waves emitted by objects in orbit. As the object moves towards or away from the telescope, the frequency of the radio waves will change, allowing for the calculation of its orbital speed.

## 5. What factors affect orbital speed?

The main factors that affect orbital speed are the mass of the object and the distance from the object it is orbiting. The greater the mass of the object, the stronger the gravitational pull, and the faster the orbital speed. The closer an object is to the center of rotation, the faster its orbital speed will be.

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