1:45 PM - 3:15 PM
[O05-P41] Measurement of the Distance between the Earth and the Sun using Radio Telescope
Keywords:Astronomical Unit, 21 cm hydrogen line, Earth, Sun
1. Motivation
We became able to calculate the relative velocity of the earth and interstellar material by observing the frequency of the hydrogen line, 21-centimeter line or H1 line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms in interstellar material (hereinafter referred to as H1 line) in the previous research. Therefore, we started this research because we thought that we may calculate the distance between the earth and the sun (so called one astronomical unit) by observing the frequency of H1 line twice in different season.
2. Previous research
We observed the frequency of H1 line. Its original frequency is 1420.40575MHz (wavelength 21.106114 cm) but the frequency we observe on the earth is slight different from it due to Doppler Effect. By observing this difference, we can calculate the relative velocity between the earth and interstellar material (hereinafter referred to as relative velocity).
2-1. Reason for focusing on H1 line
Various types of electromagnetic waves fall on the earth, but many of which are bounced off the atmosphere or absorbed by the atmosphere (figure 1). Therefore, the observable frequency of outer space origin electromagnetic waves is limited. Frequency of H1 line is fortunately in this suitable area.
2-2. Area of observation
Area where we can observe H1 line is limited to galactic plane area which galactic latitude is 0 degree.
2-3. Influence of the rotation and the revolution of the earth to the relative velocity
Relative velocity we observed is approximately between 50km/s and -100km/s. The rotation speed of the earth at the observation site (Misato Astronomical Observatory, Kimino cho, Wakayama Prefecture, Latitude 34 degrees 14 minutes north) is 0.384 km/s, which is sufficiently smaller than the relative velocity. Therefore, we do not need to think about the influence of the earth’s rotation rate. The revolution speed of the earth is 29.9 km/s, which is nearly equal to the relative velocity. Therefore, we have to take care of the revolution speed of the earth.
3. This research
3-1. Principle
Observe the relative velocity twice, first in May and second in August. Determine the revolution speed of the earth using those datas. When we considered that the earth’s orbit is an exact circle, we can calculate the distance between the earth and the sun.
3-2. Angle of observation
Areas to be observed must be the intersection point of galactic plane (latitude 0 degree) and ecliptic plane (latitude 0 degree). Galactic plane is the only angle where we can observe H1 line from interstellar material (figure 2) and ecliptic plane is the only angle where the calculation method is not so complicated. Two points will satisfy this requirement, and we chose one of them which can be observed at the time of observation (figure 3).
Coordinate of observation point
Ecliptic longitude 90 degrees, Ecliptic latitude 0 degree
Galactic longitude 186 degrees, Galactic latitude 0 degree
Equatorial longitude 90 degrees, Equatorial latitude 23.14 degrees
3-3. Observation schedule, place and instrument
Observation 1: May 9, 2015. 15:00 - 19:00 rainy then sunny
Observation 2: August 2, 2015. 08:00 - 12:00 sunny
Place: Misato Astronomical Observatory in Kimino cho, Wakayama Prefecture
Instrument: radio telescope (8 meters in diameter) (Wakayama University / Misato Astronomical Observatory)
3-4. Result (figure 4) (When the interstellar material is moving away from the earth, we defined it as a positive value.)
May 9, 2015: Relative velocity -4.06 km/s
August 2, 2015: Relative velocity 39.2 km/s
3-5. Calculation results, conclusion and consideration
We used equation 1 and equation 2 to calculate the revolution speed of the earth.
Relative velocity (May) = V (interstellar material) - V (earth) x cos48.23---equation 1
Relative velocity (August) = V (interstellar material) - V (earth) x cos129.30--equation 2
Calculation result;
Revolution speed of the earth: 33.3 km/s
Distance between the earth and the sun (one astronomical unit): 167,000,000 km
Error compared to the true value of one astronomical unit (150,000,000 km) 1): 11 %
The following can be considered as factors of the error.
The revolution orbit of earth is not a true circle.
The revolution speed of the earth is not constant.
The interstellar material’s movement is not linear at a constant speed.
Influence of rotation of the earth.
3-6. What to do next
We review the observation and consider how to explain the error. Then try to remove the cause of error, and try to get the distance closer to true value.
1) Chronological Scientific Tables 2011, page 77, National Institutes of Natural Sciences, National Astronomical Observatory of Japan.
We became able to calculate the relative velocity of the earth and interstellar material by observing the frequency of the hydrogen line, 21-centimeter line or H1 line refers to the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms in interstellar material (hereinafter referred to as H1 line) in the previous research. Therefore, we started this research because we thought that we may calculate the distance between the earth and the sun (so called one astronomical unit) by observing the frequency of H1 line twice in different season.
2. Previous research
We observed the frequency of H1 line. Its original frequency is 1420.40575MHz (wavelength 21.106114 cm) but the frequency we observe on the earth is slight different from it due to Doppler Effect. By observing this difference, we can calculate the relative velocity between the earth and interstellar material (hereinafter referred to as relative velocity).
2-1. Reason for focusing on H1 line
Various types of electromagnetic waves fall on the earth, but many of which are bounced off the atmosphere or absorbed by the atmosphere (figure 1). Therefore, the observable frequency of outer space origin electromagnetic waves is limited. Frequency of H1 line is fortunately in this suitable area.
2-2. Area of observation
Area where we can observe H1 line is limited to galactic plane area which galactic latitude is 0 degree.
2-3. Influence of the rotation and the revolution of the earth to the relative velocity
Relative velocity we observed is approximately between 50km/s and -100km/s. The rotation speed of the earth at the observation site (Misato Astronomical Observatory, Kimino cho, Wakayama Prefecture, Latitude 34 degrees 14 minutes north) is 0.384 km/s, which is sufficiently smaller than the relative velocity. Therefore, we do not need to think about the influence of the earth’s rotation rate. The revolution speed of the earth is 29.9 km/s, which is nearly equal to the relative velocity. Therefore, we have to take care of the revolution speed of the earth.
3. This research
3-1. Principle
Observe the relative velocity twice, first in May and second in August. Determine the revolution speed of the earth using those datas. When we considered that the earth’s orbit is an exact circle, we can calculate the distance between the earth and the sun.
3-2. Angle of observation
Areas to be observed must be the intersection point of galactic plane (latitude 0 degree) and ecliptic plane (latitude 0 degree). Galactic plane is the only angle where we can observe H1 line from interstellar material (figure 2) and ecliptic plane is the only angle where the calculation method is not so complicated. Two points will satisfy this requirement, and we chose one of them which can be observed at the time of observation (figure 3).
Coordinate of observation point
Ecliptic longitude 90 degrees, Ecliptic latitude 0 degree
Galactic longitude 186 degrees, Galactic latitude 0 degree
Equatorial longitude 90 degrees, Equatorial latitude 23.14 degrees
3-3. Observation schedule, place and instrument
Observation 1: May 9, 2015. 15:00 - 19:00 rainy then sunny
Observation 2: August 2, 2015. 08:00 - 12:00 sunny
Place: Misato Astronomical Observatory in Kimino cho, Wakayama Prefecture
Instrument: radio telescope (8 meters in diameter) (Wakayama University / Misato Astronomical Observatory)
3-4. Result (figure 4) (When the interstellar material is moving away from the earth, we defined it as a positive value.)
May 9, 2015: Relative velocity -4.06 km/s
August 2, 2015: Relative velocity 39.2 km/s
3-5. Calculation results, conclusion and consideration
We used equation 1 and equation 2 to calculate the revolution speed of the earth.
Relative velocity (May) = V (interstellar material) - V (earth) x cos48.23---equation 1
Relative velocity (August) = V (interstellar material) - V (earth) x cos129.30--equation 2
Calculation result;
Revolution speed of the earth: 33.3 km/s
Distance between the earth and the sun (one astronomical unit): 167,000,000 km
Error compared to the true value of one astronomical unit (150,000,000 km) 1): 11 %
The following can be considered as factors of the error.
The revolution orbit of earth is not a true circle.
The revolution speed of the earth is not constant.
The interstellar material’s movement is not linear at a constant speed.
Influence of rotation of the earth.
3-6. What to do next
We review the observation and consider how to explain the error. Then try to remove the cause of error, and try to get the distance closer to true value.
1) Chronological Scientific Tables 2011, page 77, National Institutes of Natural Sciences, National Astronomical Observatory of Japan.