Advertisements
Advertisements
Question
The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun?
Advertisements
Solution
Distance of the star from the solar system = 4.29 ly
1 light year is the distance travelled by light in one year.
1 light year = Speed of light × 1 year
= 3 × 108 × 365 × 24 × 60 × 60 = 94608 × 1011 m
∴4.29 ly = 405868.32 × 1011 m
∵1 parsec = 3.08 × 1016 m
:. 4.29 ly = `(405868.32 xx 10^(11))/(3.08xx 10^(16))`
Using the relation.
`theta = d/D`
where
Diameter of Earth's orbit, `d = 3 xx 10^(11) m`
Distance of the star from the Earth, D = `405868.32 xx 10^(11) m`
`:. theta = (3 xx 10^(11))/(405868.32xx 10^(11)) = 7.39 xx 10^(-6) rad`
But, 1 sec = 4.85 × 10–6 rad
`:. 7.39 xx 10^(-6) rad = (7.39 xx 10^(-6))/(4.85xx10^(-6)) = 1.52`
RELATED QUESTIONS
The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (second) of arc or so. A parsec is a convenient unit of length on the astronomical scale. It is the distance of an object that will show a parallax of 1” (second) of arc from opposite ends of a baseline equal to the distance from the Earth to the Sun. How much is a parsec in terms of meters?
Fill in the blank.
In the ............ system, length is measured in centimetres.
Fill in the following chart.
| Property | Definition | Basic Unit | Instrument used for measuring |
| Length | |||
| Mass | |||
| Volume | |||
| Time |
Rulers, measuring tapes and metre scales are used to measure ______
Which line is longer? C or D? Measure each line. How good is your guess?
How many stamps can be placed along its length?
You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!
- How many of you can sit in one square meter?
You can play this game on the ground. Make two squares of one square meter each. Divide your class into two teams. Ready to play!
- Which team could make more children stand in their square? How many?
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- How many cm is the length of the boundary of lake A in the drawing?(use thread to find out)
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?
There are two beautiful lakes near a village. People come for boating and picnics in both the lakes. The village Panchayat is worried that with the noise of the boats the birds will stop coming. The Panchayat wants motorboats in only one lake. The other lake will be saved for the birds to make their nests.
- A longer boundary around the lake will help more birds to lay their eggs. So which lake should be kept for birds? Which lake should be used for boats?
In which SI unit, you can measure your height?
What formula is used to measure the area of your classroom?
What is the unit of measurements of very small lengths?
- The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?
- Moon is seen to be of (½)°diameter from the earth. What must be the relative size compared to the earth?
- From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.
Mars has approximately half of the earth’s diameter. When it is closest to the earth it is at about 1/2 A.U. from the earth. Calculate what size it will appear when seen through the same telescope.
What is the SI unit of length?
The parallax method is used to measure astronomical distances because ______.
Which instruments are used to measure very small distances at the atomic scale?
