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प्रश्न
When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of Jupiter
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उत्तर १
Distance of Jupiter from the Earth, D = 824.7 × 106 km = 824.7 × 109 m
Angular diameter = 35.75" = 35.72 x 4.874 x 10-6 rad
Diameter of Jupiter = d
Using the relation,
`theta = d/D`
`d = thetaD = 824.7 xx 10^9 xx 35.72 xx 4.872 xx 20^(-6)`
=143520.76 x 103 = 1.435 x 105 km
उत्तर २
Given angular diameter θ = 35.72= 35.72 x 4.85 x 10-6 rad
= 173.242 x 10-6 = 1.73 x 10-4 rad
Diameter of Jupiter D = θ x d = 1.73 x 10-4 x 824.7 x 109 m
=1426.731 x 103 = 1.43 x 108 m
संबंधित प्रश्न
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?
Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):-
the number of air molecules in your classroom.
Write true or false.
Every measurement involves two things – a number and a unit.
Answer the following question.
Star A is farther than star B. Which star will have a large parallax angle?
Rulers, measuring tapes and metre scales are used to measure ______
Metre is the unit of ______.
Can you find the diameter of a thin wire of length 2 m using the ruler from your instrument box?
What is the length of a 100 rupee note? Guess. Now measure it using a scale.
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 stand in it?
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?
Length is a fundamental quantity.
What are the materials needed to find the length of a banana?
What is the unit of measurements of very small lengths?
What unit will you use to measure the length of our classroom?
Yard was used as the unit of length.
The radius of atom is of the order of 1 Å and the radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
The distance of a galaxy is of the order of 1025 m. Calculate the order of magnitude of time taken by light to reach us from the galaxy.
Why is Earth's orbit used instead of its diameter to measure distances to stars using the parallax method?
