Advertisements
Advertisements
प्रश्न
Solve the numerical example.
When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth, its angular diameter is measured to be 35.72'' of arc. Calculate the diameter of Jupiter.
Advertisements
उत्तर
Given: Angular diameter (α) = 35.72''
= 35.72'' × 4.847 × 10-6 rad
≈ 1.73 × 10-4 rad
Distance from Earth (D) = 824.7 million km
= 824.7 × 106 km
= 824.7 × 109 m.
To find: Diameter of Jupiter (d)
Formula: d = α D
Calculation: From the formula,
d = 1.73 × 10-4 × 824.7 × 109
= 1.428 × 108 m
= 1.428 × 105 km
The diameter of Jupiter is 1.428 × 105 km.
APPEARS IN
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?
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
What are the S.I. units of
- mass
- length
- time and
- temperature.
Write their names and symbols.
Exercise
Answer the following question.
Star A is farther than star B. Which star will have a large parallax angle?
While measuring the length of an object using a ruler, the position of your eye should be
Ten millimetre makes one centimetre.
A hand span is a reliable measure of length.
While measuring the length of a sharpened pencil, the reading of the scale at one end is 2.0 cm and at the other end is 12.1 cm. What is the length of the pencil?
Match the following.
| 1. | Length | kelvin |
| 2. | Mass | metre |
| 3. | Time | kilogram |
| 4. | Temperature | second |
Can you find the diameter of a thin wire of length 2 m using the ruler from your instrument box?
Guess the lengths to draw these things. Ask your friend to draw the same. After you make the drawing use a scale to measure the length. Whose drawing showed a better guess?
| Guess its length and draw |
Measure of your drawing |
Measure of your friend’s drawing |
| An ant of length less than 1 cm |
||
| Pencil of length about 7 cm |
||
| A glass 11 cm high with water up to 5 cm |
||
| A bangle of perimeter 20 cm |
||
| A curly hair of length 16 cm |
Now guess the length and width of many other things. Measure and find the difference between your measure and your guess.
| Size of | Your guess in cm | Your measure in cm | ||
| Length | Width | Length | Width | |
| 100 Rupee note | ||||
| 10 Rupee note | ||||
| 20 Rupee note | ||||
| 5 Rupee note | ||||
| Post card | ||||
| Math-Magic book | ||||
Difference in size 
Do this for yourself and find the difference.
How many stamps can be placed along its length?
How wide is the rectangle? ________ cm
How many stamps are needed to cover the rectangle?
How close was your earlier guess? Discuss.
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.
- Find the area of lake B on the drawing in square cm. What is its actual area in square km?
Length is a fundamental quantity.
What are the materials needed to find the length of a banana?
What formula is used to measure the area of your classroom?
What is the unit of measurements of very small lengths?
Length is ______.
Larger unit for measuring time is ______.
- 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.
In the parallax formula D = b/θ, what must be true about the angle θ for the calculation to be correct?
If a planet subtends an angle α at distance D, what formula is used to find the planet's diameter?
