Advertisements
Advertisements
Question
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
Solution
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
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?
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.
While measuring the length of an object using a ruler, the position of your eye should be
Length of one’s chest can be measured using metre scale.
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?
Find the answer for the following questions within the grid.
- 10-3 is one ______
- SI Unit of time is ______
- Cross view of reading a measurement leads to ______
- ______ is the one what a clock reads.
- ______ is the amount of substance present in an object.
- ______ can be taken to get the final reading of the recordings of different students for a single measurement.
- ______ is a fundamental quantity.
- ______ shows the distance covered by an automobile
- A tailor uses ______ to take measurements to stitch the cloth.
- Liquids are measured with this physical quantity.
Match the following.
| 1. | Length | kelvin |
| 2. | Mass | metre |
| 3. | Time | kilogram |
| 4. | Temperature | second |
Numerical Problem.
Inian and Ezhilan argue about the light year. Inian tells that it is 9.46 × 1015 m and Ezhilan argues that it is 9.46 × 10 12 km. Who is right? Justify your answer.
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 |
Which line is longer? C or D? Measure each line. How good is your guess?
Guess whose tail is the longest. Now measure the tails. How good is your guess?
What is the length of a 100 rupee note? Guess. Now measure it using a scale.
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 | ||||
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 sit in their square? How many?
Chumki, Jhumri, and Imran need wire to make a fence.
- How much wire in all will the three need?
So Anar also tried many different ways to make a boundary for 800 square meters of land.
He made rectangles A, B, and C of different sizes. Find out the length of the boundary of each. How much gold wire will he get for these rectangles?
- A
Gold wire for A = _________ metres - B
Gold wire for B = _________ metres - C
Gold wire for C = __________ metres
But then Anar made an even longer rectangle... See how long!
- D
So he will get __________ metres of gold wire!!
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?
The distance between one end and the other end is called ______.
Length is ______.
Yard was used as the unit of length.
Why is Earth's orbit used instead of its diameter to measure distances to stars using the parallax method?
If a planet subtends an angle α at distance D, what formula is used to find the planet's diameter?
