Advertisements
Advertisements
Question
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
Advertisements
Solution 1
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
Solution 2
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
RELATED QUESTIONS
The farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us?
Match the following.
| Column A | Column B |
| (1) Length | a. kilogram |
| (2) Mass | b. cubic metre |
| (3) Area | c. metre |
| (4) Volume | d. square metre |
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?
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 |
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.
What is Dinesh’s height in metres? _____ m _____ cm.
How many stamps can be placed along its length?
How wide is the rectangle? ________ cm
Arbaz plans to tile his kitchen floor with green square tiles. Each side of the tile is 10 cm. His kitchen is 220 cm in length and 180 cm wide. How many tiles will he need?
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?
Match the following:
| Prefix | Symbol | ||
| a. | Centi | i. | k |
| b. | Nano | ii. | c |
| c. | Mili | iii. | n |
| d. | Kilo | iv. | m |
The distance between one end and the other end is called ______.
What is the unit of length?
The SI unit of mass is kg.
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.
How many astronomical units (A.U.) make 1 parsec?
If a planet subtends an angle α at distance D, what formula is used to find the planet's diameter?
