Question

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.

Answer 1

Hint: Here First of all we will note down the given measures and then will find out the correlation between the two to get the required unknown term, diameter of Jupiter and will simplify accordingly.

Complete step by step solution:
First of all take the given terms and express it in the form of the mathematical terms.
Distance of Jupiter From the Earth, D \[ = 824.7 \times {10^6}km\]
Angular Diameter, $ \theta = 35.72'' = 35.72 \times 4.874 \times {10^{ - 6}}rad $
Using the relation $ \theta = \dfrac{d}{D} $
Now, diameter of the Jupiter can be defined as $ d = \theta D $
Placing the given values in the above equation-
 $ d = 824.7 \times {10^9} \times 35.72 \times 4.872 \times {10^{ - 6}} $
Simplify the above equation –
 $ d = 1.435 \times {10^5}Km $
Hence, the diameter of Jupiter is $ 1.435 \times {10^5}Km $
This is the required solution.

Additional Information:
Prime factorization is the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ $ 2 $ is the prime number as it can have only $ 1 $ factor. Factors are the number $ 1 $ and the number itself. When there is the simplification in the division form then first find the common factors from the numerator and the denominator and then remove it.

Note :
You should be very good in multiples. As, ultimately your answer depends on the multiplication of the numbers. Remember multiplies of the number at least till for the accurate and efficient solution. Remember the standard formula to solve this type of solution.