Question

Find the order of magnitude of force exerted by the sun on the earth. Mass of the sun = 1.99 × 10³⁰ kg, Mass of earth = 5.97 × 10²⁴ kg, Distance between Earth and the Sun = 1.49 × 10¹¹ m, G = 6.67 × 10⁻¹¹ Nm²/kg²

Answer 1

let's find force exerted by the sun on the earth at first.

from gravitational force, F = GMm/r²

here, M = 1.99 × 10³⁰ Kg, m = 5.97 × 10²⁴ kg , r = 1.49 × 10¹¹ m and G = 6.67 × 10⁻¹¹ Nm²/Kg²

so, F = (6.67 × 10⁻¹¹ × 1.99 × 10³⁰ × 5.97 × 10²⁴)/(1.49 × 10¹¹)²

= 35.69 × 10²¹ N

= 3.569 × 10²² N

now order of magnitude : if any number N is represented as N = a × 10ⁿ , where √10/10 ≤ a < √10 , then n is known as order of magnitude of given number.

here, 3.569 > √10

so, F = 3.569 × 10²² N = 0.3569 × 10²³ N

now you see, √10/10 ≤ 0.3569 < √10

so, 23 is order of magnitude of force exerted by sun on the earth.

Answer 2

Given:

1. Mass of sun = 1.99 x 10³⁰ kg
2. Mass of Earth = 5.97 x 10²⁴kg
3. Distance between Earth and Sun = 1.49 x 10¹¹m
4. Gravitational constant (G) = 6.67 x 10⁻¹¹ Nm²/kg²

To find:

1. Order of magnitude of the force exerted by the sun on earth

Solution:

This question can be solved using Newton's law of gravitation, according to which the force of attraction exerted by one body on another is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

This can be mathematically represented as follows:

                                       $F = \frac{Gm_{1} m_{2} }{r^{2} }$

Where,

F = Force of attraction

G = Gravitational constant

m₁ and m₂ = mass of body 1 and body 2 respectively

r = distance between body 1 and body 2

Substituting the given values into the equation while taking body 1 as earth and body 2 as the sun, we will obtain the force of attraction as follows:

F = (6.67 x 10⁻¹¹ x 5.97 x 10²⁴ x 1.99 x 10³⁰) / (1.49 x 10¹¹)²

F = (6.67 x 5.97 x 1.99) x 10²¹ / (1.49)²

F = 35.692 x 10²¹

F = 3.56 x 10²² N

Order of magnitude has the following representation: N = a x 10ᵇ

Where,

N = Order of magnitude of a number

a = integer

b = order of magnitude of the number

Representing force of attraction between the sun and the earth in this manner,

N = 3.56 x 10²²

Thus, the force of attraction between the sun and the earth is 3.56 x 10²² N, while the order of magnitude of the force exerted by the sun on the earth is 10²².