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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.2, Problem 102E

To determine

The distance from the earth to the sun.

Expert Solution

The distance from the earth to the sun is

**Formula used:**

The distance is calculated using the formula

Where, *d* is the distance from the earth to the sun, *G* is the gravitational constant, *M* is the mass of the sun, *T* is the period of the planet’s orbit in sec.

*Division of powers:*

“The division of two powers with the same base *a* and different exponents *m* and *n* is given by,

That is, while dividing two powers with same base, the exponents are subtracted and the base will remain the same.

**Law used:**

*Laws of exponents:*

“To raise a power to a new power, multiply the exponents”.

**Calculation:**

Given that, the mass of the sun is

It is known that,

Use the above unit conversion to convert

Note that, the period of earth’s orbit is about

Substitute *G*, *M*, *T* to calculate *d* as follows.

Now, move decimal 1 place to the right and subtract 1 from the power of 10 in the first bracket of the above equation to simplify the expression.

Similarly, move decimal 5 places to the left, add 5 to the power of 10 to express the above quantity in proper scientific notation as follows.

Round off the above quantity up to three decimal places.

Therefore, the distance from the earth to the sun is