# The distance from the earth to the sun.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

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 1.496×1011m_.

### Explanation of Solution

Formula used:

The distance is calculated using the formula d=(GM4π2)13T23.

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, aman=amn”.

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”.

(am)n=amn

Calculation:

Given that, the mass of the sun is 1.99×1030kg and the gravitational constant is 6.67×1011Nm2/kg2 and the period of earth’s orbit is about 365.25days.

It is known that, 1day=86400sec.

Use the above unit conversion to convert 365.25days into sec as follows.

365.25days=365.25×1day=365.25×86400sec=31557600sec

Note that, the period of earth’s orbit is about 31557600sec.

Substitute 6.67×1011Nm2/kg2 for G, 1.99×1030kg for M, 31557600sec for T to calculate d as follows.

d=(6.67×1011Nm2/kg2×1.99×1030kg4π2)13(31557600sec)23m=(13.2733×1030114π2)13(99862.5484)m=(0.3362×1019)13(99862.5484)m

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.

d=(3.362×1018)13(99862.5484)m=(1.498×106)(99862.5484)m=149594.0975×106m

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.

d=1.495940975×106+5m=1.495940975×1011m

Round off the above quantity up to three decimal places.

d=1.496×1011m

Therefore, the distance from the earth to the sun is 1.496×1011m_.

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