Law of universal gravitation (am I doing it wrong)

[Thegiver431]

Homework Statement

What is the gravitational force between Earth and the sun if the Earth has a mass of 5.98 x 10^24 and the sun has a mass of 1.99 x 10^30. The r is (1.5 x 10^11)^2[/B]

Homework Equations

F=(Gm₁m₂)/r^2

G= 6.67 x 10^-11 N m^2 /kg^2 ( note that this is a constant)[/B]

The Attempt at a Solution

I simply plugged in, and gathered the like terms and put them together accordingly so i got [( 6.67)(5.98)(1.99)]/(1.5)^2=35.277 ... Then you would move the decimal to get 3.52[/B]

Next i got all the exponent so( i canceled out the ten) -11+30+24-22= 21

so I got 3.52 x 10^21 N but the answer key said it is 3.52 x 10^22 N

What did I miss or is it a typo?

 

[Bystander]

r is (1.5 x 10)^2

You really want to take another look at this number.

 

[Thegiver431]

You really want to take another look at this number.

I meant 1.5 x 10 ^11 (sorry)

 

[haruspex]

Then you would move the decimal to get 3.52

And what did you do with the factor of 10 you removed in the process?

 

[HalfLostAndSearching]

Your calculation is correct, but you made a mistake in the exponent. The correct answer is 3.52 x 10^22 N, not 3.52 x 10^21 N. This is because when multiplying numbers in scientific notation, you add the exponents rather than subtracting them. So the final exponent should be (24+30-11-22)=21, not 22. This is a common mistake, so it's important to double check your calculations and make sure you are following the correct rules for manipulating numbers in scientific notation.