Acceleration due to gravity for a hypothetical planet

[balletgirl]

Homework Statement

A hypothetical planet has a radius 2.5 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

R(earth)= 6.38 x 10^4 m
M(earth)= 5.98 x 10^24 kg
G= 6.67 x 10^-11

Homework Equations

g=GM/r^2

The Attempt at a Solution

I did: (6.67 x 10^-11)(5.98 x 10^24kg) / [2.5(6.38 x 10^4m)]^2
and got 15,708, but know this is wrong since the answer is near only 15.

 

[shallgren]

The radius of Earth that you have looks like it's supposed to be kilometers.

Edit: Actually, no because Earth's radius is actually 6378 km so the exponent is just messed up.

 

[balletgirl]

Okay I just looked it up, the radius in km is 6.38 x 10^4, and the radius in meters is 6.38 x 10^6.

I used this instead and it worked! Thank you for pointing this out for me, and the answer was actually 1.5 m/s^2, not 15.

 

[shallgren]

No problem, just one more thing though. The radius is 6.38 x 10^3 km = 6,380 km, not 6.38 x 10^4 km = 63,800 km.

Some sources:
http://en.wikipedia.org/wiki/Radius_of_earth
http://www.universetoday.com/guide-to-space/earth/radius-of-the-earth/
http://wiki.answers.com/Q/What_is_the_radius_of_earth

Converted to meters, the exponent is 6, but in km the exponent is 3 (since km are 1000 times bigger than m)