What is the surface gravity on this distant planet?

[sam2k2002]

Homework Statement

You have been visiting a distant planet. Your measurements have determined that the planet's mass is twice that of Earth but the free-fall acceleration at the surface is only one-fourth as large. Radius = 1.8*10^7meters
Mass = 1.19484 × 10^25 kilograms

Homework Equations

U_g = -(G*M*m)/r
v_escape = sqrt(2GM/r)

The Attempt at a Solution

I just plugged in the variables to the espace velocity equation and get 94km/s, but that's incorrect.

 

[sam2k2002]

The radius was given in the first part of the problem.

 

[Dick]

Um. The radius and the mass are correct. But I get 9.4km/sec. Check the decimal point.

 

[Dick]

g_e = \frac{GM_{e}}{R_{e}}

\frac{1}{4}g_e = g_{distant planet}

\frac{1}{4}*\frac{GM_{e}}{R_{e}} = \frac{G*2M_{e}}{R_{distant planet}}

\frac{1}{4*R_{e}} = \frac{2}{R_{distant planet}}

R_{distant planet} = 8R_{e}

g=G*M/r^2. It's force/mass not potential/mass.

 

[Feldoh]

Yeah, looks like I was just being retarded

 

[Dick]

Yeah, looks like I was just being retarded

S'ok. Reminds me of my post where I was strongly suggesting an OP integrate voltage over a gaussian surface to get enclosed charge. Duh.

 

[Feldoh]

S'ok. Reminds me of my post where I was strongly suggesting an OP integrate voltage over a gaussian surface to get enclosed charge. Duh.

Lol, guess we all screw up sometimes