Answer to Question #285943 in Astronomy | Astrophysics for egonz23

Question

Can you explain this to me.

The planet Earth has 5.2 times the radius of Krypton, but has the same mass. If an object weighs 288 pounds on Krypton, how many pounds would it weigh on the Earth?

Give the answer as an integer in ordinary (not scientific) notation.

Answer 1

Given:

$R_E=5.2R_K$

$M_E=M_K$

$W_K=288 \rm \:pounds$

The weight of an object

$$W=mg$$

The acceleration due gravity is given by

$$g=G\frac{M}{R^2}$$

The ratio

$$\frac{W_E}{W_K}=\frac{M_ER_K^2}{M_KR_E^2}=1/5.2^2$$

The weigh of an object on the Earth

$$W_E=W_K/5.2^2=288/5.2^2=10.7\:\rm pounds$$