How much will he weigh on a different planet

[rcmango]

Homework Statement

A space traveler weighs 500 N on earth. What will the traveler weigh on another planet whose radius is three times that of Earth and whose mass is twice that of earth?

answer in Newtons

Homework Equations

The Attempt at a Solution

i think the formula looks something like this, F = G(m1 * m2) / r^2 but I'm wrong somehow, also there are missing variables. This problem does not look very hard, just need help setting it up.

 

[DaveC426913]

You could do it that way, but you don't actually have to do the numbers.

You are given two factors affecting your weight. What effect does each of them (individually) have generally/algebraically on your weight (as related to Earth=1)?

 

[ogb p]

I can provide a response to this question. The formula you have mentioned, F = G(m1 * m2) / r^2, is the Newton's law of universal gravitation, where F represents the force of gravity between two objects, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

In this problem, we are given the mass and radius of the planet, but we need to find the weight of the space traveler on that planet. To do this, we can use the formula for weight, W = mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity on that planet.

Now, we need to find the value of g on the new planet. We know that the force of gravity between the space traveler and the planet will be equal to the weight of the space traveler (since he is not moving), so we can set F = W. Using the Newton's law of universal gravitation, we can write this as:

W = G(m1 * m2) / r^2

Substituting the values given in the problem, we get:

W = G(m1 * 2m1) / (3r)^2

W = G(2m1^2) / 9r^2

Now, we can rearrange this equation to find the value of g:

g = W/m = G(2m1^2) / (9r^2 * m1)

g = (2Gm1) / (9r^2)

Substituting the value of m1 (mass of the space traveler) and r (radius of the new planet), we get:

g = (2 * 500 N) / (9 * (3 * 6.38 * 10^6 m)^2)

g = 0.018 m/s^2

Finally, we can calculate the weight of the space traveler on the new planet using the formula W = mg:

W = (500 N) * (0.018 m/s^2)

W = 9 N

Therefore, the space traveler will weigh 9 Newtons on the new planet.