How Does Changing Planetary Size and Orbit Radius Affect Gravitational Forces?

[nns91]

Homework Statement

1. Suppose you leave the solar system and arrive at a planet that has the same mass per unit volume as the Earth but has 10 times the Earth's radius. What would you weigh on this planet compared with what you weigh on Earth ??

2. Suppose that Kepler had found that the period of a planet's circular orbit is proportional to the square of the orbit radius. What conclusion would Newton have drawn concerning the dependence of the gravitational attraction on distance between two masses.

Homework Equations

F= -Gm1m2/r^2

The Attempt at a Solution

1. So I use Newton's law of gravitational and get you weigh 1/100 (radius is 10, square is 100) as you do on Earth. I am wrong. So how should I approach this problem ?

2. Can you guys hint me how should I do this one ?

 

[LowlyPion]

Homework Statement

1. Suppose you leave the solar system and arrive at a planet that has the same mass per unit volume as the Earth but has 10 times the Earth's radius. What would you weigh on this planet compared with what you weigh on Earth ??

2. Suppose that Kepler had found that the period of a planet's circular orbit is proportional to the square of the orbit radius. What conclusion would Newton have drawn concerning the dependence of the gravitational attraction on distance between two masses.

Homework Equations

F= -Gm1m2/r^2

The Attempt at a Solution

1. So I use Newton's law of gravitational and get you weigh 1/100 (radius is 10, square is 100) as you do on Earth. I am wrong. So how should I approach this problem ?

2. Can you guys hint me how should I do this one ?

2 things changed. Radius and what else?

 

[nns91]

Radius change so mass will change too right ??

 

[LowlyPion]

Radius change so mass will change too right ??

Correct.

How does the total mass change with the radius if the density is a constant?

And of course the distance from the center changes directly with the radius.

 

[nns91]

Mass changes at the same rate as radius does. Right ?

 

[LowlyPion]

Mass changes at the same rate as radius does. Right ?

What is the formula for that?

 

[nns91]

So F= -Gm(10M)/ 100R^2 ??

 

[LowlyPion]

So F= -Gm(10M)/ 100R^2 ??

No what is the formula for the mass given the density?

Isn't that Mass = density * volume?

 

[nns91]

Oh yeah, I misunderstood you.

but how can this help with finding your weight ?

 

[LowlyPion]

Oh yeah, I misunderstood you.

but how can this help with finding your weight ?

What is the volume of a sphere again?

 

[nns91]

V= 4/3*pi*r^3

 

[LowlyPion]

V= 4/3*pi*r^3

So that means then that M ∝ r³ ?