Star Z has 1/5 the radius of Earth and 1000 times the Earth's mass. If a mass weighs 1.0 N on Earth, what does it weight on Star Z?
Thank you.
To find out what a mass weighs on Star Z, we need to compare the gravitational forces acting on the mass on Earth and Star Z. The weight of an object is determined by the gravitational force it experiences.
First, let's find the gravitational force on Earth:
Weight on Earth = mass × acceleration due to gravity on Earth
Given that the weight on Earth is 1.0 N and acceleration due to gravity on Earth is approximately 9.8 m/s^2:
1.0 N = mass × 9.8 m/s^2
Next, we can determine the gravitational force on Star Z using the formula for gravitational force:
Force on Star Z = (G × mass1 × mass2) / radius^2
where G is the gravitational constant, mass1 and mass2 are the masses of the two objects, and radius is the distance between the centers of the two objects.
Since Star Z has 1/5 the radius of Earth, the radius on Star Z would be 1/5 times the radius on Earth. Let's denote the radius of Earth as Re and the radius of Star Z as Rz.
Rz = (1/5) × Re
Additionally, Star Z has 1000 times the Earth's mass, so the mass of Star Z would be 1000 times the mass of Earth. Let's denote the mass of Earth as Me and the mass of Star Z as Mz.
Mz = 1000 × Me
Using these values, we can calculate the gravitational force on Star Z:
Force on Star Z = (G × Me × Mz) / Rz^2
Now, we can compare the weight on Earth to the weight on Star Z:
Weight on Star Z = (mass × acceleration due to gravity on Star Z) = Force on Star Z
To find the weight on Star Z, we need to solve for the mass. Rearranging the formula for Force on Star Z, we get:
mass = Force on Star Z / acceleration due to gravity on Star Z
Plugging in the known values, we can calculate the weight on Star Z.