The gravitational force exerted by the planet Earth on a unit mass at a distance r from the center of the planet is

where M is the mass of Earth, R is its radius, and G is the gravitational constant. Is F a continuous function of r?

answer

watching

235

views

For unlimited access to Homework Help, a Homework+ subscription is required.

You have 0 free answers left.
Get unlimited access to 3.8 million step-by-step answers.

Get unlimited access

Already have an account? Log in

Tauseef ShaikhLv10

10 Jan 2021

Unlock all answers

Get 1 free homework help answer.

Already have an account? Log in

Related questions

Compute the gravitational force between the sun (M=1.99Ã10³⁰ kg) and the planet Mercury (m=5.50Ã10^-2 times the mass of the earth,orbital radius r= 0.387 A.U.).

As a moon follows its orbit around a planet, the maximum gravitational force exerted on the moon by the planet exceeds the minimum gravitational force by 5.9%. Find the ratio rmax/rmin, where rmax is the moon's maximum distance from the center of the planet and rmin is the minimum distance.

To escape Earth’s gravitational field, a rocket must be launched with an initial velocity called the escape velocity. A rocket launched from the surface of Earth has velocity v (in miles per second) given by

where v_0 is the initial velocity, r is the distance from the rocket to the center of Earth, G is the gravitational constant, M is the mass of Earth, and R is the radius of Earth (approximately 4000 miles).

(a) Find the value of v_o for which you obtain an infinite limit for r as v approaches zero. This value of v_o is the escape velocity for the earth.

(b) A rocket launched from the surface of the moon has velocity v (in miles per second) given by

Find the escape velocity for the moon.

Find the escape velocity for this planet. Is the mass of this planet larger or smaller than that of Earth? (Assume that the mean density of this planet is the same as that of Earth.)