Question

Is the acceleration of Mars' acceleration much greater than that of the Earth (encircling their orbit around the sun)? Justify your answer.

The mass of Pluto was unknown until it was discovered that it had a moon. Explain how to estimate the mass of Pluto. Explain how this made it possible to estimate the mass of Pluto.

Answer 1

The acceleration of Mars is smaller that that of Earth encircling their orbit around Sun.

A planet revolves around it's orbital when gravitational force is equal to the centrifugal force.

ie,    ----------- (1)

where G and M are constant (M = mass of Sun) and m is the mass of planet and r is the distance of the planet from Sun.

------------ (2)

we know that   is the centripetal acceleration.

So from equation (2), we can conclude that the centripetal acceleration is inversely proportional to the square of the distance between the planet and the Sun.

Since Mars is much far from Sun than Earth, Mars has smaller acceleration than that of Earth.

(2) For an object of mass m, in a circular orbit of radius r, the force of gravity is balanced by the centrifugal force of the bodies movement in a circle at a speed of v.

So from the formulae for these two forces, we get:

and

Balancing the two forces

F(gravity) = F(centrifugal)

   ------------- (1)

Now the velocity of the object revolving in its orbit is its circumference divided by orbital time:

equation (1) becomes,

Thus the mass of Pluto can be found by substituting the value of , period of the moon in seconds and its distance from Pluto in centimeters and run use , then you will get the value of Pluto in grams.