## A problem from Gravitation

Three identical bodies each of mass m are located at the vertices of an equilateral triangle with side r. At what speed they move if they all revolve under the influence of one another’s gravitation in a circular orbit circumscribing the triangle while still preserving the equilateral triangle

An equilateral triangle with equal sides and angles marked

## Variation in acceleration due to gravity (g) with depth

As we go deeper from the earth suface the gravity starts decreasing but formulla is ‘F=G*m*M/r2 where distance between the object and the earth is r2 which is inversally proportional to the ‘g’ then why as we go deeper from the earth suface the gravity starts decreasing; it should be increased because distance between the earth and the object is less. but it start decreasing why?

When we go deeper into earth, the attraction at that point is due to a sphere of earth of radius (R – d) where d is the depth below the surface of earth.

Let a body of mass m be kept on the surface of earth. The force exerted by earth on it,

$F_{surface}=mg=\frac{GMm}{R^{2}}$ where M is the total mass of earth and R is the radius of earth.

But, $M&space;=&space;\frac{4\pi&space;R^{3}\rho&space;}{3}$

Substituting for M,

$mg&space;=&space;\frac{4\pi&space;G\rho&space;m&space;R}{3}$

## GPS (Global Positioning System) Accuracy of Measurement

The 24 satellites that orbit the earth and define the Global Positioning System use
precision atomic clocks that are accurate to 1 x 10-9 s, or 1 nanosecond (1ns). A person on the earth, using their mobile phone, can usually “see” 4-12 of the 24 satellites at any one time.

An animation depicting the orbits of GPS satellites in medium Earth orbit. (Photo credit: Wikipedia)

The satellites are moving, relative to the surface of the earth, at 1.4 x 104 km/h.
a- Calculate  for one of these satellites,
Civilian GPS measurements have to be accurate at the level of 5-10m. How accurate must our knowledge of the clocks on the satellites be in order to achieve this level of accuracy in our position measurement?
[HINT: light signals are used by your phone and the satellites to perform the triangulation]
c-If we measure the passage of 1 day on earth using a clock that is identical to the clocks on the GPS satellites, how much time have the clocks on the satellites measured? What about for the passage of 2 days on earth? For this problem, it will be useful to apply the Binomial Expansion again

## Is the gravitational force between moon & earth are equal ?

Newton’s law of universal gravitation for two bodies. This law governs gravitational forces in the Earth. (Photo credit: Wikipedia)

Is the gravitational force between moon & earth are equal ?

If the question is- “Is the force exerted by earth on moon is equal to the force exerted by moon on earth?” then the answer is “Yes

I hope that more questions will follow.