You have landed on the surface of a newly-discovered planet (which is spherical

Question

You have landed on the surface of a newly-discovered planet (which is spherical and without mountains orcraters), and you have made the following observations: A rock dropped from rest from a height of 2.00 m above the surface takes 0.987 s to reach the surface. A trip by land rover around the equator of this planet covered a distance of 13,500 km. The planet has a small moon that orbits the planet once every 416 hours. At what altitude does that moon orbit above the surface of the planet? Two identical planets, each of mass m, move in a circular orbit (of radius r) diametrically opposite to each other around a star of mass M. as shown here. Find an expression (in terms of m. r. M and G) for their orbital period. T. Three stars of equal mass m move in identical circular orbits around their common center-of-mass point. As shown here, each star's center is located at one corner of an equilateral triangle with a side of length L. Find the speed v of each star, expressed in terms of m. Land G. Assume that gravity is the only force acting on the stars and that there are no objects other than those stars.

Explanation / Answer

b)balancing force on a planet,
m^2r=GMm/r^2 + Gmm/4r^2

or =(G(4M+m)/4r^3

so time period=2/

a) a=(GM/r^2) =4.1

2R=135*10^5m

or R=21.48*10^5m

and =2/T

so lastly equate the equation,

m^2(R+h)=GMm/(R+h)^2

solve this to get the value of h

c) use the concept of second part to get the result.

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