A satellite in a circular orbit of radius r has period T. A satellite in a nearby orbit with radius r + Δr, where Δr << r , has the very slightly different period T+ ΔT.
a) Show that
b) Two earth satellites are in parallel orbits with radii 6700 km and 6701 km. One day they pass each other, 1 km apart, along a line radially outward from the earth. How long will it be until they are again 1 km apart?
a) The given expression is proved.
b) They will meet again after 281.05 days
Two satellites are crossing each other. r and T are the radius of orbit and time period of first satellite whereas r + Δr, and T + ΔT, are the radius of orbit and time period of the second satellite respectively.
From Kepler's law
Now lets assume , the first satellite obeys the .
And , for the second satellite as it varies with Δr and ΔT so it will be
Now subtracting the equation for the first satellite:
On dividing with the equation for T, we get
Two satellites are in parallel orbit.
Radius of orbit of first satellite,r=6700 kmRadius of orbit of second satellite, r + Δr=6701 kmMass of Earth =5.98 x 1024 kg
In part(a) of the problem we have established
So after periods, they will meet again.
Find the value of One period
So they will meet again after 4467 periods = 4467 x 1.51 hours =6745.2 hours
.6745.2 hours =281.05 days .
You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.
a. What is the planet’s radius?
b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?
94% of StudySmarter users get better grades.Sign up for free