Home
Class 11
PHYSICS
If a satellite is revolving around a pla...

If a satellite is revolving around a planet of mass `M` in an elliptical orbit of semi-major axis `a`. Show that the orbital speed of the satellite when it is a distance `r` from the focus will be given by
`upsilon^(2) = GM[(2)/(r ) - (1)/(a)]`

Text Solution

Verified by Experts

Total mechanical energy of the system is `E=-(GMm)/(2a)` which remains conserved
`rArr` KE+PE=`-(GMm)/(2a)`
At a position .r. obital speed of the satellite is v.
The KE=`1/2mv^2` , PE=-`(GMm)/r`
So, `1/2mv^2-(GMm)/r=-(GMm)/(2a)` (or) `v^2=GM(2/r-1/a)` .
Promotional Banner

Similar Questions

Explore conceptually related problems

A satellite is moving around the earth with speed v in a circular orbit of radius r. IF the orbit radius is decreased by 1%, its speed will

A satellite of mass m orbits around the Earth of mas M in an elliptical orbit of semi - major and semi - minor axes 2a and a respectively. The angular momentum of the satellite about the centre of the Earth is

Speed of a planet in an ellioptical orbit with semimajor axis a about sun of mass M at a distance r from sun is

A satellite is revolving near by earth of radius =R_e . If its velocity is increased sqrt(3/2)v where v is the orbital speed of satellite then find maximum distance of satellite from the center of the earth.

A planet is revolving round the sun in an elliptical orbit, If v is the velocity of the planet when its position vector from the sun is r, then areal velocity of the planet is

Two satellites A and B go around a planet in circular orbits of radii 4 R and R respectively. If the speed of the satellite A is 3 V, then the speed of the satellite B will be

Two satellite of equal mass are revolving around earth in elliptical orbits of different semi - major axis . If their angular momenta about earth centre are in the ratio 3 :4 then ratio of their area l velocity is

An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kelper's Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usnig dimensional analysis, that T = (k)/(R ) sqrt((r^3)/(g)), Where k is a dimensionless constant and g is acceleration due to gravity.

A satellite which is revolving around earth has minimum distance from earth equal to r_(1) and maximum distance equal to r_(2) then time period of the satellite will be ?