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 at a distance r from the planet will be given by `v^(2)=GM[2/r-1/a]`

Text Solution

Verified by Experts

As in case of elliptic orbit with semi major axis a, of a satellite total mechanical energy remains constant, at any position of satellite in the orbit, given as
`E = -(GMm)/(2a)`
or `KE+PE= -(GMm)/(2a)` …(i)
Now, if at position r, v is the orbital speed of satellite, we have
`KE = (1)/(2)mV^(2)` and `PE = -(GMm)/(r )` ....(ii)
so from equation (i) and (ii), we have
`(1)/(2)mV^(2) - (GMm)/(r )= -(GMm)/(2a), i.e., V^(2)=GM[(2)/(r )-(1)/(a)]`
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    BANSAL|Exercise Practice Exercise|18 Videos

  • GRAVITATION

    BANSAL|Exercise EXERCISE -1 [Single Correct Choice Type]|21 Videos

  • GRAVITATION

    BANSAL|Exercise EXERCISE -4 Section - B|6 Videos

  • CENTRE OF MASS & MOMENTUM CONSERVATION

    BANSAL|Exercise EXERCISE-4 (SECTION-B) (JEE-ADVANCED Previous Year Questions)|8 Videos

  • HEAT TRANSFER

    BANSAL|Exercise Exercise|89 Videos

Similar Questions

Explore conceptually related problems

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

If a satellite is revolving around a plenet 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)]

A planet of mass m is moving around the sun in an elliptical orbit of semi-major axis a :

A satellite revolves around the earth in an elliptical orbit. Its speed is

A planet moves around the sun in an elliptical orbit. When earth is closest from the sun, it is at a distance r having a speed v . When it is at a distance 4r from the sun its speed will be:

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

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