If energy of a satellite planet system is zero then satellite will

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17. When energy of a satellite planet system is positive then satellite will (1) Move around planet in circular orbit (2) Move around planet in eliptical orbit (3) Escape out with minimum spee (4) Escape out with speed greater than escape velocity

Solution

Option 1 : the object escapes to infinity when the energy is zero

The correct answer is option 1) i.e. the object escapes to infinity when the energy is zero

CONCEPT:

• The time period of the satellite: It is the time taken by the satellite to complete one revolution around the Earth.
  • Consider a satellite orbiting the earth at a height h from the surface of the earth of radius R.
  • The circumference of orbit of satellite = 2π(R+h)
• The orbital velocity of the satellite at a height h is given by:

Where M is the mass of the Earth.

• The kinetic energy of the satellite of mass m in a circular orbit is

​

• The potential energy at distance (R +h) from the centre of the earth is

​

• The total energy of a circularly orbiting satellite ​is

EXPLANATION:

• The total energy of an orbiting satellite is inversely proportional to the radius of the orbit.
• Satellites are always at a finite distance from the earth and hence their energies cannot be positive or zero.
• The energy of the satellite can be zero when the orbital radius is infinity i.e. the object escapes to infinity.

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