HARD
Diploma
IMPORTANT
Earn 100

Deduce that a satellite orbiting a planet of mass M in a circular orbit of the radius R has a period of revolution given by

T=4π2r3GM.

Important Questions on Fields (HL)

HARD
Diploma
IMPORTANT
A grazing orbit is one in which the orbit radius is approximately equal to the radius R of the planet. Deduce that the period of revolution in a grazing orbit is given by T=3πGρ  where ρ is the density of the planet.
MEDIUM
Diploma
IMPORTANT
The period of grazing orbit around the Earth is 85 min. and around the planet Jupiter it is 169 min Deduce the ration ρearthρjupiter
HARD
Diploma
IMPORTANT
The acceleration of free fall at the surface of a planet is g and the radius of the planet is R Deduce that the period of satellite in a very low orbit is given by T=π2Rg
HARD
Diploma
IMPORTANT
Given that g=4.5 ms-2 and R=3.4 ×106 m deduce that the orbital period of the low orbit is about 91 min.
HARD
Diploma
IMPORTANT
A spacecraft in orbit around this planet g= 4.5 ms-2, R=3.4×106m has a period of 140 min. Deduce the height of the spacecraft from the surface of the planet.
MEDIUM
Diploma
IMPORTANT

Two stars of equal masses M orbit a common mass as shown in the diagram. The radius of orbit of each star is R. Assume that each star has a mass equal to 1.5 solar mass  ( solar mass=2.0×1030kg ) and the initial separation of the star is 2×109 m.

State the magnitude of the force on each star in terms of M,R and G.

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HARD
Diploma
IMPORTANT

Two stars of equal mass M orbit a common mass as shown in the diagram. The radius of orbit of each star is R.

Deduce that the period of revolution of each star is given by T2=16π2r3GM

Question Image

HARD
Diploma
IMPORTANT

Two stars of equal mass M orbit a common mass as shown in the diagram. The radius of orbit of each star is R. Assume that each star has a mass equal to 1.5 solar mass  (solar mass=2.0×1030kg ) and the initial separation of the star is 2×109 m.

Deduce that the period of revolution of each star is given by T2=16π2r3GM

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Evaluate the period numerically