The radius of a planet R1 and satellite revolves round it in a circle of radius R2. The time period of revolution is T.find the acceleration due to the gravitation of the planet at its surface.

mg´=mω²R₂=m4π²R₂/T²,

g´=4π²R₂/T²,
mg´= G•m•M/R₂²,
mg= G•m•M/R₁²,
mg´/mg = G•m•M•R₁²/R₂²•G•m•M,
g´/g =R₁²/R₂²,
g= g´R₂²/R₁²=4π²R₂³/T²•R₁².

To find the acceleration due to the gravitation of the planet at its surface, we can use Newton's law of universal gravitation and the centripetal acceleration formula.

Step 1: Define the given values:
- Radius of the planet: R1
- Radius of the satellite's orbit: R2
- Time period of revolution: T

Step 2: Use the centripetal acceleration formula:
The centripetal acceleration, denoted as ac, is given by the formula:
ac = (4π^2R2) / T^2

Step 3: Use Newton's law of universal gravitation:
The gravitational force between the planet and the satellite is given by the formula:
F = (G * M * m) / R^2

Where:
- G is the gravitational constant
- M is the mass of the planet
- m is the mass of the satellite
- R is the distance between the center of the planet and the satellite's orbit (R1 + R2)

Step 4: Replace F with the centripetal force:
Since the centripetal force is provided by the gravitational force, we can equate them:
(G * M * m) / R^2 = m * ac

Step 5: Simplify the equation:
Canceling out the mass of the satellite, we get:
(G * M) / R^2 = ac

Step 6: Substitute R with (R1 + R2) and solve for ac:
(G * M) / (R1 + R2)^2 = ac

Now you have the formula to calculate the acceleration due to gravity at the surface of the planet. Simply substitute the given values of R1, R2, and T into the equation, and solve for ac.