If the Earth has no tilt, what happens to the seasons of the Earth?

An unknown planet orbits the Sun with distance twice the semi-major axis distance of the Earth’s orbit. If the Earth’s time period is T₁, what is the time period of this unknown planet?

Assume that you are in another solar system and provided with the set of data given below consisting of the planets’ semi-major axes and time periods. Can you infer the relation connecting semi-major axis and time period?

Planet   (imaginary)	Time period(T)   (in year)	Semi major axis (a)   (in AU)
Kurinji	2	8
Mullai	3	18
Marutham	4	32
Neithal	5	50
Paalai	6	72

The Moon I₀ orbits Jupiter once in 1.769 days. The orbital radius of the Moon I₀ is 421700 km. Calculate the mass of Jupiter?

If the angular momentum of a planet is given by \(\vec{L}=5t^2\hat i-6t\hat j+3\hat k\) . What is the torque experienced by the planet? Will the torque be in the same direction as that of the angular momentum?

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. Calculate the speed of each particle.

Suppose unknowingly you wrote the universal gravitational constant value as G = 6.67\(\times\)10¹¹ instead of the correct value G = 6.67\(\times\)10¹¹, what is the acceleration due to gravity g' for this incorrect G? According to this new acceleration due to gravity, what will be your weight W'?

Calculate the gravitational field at point O due to three masses m₁, m₂ and m₃ whose positions are given by the following figure. If the masses m₁ and m₂ are equal what is the change in gravitational field at the point O?

Suppose we go 200 km above and below the surface of the Earth, what are the g values at these two points? In which case, is the value of g small?

Calculate the change in g value in your district of Tamilnadu. (Hint: Get the latitude of your district of Tamilnadu from the Google). What is the difference in g values at Chennai and Kanyakumari?

Why is the energy of a satellite (or any other planet) negative?

What are geostationary and polar satellites?

Define weight.

Why is there no lunar eclipse and solar eclipse every month?

How will you prove that Earth itself is spinning?