What keeps the planets in orbit around the sun?

Let's start by explaining that all the bodies of the universe, because they have mass, are influenced by gravity, which is an attractive force that increases with the mass of the bodies and with the diminution of the distance between them.

So, it is this gravity force that makes the bodies to attract among them.

Now, if we have two objects, the one with the least mass will be attracted by the most massive object. The same happens with the Sun (the most massive body of the solar system) and the planets.

This force is strong enough to keep the planets orbiting our star without hitting it, and this is due to inertia. For the natural state of the planets is to move constantly in a straight line, but with the gravitational attraction of the Sun acting on them, this trajectory curves in the elliptical orbits that each planet has.

Therefore, since gravity is the only force that acts here and there is no other force to stop that orbital movement, the planets remain in their trajectory around the Sun.

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft