In an accidental explosion, a satellite breaks in half while in circular orbit about earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? What happens to the other half?

The half that "stops" falls straight down to Earth, burning up and disintegrating in the process. The other half acquires double the velocity along the direction of motiuon, changing the orbit to an elliptical one with a higher apogee but the same perigee.

1. Because it had lost its horizontal velocity it will crash into the Earth.

2. It requires the momentum lost by the other half so possesses a greater velocity, which will cause it to move into a higher orbit.

When a satellite breaks in half while in a circular orbit around the Earth, several factors determine the fate of each half:

1. The half brought to rest: The half brought to rest would experience a drastic change in its velocity. It would no longer be in a state of circular motion and would start to move radially inward towards the Earth, following a trajectory similar to an object in freefall. Eventually, it would enter the Earth's atmosphere and burn up due to atmospheric friction unless it impacts the Earth's surface earlier.

2. The other half: The other half, which is not brought to rest, would retain its initial orbital velocity and continue orbiting the Earth. However, its orbit would not remain circular anymore but rather elliptical since it is only a part of the original satellite. The new orbit would depend on the specific circumstances of the breakup, such as the location and velocity of the separation. Over time, the orbital trajectory of the remaining half could intersect with the decayed half or other space debris, increasing the chances of collisions in the future.

In order to determine the fate of the half brought to rest and the other half of the satellite, we need to consider the laws of physics that govern the motion of objects in space.

When an object is in a circular orbit around the Earth, it is moving at a constant speed, known as orbital velocity. This velocity is necessary to balance the gravitational pull of the Earth and keep the object in orbit.

When the satellite breaks in half, the half brought to rest will lose its orbital velocity. Without this velocity, it will no longer be able to counteract the gravitational pull of the Earth. As a result, the half brought to rest will start to fall towards the Earth, following a trajectory determined by the laws of gravity. Eventually, it will enter the Earth's atmosphere and most likely burn up or crash onto the surface, depending on its composition and altitude.

On the other hand, the other half of the satellite will continue to possess its orbital velocity unless acted upon by an external force. It will continue to orbit the Earth in a trajectory determined by its initial velocity and the gravitational pull of the Earth. Since it is only one half of the original satellite, it may experience changes in its orbit due to the change in mass distribution and aerodynamic effects caused by the break.

Ultimately, the fate of each half of the satellite will depend on various factors such as their individual trajectories, aerodynamic properties, composition, and altitude at the time of the explosion. Additionally, the presence of any possible external forces such as atmospheric drag or orbital debris could also have an impact on their paths.