Apiece of space debris is travelling in an elliptical orbit around a planet. at its closest point to the planet, the debris is travelling at 5000ms. when the debris is 1km from the planet, it travels at 5000kmhr. how close does the debris get to the planet in its orbit?

2778 km

Explanation:

According to Kepler's Second Law of Planetary motion (also known as the law of areas), the angular momentum is constant, that is, it is preserved.

Therefore we will use the principle of conservation of angular momentum to solve this problem:

Knowing (1) Where is expressed in

Being:

(2) and  (3)

Where:

is the mass of space debris

is the velocity of space debris at apogee (closest point to the Earth)

the apogee

is the velocity of space debris at a distance of 10000km

Substituting (2) and (3) in (1):

 (4)

Isolating and solving:

 (5)

 (6)

 (7)

Finally:

 

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.