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86 lines
2.2 KiB
Markdown
86 lines
2.2 KiB
Markdown
---
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id: af4afb223120f7348cdfc9fd
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title: Map the Debris
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challengeType: 1
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forumTopicId: 16021
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dashedName: map-the-debris
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---
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# --description--
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According to Kepler's Third Law, the orbital period $T$ of two point masses orbiting each other in a circular or elliptic orbit is:
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$$
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T = 2 \pi \sqrt{\frac{a^{3}}{\mu}}
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$$
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- $a$ is the orbit's semi-major axis
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- $μ = GM$ is the standard gravitational parameter
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- $G$ is the gravitational constant,
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- $M$ is the mass of the more massive body.
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Return a new array that transforms the elements' average altitude into their orbital periods (in seconds).
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The array will contain objects in the format `{name: 'name', avgAlt: avgAlt}`.
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The values should be rounded to the nearest whole number. The body being orbited is Earth.
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The radius of the earth is 6367.4447 kilometers, and the GM value of earth is 398600.4418 km<sup>3</sup>s<sup>-2</sup>.
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# --hints--
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`orbitalPeriod([{name : "sputnik", avgAlt : 35873.5553}])` should return `[{name: "sputnik", orbitalPeriod: 86400}]`.
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```js
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assert.deepEqual(orbitalPeriod([{ name: 'sputnik', avgAlt: 35873.5553 }]), [
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{ name: 'sputnik', orbitalPeriod: 86400 }
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]);
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```
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`orbitalPeriod([{name: "iss", avgAlt: 413.6}, {name: "hubble", avgAlt: 556.7}, {name: "moon", avgAlt: 378632.553}])` should return `[{name : "iss", orbitalPeriod: 5557}, {name: "hubble", orbitalPeriod: 5734}, {name: "moon", orbitalPeriod: 2377399}]`.
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```js
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assert.deepEqual(
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orbitalPeriod([
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{ name: 'iss', avgAlt: 413.6 },
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{ name: 'hubble', avgAlt: 556.7 },
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{ name: 'moon', avgAlt: 378632.553 }
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]),
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[
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{ name: 'iss', orbitalPeriod: 5557 },
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{ name: 'hubble', orbitalPeriod: 5734 },
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{ name: 'moon', orbitalPeriod: 2377399 }
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]
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);
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```
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# --seed--
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## --seed-contents--
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```js
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function orbitalPeriod(arr) {
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const GM = 398600.4418;
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const earthRadius = 6367.4447;
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return arr;
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}
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orbitalPeriod([{name : "sputnik", avgAlt : 35873.5553}]);
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```
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# --solutions--
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```js
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function orbitalPeriod(arr) {
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const GM = 398600.4418;
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const earthRadius = 6367.4447;
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const TAU = 2 * Math.PI;
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return arr.map(function(obj) {
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return {
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name: obj.name,
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orbitalPeriod: Math.round(TAU * Math.sqrt(Math.pow(obj.avgAlt+earthRadius, 3)/GM))
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};
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});
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}
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```
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