Pengertian, Fungsi, dan Bunyi Hukum Kepler I, II, III

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Pengertian, Fungsi, dan Bunyi Hukum Kepler I, II, III Pernahkah Beberapa Sahabat mengira atau berasumsi kalau matahari bergerak melingkari bumi, sedangkan bumi diam? Sebab Sahabat lihat seolah-olah matahari beralih dari timur ke barat. Bila pernah, sangkaan Sahabat itu sesungguhnya salah. Yang sesungguhnya terjadi yaitu matahari senantiasa diam di tempat dan bumi yang mengelilinginya. Kenapa demikian? Momen ini bisa diterangkan serta dibuktikan dengan jelas oleh hukum Kepler. Ya, Hukum Kepler. Itulah yang bakal kita ulas pada kesempatan ini. Kita bakal membahasnya mulai dari pengertiaan Hukum Kepler, Hukum Kepler I, II, III dan rumus-rumus dari hukum-hukum Kepler itu.

Pengertian Hukum Kepler

Hukum Kepler ditemukan oleh seorang matematikawan yang juga merupakan seorang astronom Jerman yang bernama Johannes Kepler (1571-1630). Penemuannya dilandasi oleh data yang dicermati oleh Tycho Brahe (1546-1601), seorang astronom tenar dari Denmark.

Malignant peritoneal mesothelioma is a rare type of mesothelioma which attacks the lining of abdomen also known as peritoneum. Malignant peritoneal mesothelioma (MPM) is a universally fatal disease affecting 20% to 30% of the mesothelioma cases. It's was first described by Miller and Wynn in the year 1908. According to the statistics, in the past two decades, the incidence of malignant peritoneal mesothelioma cancer has increased. Peritoneal mesothelioma affects the lining of the abdomen also known as peritoneum. The location of malignant cell is human's abdominal lining and because of that, MPM can sometimes known as abdominal mesothelioma. However, most common term used to describe this type of cancer is peritoneal mesothelioma. The main cause of MPM in humans is asbestos. Asbestos typically is the one of most commonly roofing materials since it is not only cheaper but is easy to fix on a roof. Asbestos exposure contributed to almost 70 to 80 percent of mesothelioma lung cancer. Humans come into contact with asbestos when they swallow or inhale the fibers. Asbestos inhalation may increase risk to develop asbestos related diseases, most importantly mesothelioma. Asbestos was completely banned in UK since it was recognized to be a serious health hazard, and it is now responsible for about 4000 deaths each year and many cases of serious disease. The people at increase risk of developing health asbestos related disease are those whose work brings them into direct contact with asbestos such as builders, heating engineers, roofers and demolition workers. In addition to mesothelioma, asbestos exposure will increase the risk of other health problems such as lung cancer, asbestosis (chronic lung ailment) and other type of cancer such as larynx and kidney cancer. Symptoms of Malignant Peritoneal Mesothelioma It can takes such a long time for cancer to develop the symptoms and sometimes may take up to 30 years, between exposure to asbestos and the start of the disease. Most common symptoms of the disease are abdominal pain, abdominal swelling, abnormal weight loss, anemia, easy fatigue, nausea and vomiting. Abdominal pain and swelling result from fluid accumulation in the abdominal cavity. Other than that, people can easily get fever when the disease starts to shows its symptoms. Among the symptoms stated above, abdominal pain is the most common reported initial symptoms of MPM. Unexplained night sweats and blood coagulation problems are less frequent symptoms occurring when the cancer develops. If the cancer cells spread to the other part of the body, the symptoms may lead to trouble swallowing or swelling of the neck and face. Diagnosis of Abdominal Mesothelioma It is very difficult to diagnose peritoneal mesothelioma since there is no defined system so far that can differentiate the stages of the development of cancerous tumor cells. If required, TNM staging system normally used to detect the cancer in stages. Other than that, Serum mesothelin-related protein (SMRP) may be a potentially useful serum marker used to diagnose and to follow-up the cancer progression. Computer tomography (CT) findings may be a useful tool in detection and characterization of peritoneal mass. Malignant Peritoneal Mesothelioma is a deadly neoplasm. MPM's diagnosis is difficult to perform since the symptoms will take a long time to show up. Early detection is the key in peritoneal mesothelioma treatment since the cancer cell normally spread very fast. Peritoneal Mesothelioma can be regarded as a very dangerous cancer among other cancer.However we can prevent this problems from occur to you and your family. As i said before, early detection is the key of peritoneal mesothelioma treatment [] success since the cancer cell spread very fast. Get your free update's information about mesothelioma especially mesothelioma treatment by click > mesothelioma [] Article Source: Article Source:

Saat sebelum ditemukannya hukum ini, manusia jaman dahulu berpedoman paham geosentris, yakni suatu paham yang membetulkan kalau bumi adalah pusat alam semesta. Asumsi ini dilandasi pada pengalaman indrawi manusia yang terbatas, yang setiap hari mencermati matahari, bulan serta bintang bergerak, sedangkan bumi dirasakan diam. Asumsi ini dikembangkan oleh astronom Yunani Claudius Ptolemeus (100-170 M) serta bertahan sampai 1400 tahun. Menurut dia, bumi ada di pusat tata surya. Matahari serta planet-planet mengelilingi bumi dalam lintasan melingkar.

Lantas pada tahun 1543, seorang astronom Polandia bernama Nicolaus Copernicus (1473-1543) mencetuskan model heliosentris. Heliosentris artinya bumi bersama planet-planet yang lain melingkari matahari dalam lintasan yang melingkar. Jelas saja pendapat ini lebih baik di banding pendapat sebelumnya. Tetapi, ada yang masih kurang dari pendapat Copernicus yakni diam masih menggunakan lingkaran sebagai bentuk lintasan gerak planet.

Pada th. 1596 Kepler menerbitkan buku pertamanya di bagian astronomi dengan judul The Mysteri of the Universe. Didalam buku itu ia menuturkan kekurangan dari kedua model di atas yakni tidak ada keharmonisan antara lintasan- lintasan orbit planet dengan data pengamatan Tycho Brahe. Oleh karena itu Kepler meninggalkan model Copernicus juga Ptolemeus lantas mencari jenis baru. Pada th. 1609, barulah ditemukan bentuk orbit yang pas dengan data pengamatan Brahe, yakni bentuk elips. Lantas penemuannya itu dipublikasikan dalam bukunya yang berjudul Astronomia Nova yang juga disertai hukum keduanya. Sedangkan hukum ketiga Kepler tercatat dalam Harmonices Mundi yang dipublikasikan sepuluh th. kemudian.

Hukum I, II, dan III Kepler

Hukum I Kepler

Hukum I Kepler menerangkan mengenai bagaimana bentuk lintasan orbit planet-planet. Bunyi dari hukum ini yakni:

  • Lintasan tiap planet saat mengelilingi matahari, berupa elips, dimana matahari terdapat pada salah satu fokusnya.

Dari model di atas diperlihatkan bentuk elips dari lintasan orbit planet yang mengelilingi matahari. Di mana matahari ada disalah satu titik fokusnya yang ditandai dengan F1 serta F2. Sedangkan planet bearada pada jarak r2 dari F2 atau r1 dari F1. Bila posisi planet berubah jarak r1 dan r2 ikut berubah. Jarak a disebut dengan sumbu semimayor serta 2a disebut dengan mayor. Jarak b disebut dengan sumbu semiminor serta 2b disebut dengan minor. Jarak c dari titik pusat adalah titik fokus, di mana c2 = a2+b2.

Bentuk elips orbit ditetapkan oleh eksentrisitas (e) elips itu. Makin kecil eksentrisitasnya, bentuk elipsnya bakal makin mendekati bentuk lingkaran. Dan demikian sebaliknya, apabila eksentrisitasnya makin besar, bentuk elips bakal memanjang serta tipis. Jarak adalah perbandingan dari jarak c dengan jarak a (e = c/a). Nilai eksentrisitas elips lebih besar dari 0 serta lebih kecil dari 1.

Saat planet ada pada jarak paling jauh dari matahari, pada saat itu planet ada pada titik aphelion. Letaknya pada gambar yakni pada ujung kiri elips (bagian kiri F1). Jarak dari aphelion ke matahai bisa dihitung dengan menjumlahkan jarak a dengan c. Bila planet ada pada ujung kanan elips (bagian kanan F2) planet sedang ada pada titik perihelion. Pada saat itu planet ada pada jarak paling dekat dengan matahari. Jarak perihelion dengan matahri adalah selisih antara jarak a dengan c.

Hukum II Kepler

Hukum kedua Kepler menerangkan mengenai kecepatan orbit sebuah planet. Bunyi dari hukum keduanya yakni:

Tiap planet bergerak sedemikian hingga sebuah garis khayal yang ditarik dari matahari ke planet itu meliputi daerah dengan luas yang sama dalam waktu yang sama.

Pada gambar di atas dperlihatkan dua contoh luasan untuk menerangkan hukum II Kepler. Kedua luasan ini memiliki luas yang sama. Pada selang waktu yang sama, garis khayal yang menghubungkan planet serta matahari menyapu luasan yang mempunyai besar yang sama. Oleh karenanya, saat planet bergerak dari b ke c (titik aphelion), kecepatan orbit planet lebih kecil atau lambat. Sedangkan saat planet bergerak dari d ke e (titik perihelion) kecepatan orbit planet lebih besar atau cepat. kesimpulannya keceptan orbit maksimum planet yakni saat planet ada di titik perihelion serta kecepatan minimalnya saat ada di titik aphelion.

Hukum III Kepler

Pada hukum ini Kepler menerangkan mengenai periode revolusi tiap planet yang melilingi matahari. Hukum Kepler III berbunyi:

Kuadrat perioda sebuah planet sepadan dengan pangkat tiga jarak rata-ratanya dari Matahari.

Secara matematis Hukum Kepler bisa ditulis sebagai berikut ini:


T1= Periode planet pertama

T2= Periode planet kedua

r1 = jarak planet pertama dengan matahari

r2 = jarak planet kedua dengan matahari

Persamaan ini bisa di turunkan dengan menggabungkan 2 persamaan hukum Newton, yakni hukum gravitasi Newton serta hukum II Newton untuk gerak melingkar teratur. Penurunan rumusnya yakni sebagai berikut ini:

Persamaan hukum Newton II:




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