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Kala revolusi planet Merkurius adalah 7,6 × 106 sekon. Jika massa matahari adalah 2,01 × 1030 kg, hitunglah jarak Merkurius ke matahari!

Pertanyaan

Kala revolusi planet Merkurius adalah begin mathsize 14px style 7 comma 6 space cross times space 10 to the power of 6 end style sekon. Jika massa matahari adalah begin mathsize 14px style 2 comma 01 space cross times space 10 to the power of 30 end style kg, hitunglah jarak Merkurius ke matahari!space

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 jarak Merkurius ke matahari adalah begin mathsize 14px style bold 5 bold comma bold 8 bold space bold cross times bold space bold 10 to the power of bold 10 bold space bold m end style.space

Pembahasan

Diketahui : 

T7 comma 6 space cross times space 10 to the power of 6 sekon

m =  begin mathsize 14px style 2 comma 01 space cross times space 10 to the power of 30 end style kg,

Ditanyakan : r ... ?

Penyelesaian : 

periode orbit adalah waktu yang dibutuhkan suatu benda langit untuk melakukan perjalanan pada orbitnya.

Gaya Sentripetal

F subscript s space equals space m times omega squared r space equals m times space open parentheses fraction numerator 2 straight pi over denominator T end fraction close parentheses squared space r 

Dengan menggunakan persamaan Hukum II Newton dan Hukum Gravitasi Newton, maka didapatkan perhitungan berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell F subscript G space end cell equals cell space F subscript S end cell row cell G space fraction numerator M m over denominator r squared end fraction space end cell equals cell space m space left parenthesis fraction numerator 2 straight pi over denominator T end fraction right parenthesis squared space r end cell row cell G space M over r cubed space end cell equals cell space open parentheses fraction numerator 2 straight pi over denominator T end fraction close parentheses squared end cell row cell 6 comma 67 space cross times space 10 to the power of negative 11 end exponent space fraction numerator 2 comma 01 space cross times space 10 to the power of 30 over denominator r cubed end fraction space end cell equals cell space open parentheses 2 straight pi close parentheses squared over open parentheses 7 comma 6 space cross times space 10 to the power of 6 close parentheses squared end cell row cell fraction numerator 1 comma 34 space cross times space 10 to the power of 20 over denominator r cubed end fraction space end cell equals cell space fraction numerator 4 straight pi squared over denominator 5 comma 776 space cross times space 10 to the power of 13 end fraction end cell row cell r cubed space end cell equals cell space fraction numerator 1 comma 34 space cross times space 10 to the power of 20 space cross times space 5 comma 776 space cross times space 10 to the power of 13 over denominator 4 straight pi squared end fraction end cell row cell r cubed space end cell equals cell space 1 comma 96 space cross times space 10 to the power of 32 end cell row cell r space end cell equals cell space cube root of 1 comma 96 space cross times space 10 to the power of 32 end root end cell row cell bold italic r bold space end cell bold equals cell bold space bold 5 bold comma bold 8 bold space bold cross times bold space bold 10 to the power of bold 10 bold space bold m end cell end table 

Jadi, jarak Merkurius ke matahari adalah begin mathsize 14px style bold 5 bold comma bold 8 bold space bold cross times bold space bold 10 to the power of bold 10 bold space bold m end style.space

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