Time dilation on Jupiter due to revolution

TIME DILATION ON JUPITER’S SURFACE DUE TO REVOLUTION

INTRODUCTION

Jupiter is the 5^th planet in our Solar System. It’s 778 million km [486 million miles] from the Sun. It completes one revolution around the Sun in approximately 11.86 Earth years. Consider the planet Jupiter which revolves at a certain velocity and another analogous Jupiter which doesn’t revolve. According to the Special Theory of Relativity, a clock on revolving Jupiter would run slower than that on a non-revolving Jupiter. We’ll find the time gained by revolving Jupiter relative to the stationary one.

ASSUMPTIONS

• The revolution path is exactly circular.

• Jupiter is a perfect homogeneous sphere.

• The effect of Gravitational time dilation is negligible.

CALCULATION

The Angular velocity is given by,

ω = 2π/T [rad/s]

T – Revolution time period [T ≈ 11.86 years = 374,016,960 s]

ω = 2*3.14/374016960

ω = 1.6799*10^-8 rad/s

The tangential velocity is given by,

v = R*ω [m/s]

R – Average distance between Sun and Jupiter [R = 778 million km]

v = 778*10⁶*1000*1.6799*10^-8

v = 13069.622 m/s

According to the Special Theory of Relativity, the time dilation equation is,

t' = t/γ [s]

t’ – Actual time or Moving observer’s time. [s]

t - Proper time or Stationary observer’s time. [s]

γ – Relativistic gamma factor, γ = 1/√ [1-(v/c) ²]

c - Velocity of light [c = 3*10⁸ m/s]

t' = t*√ [1-(v/c) ²]

t' = t*√ [1-1.8979*10^-9]

t' = t*√ [0.9999999981021]

t' = t* 0.99999999905105

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on revolving Jupiter relative to the stationary one. We’ll consider 5 different t’ values and calculate t value. The larger the t’ the more is the difference between t and t’. Thus revolving Jupiter will gain time over the stationary one. In fact in one year it gains 354 milliseconds just due to revolution and 26 milliseconds due to rotation. The time gained by revolution is more than rotation because Jupiter revolves at 13 km/s as compared to rotation which is 12.2 km/s.

Time	t’ [Stationary Jupiter] (s)	t [Revolving Jupiter] (s)	Difference (s)
1 minute	60	59.999999943063	0.000000056937
1 hour	3600	3599.99999658378	0.00000341622
1 day	86400	86399.9999180107	0.0000819893
1 month	2592000	2591999.99754032	0.00245968
1 year	31536000	31535999.9700739	0.0299261
11.86 years	374016960	374016959.645077	0.354923