Time dilation on Earth's surface due to revolution

TIME DILATION ON EARTH’S SURFACE DUE TO REVOLUTION

INTRODUCTION

Earth is the 3^rd planet in our Solar System. It’s 150 million km [93 million miles] from the Sun. It completes one revolution around the Sun in approximately 365 Earth days. Consider our planet Earth which revolves at a certain velocity and another analogous Earth which doesn’t revolve. According to the Special Theory of Relativity, a clock on our Earth would run slower than that on a non-revolving Earth. We’ll find the time gained by our earth relative to the stationary one.

ASSUMPTIONS

• The revolution path is exactly circular.

• Earth 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 ≈ 365 days = 31536000 s]

ω = 2*3.14/31536000

ω = 1.9923*10^-7 rad/s

The tangential velocity is given by,

v = R*ω [m/s]

R – Average distance between Sun and Earth [R = 150 million km]

v = 150*10⁶*1000*1.9923*10^-7

v = 29884.5 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*√ [1-9.9231*10^-9]

t' = t*√ [0.9999999900769]

t' = t* 0.99999999503845

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on revolving earth 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 our Earth will gain time over the stationary one. In fact in one year it gains 0.15 seconds just due to revolution and 37microseconds due to rotation. The time gained by revolution is more than rotation because Earth revolves at 29.8 km/s as compared to rotation which is 0.463 km/s.

Time	t’ [Stationary Earth] (s)	t [Revolving Earth] (s)	Difference (s)
1 minute	60	59.999999702307	0.000000297693
1 hour	3600	3599.99998213842	0.00001786158
1 day	86400	86399.9995713221	0.0004286779
1 month	2592000	2591999.98713966	0.01286034
1 year	31536000	31535999.8435326	0.1564674

Manual Supper feeding machine

MANUAL SUPPER FEEDING MACHINE

The main purpose of this machine is to ease the user in feeding supper to kids or handicapped individuals. In general, feeding food to people especially little kids is time consuming. Also user needs to use both hands, one to hold the bowl containing supper and other to hold the spoon. So the user cannot afford to do any other job while feeding kids.

The Manual Feeding machine can help the user save some time to perform other side jobs. It is manual and not automatic because automatic moving parts within children’s reach can be fatal. Also automatic feeder cannot adjust to child’s need or pace.

The machine is easy to use. It consists of two discs [big and small] which resemble a pulley. A suitable US tablespoon (0.5 US fl oz) is connected at tangent to the big disc. The discs are connected to each other by belt drive system. The small disc is the driver [manual] while the big disc is the driven one. A knob is connected to the small disc thus permitting the user to rotate the disc and feed children. The user only needs one hand to operate the machine while the other hand is free to access phone, book, remote, etc.

Thus the user can operate machine at child’s pace also utilizing the time to do small jobs. Since it works manually, it doesn't require any form of electrical energy for its operation.

Time dilation on Earth due to Rotation

TIME DILATION ON EARTH’S SURFACE DUE TO ROTATION

INTRODUCTION

Earth is the 3^rd planet in our Solar System. It completes one rotation about its axis in 23 hours 56 minutes and 4 second. Consider our planet Earth which rotates at a certain velocity and another analogous earth which doesn’t rotate. According to the Special Theory of Relativity, a clock on our Earth would run slower than that on a non-rotating Earth. We’ll find the time gained by our earth relative to the stationary one.

ASSUMPTIONS

• Earth is not revolving around the Sun.

• Earth 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 – Rotational time period [T ≈ 24 hours = 86400s]

ω = 2*3.14/86400

ω = 7.2722*10^-5 rad/s

The angular velocity is same at all points on earth since it doesn’t exhibit differential rotation. But the tangential velocity on surface varies with the distance from the center.

The tangential velocity is given by,

v = R*ω [m/s]

R – Average radius of earth [R = 6371000m]

v = 6371*1000*7.2722*10^-5

v = 463.311m/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*√ [1-2.39*10^-12]

t' = t*√ [0.999999999997615]

t' = t* 0.999999999998808

CONCLUSION

We can observe that proper and actual time isn’t the same which proves that time dilates on rotating earth relative to the non-rotating 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 our Earth will gain time over the non-rotating one. In fact it’ll gain 37 microseconds in one year.

Time	t’ [Non-rotating Earth] (s)	t [Rotating Earth] (s)	Difference (s)
1 minute	60	59.9999999999285	0.0000000000715
1 hour	3600	3599.99999999571	0.00000000429
1 day	86400	86399.999999897	0.000000103
1 month	2592000	2591999.99999691	0.00000309
1 year	31536000	31535999.9999624	0.0000376