# What is the distance between the Sun and the Earth?

• Indranil
In summary, the new unit of length is called the light-second and the distance between the sun and the Earth is 500 light-seconds.
Indranil

## Homework Statement

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the Earth in terms of the new unit, if light takes 8 mins and 20 sec to cover this distance?

## Homework Equations

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the Earth in terms of the new unit, if light takes 8 mins and 20 sec to cover this distance?[/B]

## The Attempt at a Solution

Sol-
The speed of light in vacuum (c) = 1 (new unit of length s–1 ) Time taken by light to reach the Earth t = 8 min + 20 s = (8 × 60 + 20) s = 500 s ∴ Distance between the sun and the Earth = Speed of light × Time x = c × t = 1 (new unit of length s–1 ) × 500 s = 500 new unit of length
*here I don't understand why C = S^-1. Could you explain, please?

Let ## L_o ## be the distance that light travels in one second. Then ## c=1.000 \, L_o/sec ##. The basic units on ## c ## of 'distance per unit time" do not change, and can not be changed.

Indranil
Let ## L_o ## be the distance that light travels in one second. Then ## c=1.000 \, L_o/sec ##. The basic units on ## c ## of 'distance per unit time" do not change, and can not be changed.
This depends on the unit system. In relativity it is usual to use a unit system where ##c = 1## is dimensionless, which underlines the intricate relationship between space and time coming together as a single spacetime. In such a unit system, you can use time units to measure lengths and vice versa. Such systems are particularly popular among particle physicists. For example, the Higgs discovery paper by CMS (just as an example) does not say that the Higgs mass is 125 GeV/c^2, it just states that the Higgs mass is 125 GeV. In fact, I would say that this question is ill defined if this is not what is intended here, since it does not specify anything about which time unit is being used. The only way of having ##c = 1## is then to use the same unit for time and length, i.e., seconds. The correct argument would be that ##d = c \cdot 500\, {\rm s} = 500\, {\rm s}##.

Indranil said:
A new unit of length is chosen such that the speed of light in a vacuum is unity.
Orodruin said:
I would say that this question is ill defined
I would go further... it is wrong.
Making the speed of light unity in the new unit requires a unit of speed to be defined, not a unit of length. If the thinking is that the distance unit - call it a lunge - equals a light-second, say, then that would make the speed of light one lunge per second, not one lunge.
Making the speed of light unity in the dimensionless sense requires more than just the invention of a new unit.

haruspex said:
I would go further... it is wrong.
Making the speed of light unity requires a unit of speed to be defined, not a unit of length.
This is not true if length and time have the same dimensions. This makes velocities dimensionless and you do not need to define a unit of speed. This is how I would interpret a unit system where the speed of light is unity (i.e., identically one without dimensions).

I think this problem redefines the meter by using ##c=1## i.s.u.*, but explicitly keeps the second as the unit of time. Part of the problem statement is that "light takes 8 min and 20 sec to cover this distance".
@Indranil : Repeating the problem statement is not a "relevant equation".

*i.s.u. = in some units.

Orodruin said:
This is not true if length and time have the same dimensions.
This is how I would interpret a unit system where the speed of light is unity (
Sure, but that cannot be achieved merely by defining a new unit of distance.

'
Let ## L_o ## be the distance that light travels in one second. Then ## c=1.000 \, L_o/sec ##. The basic units on ## c ## of 'distance per unit time" do not change, and can not be changed.
Here what is the unit of 'L₀'? meter or centimeter
Could you explain what does it really mean 'A new unit of length is chosen such that the speed of light in a vacuum is unity'?
.

Indranil said:
Here what is the unit of 'L₀'? meter or centimeter
It is a length. You can measure lengths using any length unit. In fact, here it is the unit. Its value in m or cm is just a conversion factor between this new unit and m or cm. Of course it will be 100 times larger when you convert to cm. You need to separate the notions of units from the notion of physical dimension.

Delta2
Orodruin said:
It is a length. You can measure lengths using any length unit. In fact, here it is the unit. Its value in m or cm is just a conversion factor between this new unit and m or cm. Of course it will be 100 times larger when you convert to cm. You need to separate the notions of units from the notion of physical dimension.
Could you explain what does it really mean 'A new unit of length is chosen such that the speed of light in a vacuum is unity'?

Isn’t the new unit of length 1 light-year, so the speed of light is 1 light-year/year?

Delta2
Chestermiller said:
Isn’t the new unit of length 1 light-year, so the speed of light is 1 light-year/year?
This is part of why the question is ambiguous. It does not specify the time unit to be used. Also, if you use a system of units where time and length does not have the same dimension then c is not unity, it is will be dimensionful and therefore subject to change in its numerical value if you change the time unit without changing the length unit.

Indranil said:
A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the Earth in terms of the new unit, if light takes 8 mins and 20 sec to cover this distance?
1 A.U. (Astronomical Unit)

Tom.G said:
1 A.U. (Astronomical Unit)
This is incorrect. You made the measured value of the distance unity instead of that of the speed of light.

Chestermiller said:
Isn’t the new unit of length 1 light-year, so the speed of light is 1 light-year/year?
Then why not a light second, making the speed of light one light second/second?
Either way, it does not make the speed of light a dimensionless 1, as the question implies.

The standard answer is 1 AU. But I would like to highlight that common illustrations of Earth's orbit around sun are shown highly elliptical which is misleading, and that's what most people visualize. In reality it is almost a circle with eccentricity of 0.0167. Recently we were making simulations of solar system, and had to correct the developers on this aspect.

The standard answer is 1 AU
No it is not. If you put the length unit to be 1 AU your speed of light will be 1/500 AU/s.

haruspex said:
Then why not a light second, making the speed of light one light second/second?
Breaking that down to details:

• A) Define speed of light to be 1 lightsecond per second. (hard to argue with? after all, the Meter was originally defined as 1/107 the distance between the Earth Equator and the North Pole. just pick any arbitrary distance for a 'standard' to get units you like!)
• B) Time to travel Sun to Earth = 8Min 20Sec = 500Sec.
Ergo 1AU = 500lightseconds.

Tom.G said:
Breaking that down to details:

• A) Define speed of light to be 1 lightsecond per second. (hard to argue with? after all, the Meter was originally defined as 1/107 the distance between the Earth Equator and the North Pole. just pick any arbitrary distance for a 'standard' to get units you like!)
• B) Time to travel Sun to Earth = 8Min 20Sec = 500Sec.
Ergo 1AU = 500lightseconds.
No, you are missing my point. The question says:
Indranil said:
A new unit of length is chosen such that the speed of light in a vacuum is unity
This is not possible.
You can
• define a new unit of speed such that the speed of light is 1 (of that unit); or
• define a new unit of length such that the speed of light is 1 of that unit per second (or whatever unit of time you care to fill in); or
• define an equivalence between time and distance dimensions such the speed of light is 1, dimensionless.
But none of those is what the question prescribes.

Tom.G

## 1. What is the distance between the Sun and the Earth?

The average distance between the Sun and the Earth is approximately 93 million miles, or 149.6 million kilometers.

## 2. How do scientists measure the distance between the Sun and the Earth?

Scientists use a unit called an astronomical unit (AU) to measure the distance between the Sun and the Earth. One AU is equivalent to the average distance between the Earth and the Sun.

## 3. Does the distance between the Sun and the Earth vary?

Yes, the distance between the Sun and the Earth does vary slightly throughout the year. This is due to the elliptical orbit of the Earth around the Sun. At its closest point (perihelion), the Earth is about 91.4 million miles from the Sun, while at its farthest point (aphelion), it is about 94.5 million miles away.

## 4. How long does it take for light to travel from the Sun to the Earth?

It takes approximately 8 minutes and 20 seconds for light to travel from the Sun to the Earth, traveling at a speed of about 186,282 miles per second.

## 5. How does the distance between the Sun and the Earth affect life on Earth?

The distance between the Sun and the Earth plays a crucial role in sustaining life on our planet. The Earth's distance from the Sun allows for a stable and habitable climate, with temperatures that are neither too hot nor too cold for life to exist. The Sun's energy also provides the necessary light and heat for photosynthesis to occur, which is essential for the survival of plants and the production of oxygen.

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