# Effect of Dark Matter and Dark Energy on Gravitation

by Ron Kurtus

Although there are several laws and theories that seem to explain gravitation, astronomical studies have indicated that some other factors may be influencing or may be a part of gravitation. These factors have been called dark matter and dark energy.

Dark matter is invisible material that seems to add to the gravitation caused by the visible matter in or around galaxies. The effect was first observed by astronomer Fritz Zwiky in 1933, when making luminosity and Doppler shift measurements to determine galaxy mass. The measurements implied there was more mass available than could be seen, thus causing increased gravitation.

On the other hand, dark energy seems to be a force that acts opposite of gravitation, pushing stars and galaxies apart instead of toward each other. It seems to be a form of anti-gravitation.

Neither dark matter nor dark energy has been directly observed, so each is really a way to explain anomalies in gravitation for objects at the galaxy scale of measurement.

Questions you may have include:

• What is dark matter?
• What is dark energy?
• What are problems and alternatives to these theories?

This lesson will answer those questions. Useful tool: Units Conversion

## Dark matter

The existence of invisible dark matter can explain why observations on gravitational forces in distant galaxies indicate that there must be more matter than expected.

### Background

Upon studying the motion of distant galaxies, astronomer Fritz Zwiky performed measurements to determine their mass by measuring the amount of light they emitted. He then used the Doppler Effect to find the velocity of the suns moving around various galaxies as another way to determine galaxy mass.

What Zwiky discovered was that the velocity of outer suns were traveling much faster than they should for the previously calculated mass of the galaxy, according to Newton's Law of Gravitation and Einstein's General Relativity Theory.

His conclusion was that there must be some sort of "dark matter" that did not emit light but added to the mass of the galaxies. Since then, numerous astronomers have performed similar experiments and have stated various theories on what is happening.

### Using luminosity to measure mass

Luminosity is the amount of electromagnetic energy an astronomical body radiates per unit of time. It is independent of distance and related to the mass of the emitting body. Since the luminosity and mass of the Sun have been calculated, the mass-luminosity relation is handy for astronomers to use to determine the mass of a distant star or galaxy:

L/Ls = (M/Ms)4

or

M = Ms[4√(L/Ls)]

where

• 4 is the 4th root (square root of the square root)
• M is the mass of the star or galaxy in kg
• Ms is the mass of the Sun = 1.988*1030 kg
• L is the luminosity of the star or galaxy in watts (W)
• Ls is the luminosity of the Sun = 3.84*1026 W

Substitute values for the Sun to get the formula:

M = (1.988*1030/4.4*106)*[4√(L)] kg

M = (4.5*1023)*[4√(L)] kg

By measuring the luminosity of distant galaxies, Zwiky and other astronomers calculated their mass.

### Using Doppler Effect to measure mass

The wavelength of a luminous object that is moving with respect to the observer changes according to the direction and velocity of the object. This phenomenon is known as the Doppler Effect.

When the object is moving away from the observer, the effect is known as a red-shift, since the wavelengths increase toward red. When moving toward the observer, it is called a blue-shift.

By using a spectrometer, the change in wavelength from the expected or normal spectrum can be measured and the velocity of the object calculated. Then the equation for the velocity of an orbiting object can be used to determine the center mass.

#### Velocity equation for planets in orbit

The velocity of planets orbiting the Sun can be approximated—assuming circular orbits—from the equation:

vT = √(GMs/R)

where

• vT is the linear tangential velocity of the planet in orbit in km/s
• G is the Universal Gravitational Constant = 6.674*10−20 km3/kg-s2
• Ms is the mass of the Sun = 1.988*1030 kg
• R is the separation between the centers of the planet and Sun in km

This relationship shows that the further a planet is from the Sun the slower its velocity.

#### Applying to galaxies

The equation can also apply to galaxies, assuming that the mass of the galaxy is concentrated at its center of mass (CM).

Using the Doppler Effect to find the velocities of the various suns in the galaxy, the mass of the galaxy can be calculated by rearranging the above equation into:

Mg = v2rg/G

where

• v is the velocity of a sun in the galaxy
• Mg is the mass of the galaxy at its center
• rg is the separation between the CM and the center of the sun

### Comparison of results

The suns at the outer edges of the galaxy should be moving slower than those closer toward the center. However, measurements of the velocities of the outer suns resulted in much higher values than expected for the mass determined from the luminosity measurements.

In order for the suns to remain in orbit for the measured velocities, the mass of the galaxy would have to be much higher. In fact, Zwiky's measurements came up with a mass 400 times of what was expected.

Other scientists confirmed the measurements. They estimate that 90 to 99 percent of the total mass of the universe is dark matter or matter that they cannot see.

## Dark Energy

While dark matter seems to be adding to the gravitation in the Universe, dark energy seems to be a force pushing stars and galaxies apart.

The Universe appears to be expanding away from a center point, presumably the source of the Big Bang. Scientists and astronomers have calculated that the expansion would slow down with time, due to the mutual gravitational attraction between the galaxies. However, this does not seem to be the case, as the Universe is actually expanding at a faster rate than before. Dark energy seems to push objects apart

A possible explanation for the increased rate of expansion is a form of anti-gravitational force called dark energy. Unfortunately, dark energy has never been observed or measured. Instead, it is one of many efforts to explain the increased rate of expansion of the Universe.

## Problems and alternatives

The idea of invisible matter and energy is troubling to scientists and astronomers. Some have established alternatives or flaws in the assumptions.

### Alternatives to dark matter

One alternative to the existence of dark matter is that the added gravitational forces are actually caused by numerous Black Holes in the galaxies. Since light cannot escape Black Holes, they would be unseen. They also exhibit a large gravitational force.

A problem with the argument is that the Black Holes would also affect the orbits of any galaxies or suns that passed by, and that has not been observed.

(See Black Holes and Gravitational Escape Velocity for a Black Hole for more information.)

Another alternative to dark matter is the Modified Newtonian Dynamics Theory, which proposes that at higher speeds or accelerations seen in stars at the outer edges of galaxies, gravitational attraction would fall off as a simple inverse of the separation instead of the inverse square of the separation in the Universal Gravitation Equation. This would allow stars on the outer edge of a galaxy to be held by a stronger gravitational pull.

One more concept is the existence of large quantities of particles, such as the neutrino, that do not readily interact with other forms of matter and are difficult to detect.

### Problem with dark energy

Likewise, the existence of dark energy begs the question of why it only affects galaxies and not smaller objects of matter. Instead of being anti-gravitation, it could be a characteristic of space or perhaps some other unknown force that is applicable for only extremely large masses.

Some feel that dark energy implies that the General Relativity Theory does not apply in certain situations.

## Summary

Dark matter and dark energy affect gravitation in opposite ways. Dark matter is invisible material that seems to add to the gravitation in galaxies. Dark energy seems to accelerate the expansion of the Universe with an anti-gravitation force. Both dark matter and dark energy are theories to explain anomalies in gravitation for objects at the galaxy scale of measurement.

Don't be kept in the dark about things

## Resources and references

Ron Kurtus' Credentials

### Websites

Dark Matter - Wikipedia

Cosmic Hide and Seek: the Search for the Missing Mass - Chris Miller

Dark Matter - Dr. Martin White - Astronomy Dept. Univ. of California-Berkeley

Dark Matter Essay - Joe Silk - Astronomy Dept. Univ. of California-Berkeley

Dark Energy - Wikipedia

Dark Energy - NASA

Gravitation Resources

### Books

(Notice: The School for Champions may earn commissions from book purchases)

The 4-Percent Universe: Dark Matter, Dark Energy, and the Race to Discover the Rest of Reality by Richard Panek; Houghton Mifflin Harcourt (2011)

Dark Side of the Universe: Dark Matter, Dark Energy, and the Fate of the Cosmos by Iain Nicolson; The Johns Hopkins University Press (2007)

Einstein's Telescope: The Hunt for Dark Matter and Dark Energy in the Universe by Evalyn Gates; W. W. Norton & Company (2010)

Top-rated books on Gravity Top-rated books on Gravitation Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

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