Can Hubble Space Telescope See Flag on the Moon?

What Is the Smallest Detail HST Can Photograph on Lunar Surface?

Mar 14, 2009 Paul A. Heckert

Basic physics provides a formula for calculating the smallest detail the Hubble Space Telescope can resolve on the surface of the Moon. It is larger than a flag.

People often wonder if it is possible for a large enough telescope to see the flag or other objects that the Apollo astronauts left behind on the Moon. Even the largest ground based telescope would not be able to resolve such small details because the blurring effect of Earth's atmosphere limits the resolving power of large ground based telescopes long before the theoretical best performance of the telescope. The Hubble Space Telescope is however above Earth's atmosphere, so it can achieve its maximum theoretical resolving power. Is it enough?

Diffraction Limit of Optical Instruments

The theoretical best resolution of a telescope or any other optical instrument is called the diffraction limit. The diffraction limit of an optical instrument is measured as an angle, theta, which must be expressed in radians. The diffraction limit depends on the wavelength, lambda, of the light used and on the diameter, d, of the main mirror or lens in the optical instrument. The diffraction limit in radians is given by the formula:

theta = 1.22 (lambda)/d

The angle, theta, that an object, such as the flag on the Moon, subtends depends on the object's distance, r, and its size, s. According to the definition of an angle in radians:

theta = s/r

Equating these two formulas for theta and solving for s gives the size of the smallest feature that a telescope, or other optical instrument can resolve.

s = ((1.22)(lambda)r)/d

This formula gives the size of the smallest feature that a telescope can theoretically resolve under the best conditions. Ground based astronomical telescopes will not reach this theoretical diffraction limit because Earth's atmosphere blurs the image. Also, an optical instrument with poor quality optics will not perform at the diffraction limit. The Hubble Space Telescope however can approach the diffraction limit because it is above Earth's atmosphere. That is why it produces such sharp images.

Hubble Photographs the Moon

When NASA officials decided to use the HST to photograph the Moon, they encountered difficulties. The Moon and Sun are so bright that they could damage sensitive instruments on the HST. Hence the pointing software has built in safeguards to prevent controllers from accidentally pointing the Hubble telescope at the Sun or Moon.

Before the Hubble Space Telescope could photograph the Moon, controllers had to figure out how to override these protective features in the very complex pointing programs.

Smallest Feature Visible on the Moon

The main mirror in the HST has a diameter of 2.4 meters. Visible light has an average wavelength of about 0.5E-6 meters. The Moon is at a distance of 3.8E8 meters. Putting these numbers into the formula gives the size of the smallest feature that the Hubble Space Telescope can resolve on the Moon's surface. It is just under 100 meters.

Flags are seldom this big, so Hubble Space Telescope images of the Moon can not resolve the flags or other objects left behind by the Apollo astronauts. To recognize a flag and see details, such as stars and stripes, would require resolving details as small as about a centimeter. This resolution would require a space telescope with a diameter of about 20 kilometers.

Even though it can not see the flag on the Moon, the HST can resolve unprecedented detail.

Further Reading

Wilson, J.D., Buffa, A.J., and Lou, B., College Physics 6th ed., Pearson, 2007.

The copyright of the article Can Hubble Space Telescope See Flag on the Moon? in Physics is owned by Paul A. Heckert. Permission to republish Can Hubble Space Telescope See Flag on the Moon? in print or online must be granted by the author in writing.

Hubble Telescope Image of Apollo 17 Landing Site

Hubble Telescope Image of Lunar Crater Copernicus