Receiver Riddle - New for 2024

In December 2023, NASA transmitted the first ultra-high-definition video from deep space using new technology known as Deep Space Optical Communications, or DSOC. DSOC uses an infrared laser to transmit data at a much higher rate than current radio transmitters. The 15-second video, featuring a cat chasing a laser, was beamed to Earth from the Psyche spacecraft at a rate faster than many terrestrial internet connections.

DSOC’s transmission had to travel 30,199,000 km to reach Earth. Even traveling at the speed of light, that takes a long time! And all that time, Earth was still moving along its orbit. That meant that the team needed to aim the laser transmission at where Earth would be when the signal arrived.

Given this, how many kilometers ahead along Earth’s orbit did the team need to aim the laser?

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Daring Deflection - New for 2024

The asteroid Dimorphos has a mass of about 4.3 billion kg and orbits the larger Didymos asteroid, which has a mass of 560 billion kg. In 2022, the DART spacecraft impacted Dimorphos to see if it was possible to change its orbit.

Before the impact, Dimorphos orbited Didymos every 11 hours and 55 minutes at a distance of 1.16 km in a nearly circular orbit with an eccentricity (e) of 0. After impact, Dimorphos orbited Didymos every 11 hours and 23 minutes with an eccentricity of 0.02. Use Kepler’s third law to calculate the semi-major axis (a) of the new orbit, given that T = 2π√(a³/GM).

T = orbital period in seconds
a = semi-major axis in meters
G = gravitational constant (6.674×10⁻¹¹ N⋅m²/kg²)
M = total mass of the binary system

Use the semi-major axis and eccentricity to calculate Dimorphos’ farthest distance from Didymos (apoapsis = a(1+e)) and closest distance to Didymos (periapsis = a(1-e)). How do these differ from the circular orbit?

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Orbit Observation - New for 2024

NISAR is an Earth-orbiting satellite mission designed to measure centimeter-scale movements and other changes of Earth's land- and ice-covered surfaces twice every 12 days – a scale of coverage and sampling never before achieved.

Using a technique called Synthetic Aperture Radar, NISAR will produce more than 85 terabytes of data products every day (1 TB = 1,000 gigabytes) that will allow scientists to better monitor and mitigate natural disasters and understand the effects of climate change.

NISAR has an imaging swath of 240 kilometers, but the ground track spacing is 231 km to allow overlap between swaths. Given that Earth’s radius is 6,371 km, how many orbits are executed in one day? How much data is produced per orbit on average?

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Moon Mappers - New for 2024

NASA’s CADRE project is made up of a network of three small rovers. The rovers are designed to work together to create a 3D map of a scientifically intriguing area of the Moon's surface known as Reiner Gamma. Communicating with each other and a base station aboard a lunar lander, the rovers will be largely autonomous, making decisions and acting without the need for constant human intervention.

Each suitcase-size rover has a field of view that is about π/2 radians wide, and its sensors can accurately map as far as 2 meters ahead. Assuming the rovers drive in a “lawnmower” pattern, how far does each rover have to drive to survey its portion of a 20 m x 20 m square of the Moon’s surface?

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Tubular Tally

The Perseverance Mars rover is designed to collect rock samples that will eventually be brought to Earth for further study. This would be the first time we've ever brought back samples from Mars! After scientists identify an interesting rock they would like the rover to collect, Perseverance uses a special coring bit to drill out a rock cylinder 13 mm in diameter. As the rover drills, the rock core moves into one of 38 available tubes that will store the rock sample – sealed until it is opened one day in a lab on Earth.

If the coring bit collects a rock cylinder 60 mm in length, what is the volume of the rock in the sample tube?

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Rad Reflection

The James Webb Space Telescope was designed to look back at some of the earliest galaxies in the universe. To capture light from these distant and faint objects, the telescope must be very sensitive. Webb uses 18 hexagonal mirrors that combine to form a massive primary mirror with a surface area of 26.4 m². This large mirror allows the telescope to collect incredibly faint infrared light and reflect it onto four onboard science instruments, like the Mid-Infrared Instrument, or MIRI. This science instrument can reveal stars hidden within gas and dust clouds and tell scientists about the materials that make up distant galaxies.

Launched in 1990, the Hubble Space Telescope changed our understanding of the universe when it began operations using a primary mirror that had a diameter of just 2.4 meters.

How much bigger is the area of Webb’s primary mirror than Hubble’s?

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Metal Math

Asteroid (16) Psyche is of particular interest to scientists because ground-based observations indicate that the surface may be metallic. Earth and other terrestrial planets have metal cores, but they are buried deep inside the planets, so they are difficult to study. If Psyche consists of a large amount of metal, it might resemble a planetary core from which we could learn about terrestrial planet core formation. Determining how much metal exists on the asteroid is one of the goals of NASA’s Psyche mission, which will use specialized tools to study the asteroid's composition from orbit.

Psyche has a roughly triaxial ellipsoid shape with axes of about 290 km, 245 km, and 170 km. Its mass, as estimated from its gravitational effects on nearby bodies such as Mars, is about 2.7 x 10¹⁹ kg. Use the formula for volume, V = 4/3 πabc, where a, b, and c are the lengths of the semi-axes, to compute Psyche's approximate density.

Based on the average density of terrestrial materials (listed below), does Psyche's density support the observations indicating the presence of metal?

Average density of:

• ice: 917 kg/m³
• water: 997 kg/m³
• rock: 1,600 - 3,500 kg/m³
• metal: 534 - 22,590 kg/m³

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Eclipsing Enigma

A solar eclipse occurs when the Moon passes between Earth and the Sun, fully or partially blocking the Sun's light from our perspective. Because Earth’s orbit around the Sun and the Moon’s orbit around Earth are not perfect circles, the distances between them change throughout their orbits. During a total eclipse, the distances are such that the Moon covers all of the Sun's disk area. When the Moon is farther from Earth during an eclipse, it leaves a glowing ring of sunlight shining around the Moon, resulting in an annular eclipse.

On Oct. 14, 2023, a solar eclipse will be visible across North and South America. The Sun, with a radius of 695,700 km, will be 148,523,036 km from Earth. The Moon, with a radius of 1,737 km, will be 388,901 km from Earth.

What percentage of the Sun’s disk area will be obscured by the Moon?

Will the eclipse be an annular eclipse or a total eclipse?

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Lunar Logic

NASA’s Lunar Flashlight mission will observe and map the location of frost within permanently shadowed craters in the Moon’s south polar region. Knowing how much frost is in these craters and where to find it can help us prepare for extended missions on the Moon, when water will be a valuable resource.

The spacecraft, a backpack-size cubesat, will collect data during 10 orbits over a two-month period, making repeated measurements over multiple points to map ice in these dark craters. To take measurements, Lunar Flashlight will send infrared laser pulses to the surface of the Moon and measure the signal that is reflected. The amount of light that is reflected back will help scientists determine where the lunar surface is dry and where it contains water-ice.

At 20 km altitude, the spacecraft's infrared lasers have a radius of 17.5 meters when they reach the surface of the Moon.

How much area do they cover in a single pulse?

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Core Conundrum

The InSight Mars lander is equipped with several tools to help scientists learn more about the interior of the Red Planet, including a seismometer that detects marsquakes. By measuring the vibrations that travel across the surface of Mars and through its interior layers, scientists were able to accurately measure the size of Mars’ liquid core and estimate its density. Knowing the size and density of Mars' core will help us learn more about how the planet formed, how its magnetic field developed, and what materials make up the core, which will ultimately lead to a better understanding of how Earth and other planets form.

If Mars' core has a mass of 1.54 x 10²³ kg and a radius of 1,830 km, as measured by InSight, what is the density of the core?

How does that compare to the density of Earth’s core, which ranges from 10 to 13 g/cm³?

What does that tell us about the makeup of Mars’ core?

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Dam Deduction

Water exiting a hydropower dam is called non-powered or powered outflow. Non-powered outflow exits via a spillway, on top of the dam. Powered outflow, which is used to generate electricity, travels through penstocks, pipes at the bottom of a dam. Powered outflow is usually colder and travels at a higher velocity, so it can disturb sediments, temperatures, and water quality of downstream rivers, especially when it’s a high percentage of the total outflow.

The SWOT mission, a satellite designed to survey all of Earth’s surface water, including lakes, rivers, oceans, and reservoirs, can help scientists better analyze these impacts.

A dam has 3 penstocks with diameters of 6.2 meters and a measured total outflow of 1,350 m³/s. If SWOT measured the reservoir’s water depth (H) at 100 m above the penstocks, compute the velocity (m/s) of the powered outflow using V=√(2gH).

What is the powered outflow if 1 penstock is open?

Is this a high or low percentage of the total outflow?

What can this tell you about the potential environmental impacts?

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Telescope Tango

NASA's TESS mission is designed to survey the entire sky in search of exoplanets, or planets orbiting stars other than our Sun. In its two-year primary mission, TESS identified more than 2,600 possible exoplanets and counting.

To locate exoplanets, the space telescope flies in a highly eccentric elliptical orbit, which had never been attempted before. This orbit, called P/2, minimizes the amount of time that light and heat from Earth and the Moon can interfere with data collection. And it still allows the spacecraft to make close passes by Earth to transmit data about its findings back to scientists. The spacecraft's 13.7 day orbit has an axis of 376,000 km at apogee and an axis of 108,400 km at perigee. Each downlink from TESS takes about three hours to complete.

While TESS actually moves at different speeds throughout its orbit – from 0.5 km/s at apogee to 4 km/s at perigee – if its velocity stayed uniform, how many kilometers would TESS need to travel to successfully transmit its data?

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Sample Science

NASA’s OSIRIS-REx mission was designed to travel to an asteroid called Bennu and bring a small sample back to Earth for further study. To achieve its mission, the spacecraft needed to make contact with 26 cm² of asteroid Bennu’s surface and collect millimeter-size particles using its "contact-pad samplers." These are 1.5-centimeter diameter circular pads of Velcro-like stainless steel. There are 24 pads on the mechanism designed to collect the samples.

How many pads needed to make contact with Bennu's surface to meet the mission requirement?

If all 24 pads contacted Bennu, how much asteroid surface area would the contact pads sample?