1. Satellite Laser Ranging
Exactly as cool as it sounds

2. How fast does light move?
𝑑 𝑡 =𝑣 !! d
Calculating the speed of light was difficult. Galileo’s first experiment required two people to stand on top of two hills a known distance apart (about a mile). Person 1 would uncover his lantern and start a clock. Person 2 would wait until he saw the light and uncover his lantern. When person 1 saw person 2’s light, he would stop the clock. The quote is from Galileo’s notes.
“If not instantaneous, it is extraordinarily rapid”

3. How fast does light move?
Eclipse occurs on time
Eclipse occurs 11 min late
Lapse in timing due to time the light takes to travel across Earth’s orbit

4. How fast does light move?
Degrees of spin = θ
Degrees/second = ω
Image by Brews Ohare
Time of gear/mirror rotation
A rotating mirror can be used as long as the mirrors are far apart, separated by a known distance. As the mirror/gear turns, the light travels back and forth between the mirrors and hits a detector. The rate of rotation can be tied to the speed of light as given above.
Time of light transit
𝜃 𝜔 =𝑡= 2𝑑 𝑐
𝑐= 2𝑑𝜔 𝜃
Image by Brews Ohare

5. How fast does light move?
Mirrors
Laser
(𝑘𝑛𝑜𝑤𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦=𝑓)
Beam Splitter
Detector

6. How fast does light move?
Mirrors
Laser
(𝑘𝑛𝑜𝑤𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦=𝑓)
Beam Splitter
= 𝜆 4 𝑑
𝑐=𝑓𝜆=𝑓∙(4𝑑)
Detector

7. Satellite Laser Ranging
High-powered laser reflected off objects
Delay time measured
Distance to object calculated
We bounce lasers off of satellites and the moon to determine their distance from us.
Image used with permission from NASA

8. Satellite Laser Ranging
Laser reflectors placed on the moon
A map of the reflectors on the moon
Images used with permission from NASA

9. Satellite Laser Ranging
Calculate the distance to the moon given:
𝑣 𝑙𝑖𝑔ℎ𝑡 =3× 𝑚 𝑠
𝑡 𝑑𝑒𝑙𝑎𝑦 =2.5 𝑠𝑒𝑐
Why divide by 2?
∆𝑥= 𝑣 𝑙𝑖𝑔ℎ𝑡 × 𝑡 𝑑𝑒𝑙𝑎𝑦 2 = 3× ×
=375,000,000 𝑚
Practice calculation

10. Satellite Laser Ranging
LAGEOS Satellite
Orbiting laser reflector
Extremely stable orbit (high density)
Known, constant distance from Earth
Mass = 400 kg
Diameter = 60 cm
Image used with permission from NASA

11. Satellite Laser Ranging
Orbit more stable than other satellites
Still changes slightly due to
Solar wind
Radiation pressure
Gravity issues
A stable orbit allows us to detect the changing shape of the Earth.