9/9/2020

Today’s Class: Gravity & Spacecraft Trajectories CU Astronomy Club

• Read about Explorer 1 at • Need some Space? http://en.wikipedia.org/wiki/Explorer_1 • Read about Van Allen Radiation Belts at • Escape the light pollution, join us on our Dark Sky http://en.wikipedia.org/wiki/Van_Allen_radiation_belt Trips • Complete Daily Health Form – Stargazing, astrophotography, and just hanging out – First trip: September 11

• Open to all majors!

• The stars respect social distancing and so do we

• Head to our website to join our email list: https://www.colorado.edu/aps/our- department/outreach/cu-astronomy-club • Email Address: [email protected]

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 1 2

Last Class Commercial C rew s a n d Private Astronauts will boost International S p a c e • Where do objects get their energy?

Article by Elizabeth Howell Station's Sci enc e Presentation by Henry Universe Today/SpaceX –Conservation of energy: energy Larson cannot be created or destroyed but ● SpaceX’s Demo 2 flight showed what human spaceflight Question: can look like under private enterprise only transformed from one type to ● NASArelied on Russia’s Soyuz spacecraft to send astronauts to the ISS in the past another. ● "We're going to have more people on the International Space Station than we've had in a long time,” NASA –Energy comes in three basic types: Administrator Jim Bridenstine ● NASAis primarily using SpaceX and Boeing for their kinetic, potential, radiative. “commercial crew”program

Astronomy 2020 – Space Astronomy & Exploration 3 4

Class Exercise: Which of the following Today’s Learning Goals processes violates a conservation law?

• What are range of common Earth a) Mass is converted directly into energy. b) An object orbiting the Sun and affected only by the Sun's orbits? gravity spirals into the Sun. • How do spacecraft travel from one c) One ball hits a second ball and stops moving while the second ball starts moving in the same direction. orbit to another? d) An object speeds up as it approaches the Sun and turns • How can we use the gravitational around it, and then slows down as it moves further away, never to return. energy of planets to assist in exploring e) An object orbits Earth on a perfectly circular orbit with no the solar system? rockets firing.

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 5 6

1 9/9/2020

Which of the following processes violates What determines the strength of gravity? a conservation law? The universal law of gravitation: a) Mass is converted directly into energy. 1. Every mass attracts every other mass. b) An object orbiting the Sun and affected only by the Sun's 2. Attraction is directly proportional to the product of their gravity spirals into the Sun. masses. c) One ball hits a second ball and stops moving while the 3. Attraction is inversely proportional to the square of the second ball starts moving in the same direction. distance between their centers. d) An object speeds up as it approaches the Sun and turns around it, and then slows down as it moves further away, never to return. e) An object orbits Earth on a perfectly circular orbit with no rockets firing.

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 7 8

Why do all objects fall at the same rate? Spacecraft in Circular Orbit Combine Newton’s 2nd Law (F=ma) with Law of Gravity: • To stay in a circular orbit requires a 푣2 constant centripetal acceleration a = , 푅 where R = orbit radius, 푣 = orbital velocity. • Combine Newton’s Second Law (F=ma) with centripetal acceleration & Law of Gravity: • The gravitational acceleration of an object like a rock does 퐺푚푀 푚푣2 not depend on its mass because M in the equation for 퐸 = 푣 = 퐺푀 /푅, M = Earth rock 푅2 푅 퐸 E acceleration cancels Mrock in the equation for gravitational force. mass, m = spacecraft mass. • This ''coincidence'' was not understood until Einstein's general theory of relativity.

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 9 10

Orbiting the Earth: some numbers Class Exercise

• Derive an expression for the orbital period (P) of a spacecraft in a 푣 = orbital velocity= 퐺푀퐸/푅 circular orbit around the Earth in terms of Earth’s mass (ME) & and orbital radius (R). This was originally derived by Newton as his • G = 6.67 x 10-11 version of Kepler’s third law. 24 13 • ME = 6 x 10 kg → GME = 40 x 10 2휋푅 4휋2푅2 • Want an orbit with an altitude of 200 km: 푃 = 표푟 푃2 = R 푣 푣2 ➢R = Earth radius + altitude = 6600 km = 6.6 x 106 m Now, plug in 푣 from previous ME page so (after a little algebra): • 푣 ≅ 7785 meters/s ≅ 28,000 km/hr ≅17,500 4휋2 miles/hr 푃2 = 푅3 퐺푀퐸 • And it takes about 1.5 hours (90 minutes) to complete an orbit (P = 2πR/푣).

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 11 12

2 9/9/2020

How do gravity and energy together allow us to understand orbits? Escape Velocity • Total orbital energy • If an object gains (TE) (gravitational + enough orbital kinetic) stays energy, it may escape constant if there is (change from a no external force. bound to unbound • Orbits cannot orbit). change • Escape velocity spontaneously. from Earth ≈ 11 km/s from sea level Total orbital energy stays constant. (about 40,000 −퐺푀푚 TE = KE + PE = ½ mv2 + ) ( 푟 km/hr)

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 13 14

Common Earth Orbits Distribution of Satellites in Orbits

• Low Earth Orbit (LEO) [Hubble Space Telescope, HST] • Geostationary Orbit (GEO) [Communications satellites] • High Earth Orbit (HEO) [Chandra X-ray Observatory] • Sun Synchronous Orbits [Remote sensing satellites, COBE]

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 16 17

Hohmann transfer orbit Gravitational Slingshot

• The Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane. The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. • Use conservation of energy to calculate total required Δ푣.

Astronomy 2020 – Space Astronomy & Exploration Astronomy 2020 – Space Astronomy & Exploration 22 25

3 9/9/2020

What have we learned? • What are range of common Earth orbits? – LEO, GEO, HEO • How do spacecraft travel from one orbit to another? – Hohmann transfer: use elliptical orbit to transfer between 2 circular orbits • How can we use the gravitational energy of planets to assist in exploring the solar system? – Gravitational assist (slingshot): tap gravity well and motion of planets around the Sun.

Astronomy 2020 – Space Astronomy & Exploration 27

4