Cycle II Physics

John Dewey High School

Mr. Klimetz

What is the true nature of the force that accelerates all objects towards Earth's center and how can this be quantitatively expressed?

What is the nature of the force exerted by the Sun that gives the planets the centripetal acceleration needed to keep them in their orbits and how can it be quantitatively expressed?

How can the observed relationship between the orbital radius, orbital speed, and mass of natural satellites in our solar system be applied to the launching of artificial satellites as well as to the motions of bodies in hypothetical solar systems?

How does the strength of an object's gravitational field change with increasing distance from its center and how can this be quantitatively expressed?

In this particular exercise you are going to evaluate the dynamic and kinematic relationships between three orbiting members of a hypothetical solar system and their central star. On the basis of your understanding of two-dimensional kinematics, Newton's Laws of Motion, the Universal Law of Gravitation, Kepler's Third Law of Planetary Motion, centripetal acceleration, and centripetal force, you are expected to

Calculate the force of attraction (Fg) between each planet and its central star.

Calculate the field strength (g) of the central star at each planet.

Calculate the average orbital velocity (v) for each planet.

Calculate the average orbital period (T) of each planet.

Calculate the orbital circumference (C) of each planet.

Confirm Kepler's Third Law by calculating the Kepler Constant (k) for each planet

Solar System Map showing positions of central star, planets, and orbits

"Nerf" foam plastic model of central star (half of a 4.50 cm diameter sphere)

Glass/polystyrene single-hole bead models of planets (three-0.30 cm-diameter spheres)

Four thumbtacks

Metric ruler

Scientific calculator

Graph paper

Pencils with erasers

1. Assemble a single model of the solar system using the foam "Nerf" ball and glass/plastic beads provided from a separate Solar System Map sheet for the entire lab for reference purposes. Thumbtacks can be inserted through the bottom of the sheet so that their protruding points can serve as mounts for the planets and central star. Each lab member must have their own Solar System Map sheet. __Caveat__: Be mindful of the fact that this map sheet has been drawn to-scale and that all of the planets lie in the same plane which in turn bisects the central star.

2. Measure all required distances such as stellar and planetary radii, orbital radii, etc., directly from the Solar System Map and model sheets and record in the places provided. (__Map Scale__: 1 cm = 10exp9 m)

3. Perform all calculations and graph all data sets as instructed.

4. Answer any follow-up questions provided by your instructor at the end of your report.

Radius of Central Star (rs) = 2.25 cm = ________ m

Radius of Planet 1 (r1) = 0.15 cm = ________ m

Radius of Planet 2 (r2) = 0.15 cm = ________ m

Radius of Planet 3 (r3) = 0.15 cm = ________ m

Orbital Radius of Planet 1 (R1) = ________ cm = ________ m

Orbital Radius of Planet 2 (R2) = ________ cm = ________ m

Orbital Radius of Planet 3 (R3) = ________ cm = ________ m

Mass of Central Star (ms) = 1.6 x 10exp31 kg

Mass of Planet 1 (m1) = 9.8 x 10exp28 kg

Mass of Planet 2 (m2) = 8.4 x 10exp28 kg

Mass of Planet 3 (m3) = 7.0 x 10exp28 kg

A. Calculate the force of gravitational attraction (Fg) between each planet and the central star.

Fg1 = ________ N

Fg2 = ________ N

Fg3 = ________ N

B. Calculate the gravitational field strength (g) of the central star at each planet.

g1 = ________ m/sexp2

g2 = ________ m/sexp2

g3 = ________ m/sexp2

C. Calculate the average orbital velocity (v) of each planet.

v1 = ________ m/s

v2 = ________ m/s

v3 = ________ m/s

D. Calculate the orbital circumference (C) of each planet.

C1 = ________ m

C2 = ________ m

C3 = ________ m

E. Calculate the orbital period (T) of each planet.

T1 = ________ s

T2 = ________ s

T3 = ________ s

F. Calculate the Kepler Constant (k) of each planet.

k1 = ________ mexp3/sexp2

k2 = ________ mexp3/sexp2

k3 = ________ mexp3/sexp2

A. Plot Fg (N) versus R (m) for each planet. Gravitational force (Fg) should appear on the ordinate and orbital radius (R) should appear on the abscissa. Use different colored dots to indicate each planet. Connect with a smooth curve.

B. Plot g (m/sexp2) of the central star versus R (m) at the location of each planet. Gravitational field strength (g) should appear on the ordinate and orbital radius (R) should appear on the abscissa. Use different colored dots to indicate each planet. Connect with a smooth curve.

C. Plot v (m/s) versus R (m) for each planet. Average orbital velocity (v) should appear on the ordinate and orbital radius (R) should appear on the abscissa. Use different colored dots to indicate each planet. Connect with a smooth curve.

A. Based on your understanding of the Universal Law of Gravitation and the weight equation,

calculate the local gravitational acceleration at the surface of the star.

B. Based on your understanding of the Universal Law of Gravitation and the weight equation,

calculate the weight of a 5.00 kg mass at the surface of the star.

C. Based on your understanding of the Universal Law of Gravitation and the centripetal force equation, calculate the minimum speed required to launch a satellite into an orbit around the star at its surface.

D. Based on your understanding of the Universal Law of Gravitation, the centripetal force equation, and your calculation of the Kepler Constant [k] for the given solar system, calculate the orbital radius at which the orbital period of a satellite would be exactly one year.

E. Based on your understanding of the Universal Law of Gravitation, the centripetal force equation, and your calculation of the Kepler Constant [k] for the given solar system, calculate the orbital period of a satellite located at an average orbital radius of 4.50 x 10exp9 m.