Imagine a planet orbiting a star. Observations show a Doppler shift in the star's spectrum of 58 m/s over the 3.3 day orbit of the planet. What is the mass of the planet in kg? Assume  the star has the same mass as the Sun (2.0 x1030 kg), there are 365.25 days in a year, and 1AU = 1.5 x 1011 m.

Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. The typical temperature of a sunspot is 3500 K the equipartition equation for velocity v, temperature T and mass m of a particle, is, 3kgT V = m kB is Boltzmann's constant (1.38×10–23 J/K). a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor- mation given above to compute the acceleration g due to gravity at the surface of the Sun. b) Compute the drift velocity Ūg due to gravity for a proton and an electron located within a sunspot. c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun is comprised of pure ionized hydrogen. d) Calculate the total current density J (accounting for the contributions of both electrons and tons) within sunspots. You may assume that you can treat the ensemble of…

In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5 km, and it has an average density of 1.4x10^3 kg/m^3. The diameter of the moon is 2.16x10^3 miles.

D Gm₁m₂ Fg KE = mv², Ug = - 2πr , ac = =²₁, v = ²7₁ T Gm₁m₂ GM g = G, Vesc = 2GM R , E = KE + Ug, G = 6.674 x 10-¹1 Nm²/kg² Problem 1: You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its radius to be 9 x 106 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2 x 10¹¹ m from its star with a period of 402 days (3.473 x 107 sec). Once on the surface you find that the free-fall acceleration is 12.2 m/sec². a) What is the mass of the planet? Answer: 1.5 x 1025 kg. b) What is the mass of the star? Answer: 5.2 x 1030 kg.

Astronomical Datat Mass (kg) 1.99 × 1030 7.35 × 1022 3.30 × 1023 4.87 X 1024 5.97 X 1024 6.42 × 1023 1.90 × 1027 5.68 X 1026 8.68 x 1025 1.02 × 1026 1.31 × 1022 Body Sun Moon Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 8.43 x 10^24 N 2.07 x 10^10 N O 843 N Radius (m) 6.96 × 108 1.74 X 106 2.44 X 106 6.05 × 106 6.37 X 106 3.39 X 106 6.99 X 107 5.82 X 107 2.54 x 107 2.46 X 107 1.15 X 106 What is the weight of a 75 kg astronaut on the surface of Neptune? O 2.07 x 10^5 N Orbit radius (m) 3.84 × 108 5.79 × 1010 1.08 × 10¹1 1.50 × 10¹1 2.28 × 10¹1 7.78 x 10¹1 1.43 × 10¹2 2.87 × 10¹2 4.50 × 1012 5.91 X 1012 Orbital period 27.3 d 88.0 d 224.7 d 365.3 d 687.0 d 11.86 y 29.45 y 84.02 y 164.8 y 247.9 y

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V = 210 km/s and the orbital period of each is 11.5 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM M

We sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Calculate the mass of planet Kerbal. Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2

The supermassive black hole at the center or our galaxy (Sagittarius A*) has a mass equal to 4.3 million Suns (the mass of the Sun is 1.99 × 1030 kg). The distance from Sgr A* to Earth is 7,940 parsecs, where one parsec is equal to 3.09 × 1016 m. (a) What is the gravitational force that Sgr A* exerts on a 75 kg person on Earth, in units of Newtons? Hint: use Newton's law of universal gravitation. (b) Suppose the same person is sitting 1.0 meter away from a paperclip with a mass of 1.0 grams. What is the gravitational force that the paperclip exerts on the person? (c) Compare the forces from parts (a) and (b). Which is greater?

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is |v| 190 km/s and the orbital period of each is 12.9 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM M

A black hole is an object so massive that not even light can escape, one way to define the size of a black hole is by the Schwarzschild Radius, which is the radius at which the escape velocity is equal to the speed of light. If we were to condense the Earth into a black hole, what would be the size of its Schwarzschild Radius?