PLS help! A planet orbits a star.

Question

b) In general, the gravitational potential energy for a planet orbiting a star is given by U = -(G*m_planet*m_star)/r. The maximum distance of this planet from its star is 700,000,000 km, and the minimum distance is 600,000,000 km. The mass of the planet is 4 × 10²² kg, and the mass of the star is 5 × 10³¹ kg. How much does the GPE change during one full orbit?

c) A comet of mass 2 × 10⁸ kg is pulled toward the star. If the comet's initial velocity is very small, and the comet starts moving toward the star from 700,000,000 km away, how fast is it going right before it hits the surface of the star? (Assume that it does not lose any mass by melting as it approaches the star.)

Answer 1

Hello Anika;

b) Change in GPE = U_max - U_min

Plug in the values:

Change in GPE = [-(G * m_planet * m_star) / r_max] - [-(G * m_planet * m_star) / r_min]

Change in GPE = [-((6.674 × 10^-11 N(m/kg)^2) * (4 × 10^22 kg) * (5 × 10^31 kg)) / (700,000,000,000 m) ] - [-((6.674 × 10^-11 N(m/kg)^2) * (4 × 10^22 kg) * (5 × 10^31 kg)) / (600,000,000,000 m)]

I hope no calculation mistake;

Change in GPE ≈ (3.8114 × 10¹⁰ J) - (4.4467 × 10¹⁰ J)

Change in GPE ≈ -6.353 × 10⁹ Joules ~ your -6.4 x 10⁹ J